Lexicographic degrees of two-bridge knots with 12 crossings


E. Brugallé, P. -V. Koseleff, D. Pecker

The two-brige knots are knots that admit trigonal form diagrams. They admit a polynomial parametrisation of degree $(3,b,c)$, where $3 < b < c$.
We proved in [BKP3]that the lexicographic degree of a two-bridge knot with $N \leq 11$ crossings or fewer, is $(3,b,c)$ where $b+c=3N$, see also details. When $N\geq 12$, we have $b+c \geq 3N$.
We list here the degree $b$ corresponding to the lexicographic degree $(3,b,c)$ for two-bridge knots with 12 crossings.
For each knot we show that there exists a diagram with $s$ sign changes in its Gauss sequence, such that there exists $c$ such that $b+c=3N=36$.
We list all (simple) diagrams that could have a smaller degree if the braid condition hold (quasipositity of the associated braid, see [BKP2]).

Lexicographic degrees of 2-bridge knots
NameDegreeNameDegreeNameDegreeNameDegreeNameDegreeNameDegreeNameDegreeNameDegree
$12a_{38}$16$12a_{169}$16$12a_{197}$17$12a_{204}$14$12a_{206}$16$12a_{221}$14$12a_{226}$16$12a_{239}$14
$12a_{241}$16$12a_{243}$14$12a_{247}$14$12a_{251}$14$12a_{254}$16$12a_{255}$14$12a_{257}$14$12a_{259}$14
$12a_{300}$14$12a_{302}$16$12a_{303}$14$12a_{306}$14$12a_{307}$14$12a_{330}$14$12a_{378}$14$12a_{379}$16
$12a_{380}$14$12a_{384}$14$12a_{385}$14$12a_{406}$14$12a_{425}$16$12a_{437}$14$12a_{447}$14$12a_{454}$14
$12a_{471}$17$12a_{477}$17$12a_{482}$17$12a_{497}$13$12a_{498}$13$12a_{499}$13$12a_{500}$13$12a_{501}$13
$12a_{502}$16$12a_{506}$13$12a_{508}$14$12a_{510}$13$12a_{511}$16$12a_{512}$13$12a_{514}$13$12a_{517}$13
$12a_{518}$14$12a_{519}$16$12a_{520}$13$12a_{521}$13$12a_{522}$13$12a_{528}$13$12a_{532}$13$12a_{533}$16
$12a_{534}$13$12a_{535}$13$12a_{536}$13$12a_{537}$14$12a_{538}$16$12a_{539}$14$12a_{540}$13$12a_{541}$13
$12a_{545}$13$12a_{549}$14$12a_{550}$14$12a_{551}$14$12a_{552}$14$12a_{579}$13$12a_{580}$16$12a_{581}$14
$12a_{582}$13$12a_{583}$13$12a_{584}$13$12a_{585}$14$12a_{595}$14$12a_{596}$14$12a_{597}$14$12a_{600}$13
$12a_{601}$14$12a_{643}$16$12a_{644}$14$12a_{649}$13$12a_{650}$14$12a_{651}$13$12a_{652}$14$12a_{682}$14
$12a_{684}$14$12a_{690}$17$12a_{691}$17$12a_{713}$16$12a_{714}$16$12a_{715}$16$12a_{716}$16$12a_{717}$16
$12a_{718}$16$12a_{720}$16$12a_{721}$16$12a_{722}$16$12a_{723}$16$12a_{724}$16$12a_{726}$16$12a_{727}$16
$12a_{728}$16$12a_{729}$16$12a_{731}$16$12a_{732}$16$12a_{733}$16$12a_{736}$16$12a_{738}$16$12a_{740}$16
$12a_{743}$16$12a_{744}$16$12a_{745}$16$12a_{758}$16$12a_{759}$16$12a_{760}$16$12a_{761}$16$12a_{762}$16
$12a_{763}$16$12a_{764}$16$12a_{773}$16$12a_{774}$16$12a_{775}$16$12a_{791}$16$12a_{792}$16$12a_{796}$16
$12a_{797}$16$12a_{802}$16$12a_{803}$17$12a_{1023}$16$12a_{1024}$13$12a_{1029}$16$12a_{1030}$13$12a_{1033}$16
$12a_{1034}$14$12a_{1039}$13$12a_{1040}$14$12a_{1125}$16$12a_{1126}$14$12a_{1127}$17$12a_{1128}$16$12a_{1129}$16
$12a_{1130}$16$12a_{1131}$16$12a_{1132}$14$12a_{1133}$13$12a_{1134}$16$12a_{1135}$16$12a_{1136}$16$12a_{1138}$16
$12a_{1139}$14$12a_{1140}$16$12a_{1145}$16$12a_{1146}$16$12a_{1148}$16$12a_{1149}$16$12a_{1157}$16$12a_{1158}$14
$12a_{1159}$13$12a_{1161}$14$12a_{1162}$16$12a_{1163}$14$12a_{1165}$16$12a_{1166}$17$12a_{1273}$16$12a_{1274}$16
$12a_{1275}$14$12a_{1276}$16$12a_{1277}$13$12a_{1278}$16$12a_{1279}$14$12a_{1281}$16$12a_{1282}$16$12a_{1287}$17



NameSchub.Conway Not.Lex. Deg.Details
$12a_{38}$ 71/33 $C(2,6,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
56 diagrams of degree $(3,16,20) $. For example
$\quad C(2,6,1,2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(2,6,1,1,2)$ $b \geq 16$
$\quad D(2,7,2,2)$ $b \geq 17$
$\quad D(3,2,6,2)$ $b \geq 19$
$\quad D(2,5,1,2,1,2)$ $b \geq 16$
$12a_{169}$ 49/23 $C(2,7,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
56 diagrams of degree $(3,16,20) $. For example
$\quad C(2,6,1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(2,7,1,2)$ $b \geq 16$
$\quad D(3,8,2)$ $b \geq 19$
$\quad D(2,6,1,2,2)$ $b \geq 16$
$12a_{197}$ 69/32 $C(2,6,2,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
149 diagrams of degree $(3,17,19) $. For example
$\quad C(2,7,-1,-2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 4 simple diagrams with 15 crossings or fewer
$\quad D(2,6,2,2)$ $b \geq 17$
$\quad D(2,5,1,3,2)$ $b \geq 17$
$\quad D(3,2,7,2)$ $b \geq 19$
$\quad D(2,4,1,2,3,2)$ $b \geq 17$
$12a_{204}$ 173/76 $C(2,3,1,1,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,14,22)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,1,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,1,1,1,1,1,2)$ $b \geq 14$
$12a_{206}$ 105/47 $C(2,4,3,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(2,4,2,1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(2,4,3,1,2)$ $b \geq 16$
$\quad D(3,4,4,2)$ $b \geq 19$
$\quad D(2,3,1,4,1,2)$ $b \geq 16$
$\quad D(2,4,2,1,2,2)$ $b \geq 16$
$12a_{221}$ 169/66 $C(2,1,1,3,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,14,22)$
8 diagrams of degree $(3,14,22) $. For example
$\quad C(2,1,1,3,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,1,1,3,1,1,1,2)$ $b \geq 14$
$12a_{226}$ 181/75 $C(2,2,2,2,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
52 diagrams of degree $(3,16,20) $. For example
$\quad C(2,2,1,1,-3,-1,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 6 simple diagrams with 13 crossings or fewer
$\quad D(2,2,3,2,2,2)$ $b \geq 19$
$\quad D(2,2,2,2,1,1,2)$ $b \geq 16$
$\quad D(3,2,2,2,2,2)$ $b \geq 19$
$\quad D(2,1,1,3,2,1,1,2)$ $b \geq 16$
$\quad D(2,2,1,1,3,1,1,2)$ $b \geq 16$
$\quad D(2,2,2,1,1,2,1,2)$ $b \geq 16$
$12a_{239}$ 87/40 $C(2,5,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,5,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,5,1,2,2)$ $b \geq 14$
$12a_{241}$ 127/57 $C(2,4,2,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
51 diagrams of degree $(3,16,20) $. For example
$\quad C(2,4,2,1,2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(2,4,2,1,1,2)$ $b \geq 16$
$\quad D(2,4,3,2,2)$ $b \geq 16$
$\quad D(3,2,2,4,2)$ $b \geq 19$
$\quad D(2,3,1,3,1,1,2)$ $b \geq 16$
$\quad D(2,4,1,1,2,1,2)$ $b \geq 16$
$12a_{243}$ 133/60 $C(2,4,1,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,4,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,4,1,1,1,1,2)$ $b \geq 14$
$12a_{247}$ 163/71 $C(2,3,2,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,1,-3,-1,-1,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,2,1,1,1,2)$ $b \geq 16$
$12a_{251}$ 159/59 $C(2,1,2,3,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(2,1,2,3,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,1,2,3,1,1,2)$ $b \geq 14$
$12a_{254}$ 97/23 $C(4,4,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
59 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-5,-1,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,4,1,1,2)$ $b \geq 16$
$\quad D(4,4,2,3)$ $b \geq 19$
$\quad D(4,5,2,2)$ $b \geq 16$
$\quad D(4,3,1,2,1,2)$ $b \geq 16$
$12a_{255}$ 107/28 $C(3,1,4,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,4,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,4,1,1,2)$ $b \geq 14$
$12a_{257}$ 191/80 $C(2,2,1,1,2,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,1,1,2,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,2,1,1,2,1,1,2)$ $b \geq 14$
$12a_{259}$ 115/52 $C(2,4,1,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,4,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,4,1,2,1,2)$ $b \geq 14$
$12a_{300}$ 155/68 $C(2,3,1,1,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,1,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,1,1,2,1,2)$ $b \geq 14$
$12a_{302}$ 147/61 $C(2,2,2,3,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
50 diagrams of degree $(3,16,20) $. For example
$\quad C(2,2,1,1,-4,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(2,2,2,3,1,2)$ $b \geq 16$
$\quad D(3,4,2,2,2)$ $b \geq 19$
$\quad D(2,2,1,1,4,1,2)$ $b \geq 16$
$\quad D(2,2,2,2,1,2,2)$ $b \geq 16$
$12a_{303}$ 153/64 $C(2,2,1,1,3,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,1,1,3,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,2,1,1,3,1,2)$ $b \geq 14$
$12a_{306}$ 147/64 $C(2,3,2,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,2,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,2,1,2,2)$ $b \geq 14$
$12a_{307}$ 157/69 $C(2,3,1,1,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,-2,-1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,1,1,1,2,2)$ $b \geq 16$
$12a_{330}$ 95/43 $C(2,4,1,3,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,2,-1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,4,1,3,2)$ $b \geq 16$
$12a_{378}$ 127/45 $C(2,1,4,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(2,1,4,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,1,4,1,1,1,2)$ $b \geq 14$
$12a_{379}$ 71/17 $C(4,5,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
59 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-6,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(4,5,1,2)$ $b \geq 16$
$\quad D(4,6,3)$ $b \geq 19$
$\quad D(4,4,1,2,2)$ $b \geq 16$
$12a_{380}$ 77/20 $C(3,1,5,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,5,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,5,1,2)$ $b \geq 14$
$12a_{384}$ 151/62 $C(2,2,3,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,2,1,-3,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,2,3,2,1,2)$ $b \geq 16$
$12a_{385}$ 161/66 $C(2,2,3,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(3,-2,-1,-3,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,2,3,1,1,1,2)$ $b \geq 16$
$12a_{406}$ 179/74 $C(2,2,2,1,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,1,2,-1,-1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,2,2,1,1,2,2)$ $b \geq 16$
$12a_{425}$ 81/37 $C(2,5,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
67 diagrams of degree $(3,16,20) $. For example
$\quad C(2,4,-1,-4,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 1 simple diagrams with 13 crossings or fewer
$\quad D(2,5,3,2)$ $b \geq 16$
$12a_{437}$ 149/65 $C(2,3,2,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(2,2,1,-3,-2,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,2,2,1,2)$ $b \geq 16$
$12a_{447}$ 121/43 $C(2,1,4,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(2,1,4,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,1,4,2,1,2)$ $b \geq 14$
$12a_{454}$ 103/27 $C(3,1,4,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,3,1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,4,2,2)$ $b \geq 16$
$12a_{471}$ 85/38 $C(2,4,4,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
71 diagrams of degree $(3,17,19) $. For example
$\quad C(2,5,-1,-4,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 1 simple diagrams with 15 crossings or fewer
$\quad D(2,4,4,2)$ $b \geq 17$
$12a_{477}$ 169/70 $C(2,2,2,2,2,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
74 diagrams of degree $(3,17,19) $. For example
$\quad C(2,-3,-3,1,1,2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 5 simple diagrams with 15 crossings or fewer
$\quad D(2,2,2,2,2,2)$ $b \geq 17$
$\quad D(2,3,2,3,2,2)$ $b \geq 19$
$\quad D(3,2,3,2,2,2)$ $b \geq 19$
$\quad D(3,2,3,1,1,3,2)$ $b \geq 19$
$\quad D(3,2,3,2,1,1,3)$ $b \geq 19$
$12a_{482}$ 93/22 $C(4,4,2,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
154 diagrams of degree $(3,17,19) $. For example
$\quad C(3,1,-5,-3,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 6 simple diagrams with 15 crossings or fewer
$\quad D(4,4,2,2)$ $b \geq 17$
$\quad D(4,3,1,3,2)$ $b \geq 17$
$\quad D(4,4,1,1,3)$ $b \geq 17$
$\quad D(4,5,2,3)$ $b \geq 17$
$\quad D(4,2,1,2,3,2)$ $b \geq 17$
$\quad D(4,1,1,2,2,3,2)$ $b \geq 19$
$12a_{497}$ 209/81 $C(2,1,1,2,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,1,2,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{498}$ 207/76 $C(2,1,2,1,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,2,1,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{499}$ 233/89 $C(2,1,1,1,1,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,13,23)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,1,1,1,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{500}$ 167/60 $C(2,1,3,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,14,22)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,3,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{501}$ 199/55 $C(3,1,1,1,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,14,22)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,1,1,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{502}$ 91/37 $C(2,2,5,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
58 diagrams of degree $(3,16,20) $. For example
$\quad C(3,-1,-1,-5,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(2,2,5,1,2)$ $b \geq 16$
$\quad D(3,6,2,2)$ $b \geq 19$
$\quad D(2,2,4,1,2,2)$ $b \geq 16$
$12a_{506}$ 185/68 $C(2,1,2,1,1,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,2,1,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{508}$ 129/56 $C(2,3,3,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(2,3,2,1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(2,3,3,2,2)$ $b \geq 16$
$12a_{510}$ 193/81 $C(2,2,1,1,1,1,2,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,2,1,1,1,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{511}$ 125/51 $C(2,2,4,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
48 diagrams of degree $(3,16,20) $. For example
$\quad C(2,2,3,1,-2,-2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(2,2,4,1,1,2)$ $b \geq 16$
$\quad D(3,2,4,2,2)$ $b \geq 19$
$\quad D(2,2,3,1,2,1,2)$ $b \geq 16$
$12a_{512}$ 151/64 $C(2,2,1,3,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,2,1,3,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{514}$ 187/79 $C(2,2,1,2,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,2,1,2,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{517}$ 145/52 $C(2,1,3,1,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,3,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{518}$ 157/34 $C(4,1,1,1,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,14,22)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(4,1,1,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,1,1,1,1,1,1,2)$ $b \geq 14$
$12a_{519}$ 111/25 $C(4,2,3,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
61 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,1,-4,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,2,3,1,2)$ $b \geq 16$
$\quad D(4,2,4,3)$ $b \geq 19$
$\quad D(4,1,1,4,1,2)$ $b \geq 16$
$\quad D(4,2,2,1,2,2)$ $b \geq 16$
$12a_{520}$ 133/36 $C(3,1,2,3,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,3,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{521}$ 113/48 $C(2,2,1,4,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,2,1,4,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{522}$ 173/73 $C(2,2,1,2,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,2,1,2,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{528}$ 183/67 $C(2,1,2,1,2,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,1,2,1,2,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{532}$ 125/33 $C(3,1,3,1,2,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,3,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{533}$ 137/31 $C(4,2,2,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
49 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-3,-2,-1,-2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(4,2,2,1,1,2)$ $b \geq 16$
$\quad D(4,2,2,2,3)$ $b \geq 19$
$\quad D(4,2,3,2,2)$ $b \geq 16$
$\quad D(4,1,1,3,1,1,2)$ $b \geq 16$
$\quad D(4,2,1,1,2,1,2)$ $b \geq 16$
$12a_{534}$ 163/44 $C(3,1,2,2,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,2,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{535}$ 175/47 $C(3,1,2,1,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{536}$ 137/29 $C(4,1,2,1,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,1,2,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{537}$ 179/50 $C(3,1,1,2,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(3,-2,-1,-2,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,1,2,1,1,1,2)$ $b \geq 14$
$12a_{538}$ 83/13 $C(6,2,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
62 diagrams of degree $(3,16,20) $. For example
$\quad C(6,1,1,-2,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(6,2,1,1,2)$ $b \geq 16$
$\quad D(6,2,2,3)$ $b \geq 19$
$\quad D(6,3,2,2)$ $b \geq 16$
$\quad D(6,1,1,2,1,2)$ $b \geq 16$
$12a_{539}$ 145/44 $C(3,3,2,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(3,2,1,-3,-1,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,3,2,1,1,2)$ $b \geq 16$
$12a_{540}$ 165/49 $C(3,2,1,2,1,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,2,1,2,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{541}$ 153/41 $C(3,1,2,1,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{545}$ 143/63 $C(2,3,1,2,2,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(2,3,1,2,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{549}$ 111/26 $C(4,3,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(4,3,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,3,1,2,2)$ $b \geq 14$
$12a_{550}$ 149/34 $C(4,2,1,1,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(4,2,1,1,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,2,1,1,1,1,2)$ $b \geq 14$
$12a_{551}$ 103/18 $C(5,1,2,1,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(5,1,2,1,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(5,1,2,1,1,2)$ $b \geq 14$
$12a_{552}$ 131/30 $C(4,2,1,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(4,2,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,2,1,2,1,2)$ $b \geq 14$
$12a_{579}$ 177/49 $C(3,1,1,1,1,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,1,1,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{580}$ 69/11 $C(6,3,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
56 diagrams of degree $(3,16,20) $. For example
$\quad C(7,-1,-2,-2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(6,3,1,2)$ $b \geq 16$
$\quad D(6,4,3)$ $b \geq 19$
$\quad D(6,2,1,2,2)$ $b \geq 16$
$12a_{581}$ 119/36 $C(3,3,3,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(3,2,1,-4,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,3,3,1,2)$ $b \geq 16$
$12a_{582}$ 131/39 $C(3,2,1,3,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,2,1,3,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{583}$ 161/45 $C(3,1,1,2,1,2,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,1,2,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{584}$ 143/31 $C(4,1,1,1,1,2,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,1,1,1,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{585}$ 181/50 $C(3,1,1,1,1,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,1,1,1,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,1,1,1,1,2,2)$ $b \geq 14$
$12a_{595}$ 139/30 $C(4,1,1,1,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(4,1,1,1,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,1,1,1,2,1,2)$ $b \geq 14$
$12a_{596}$ 81/14 $C(5,1,3,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(5,1,3,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(5,1,3,1,2)$ $b \geq 14$
$12a_{597}$ 123/26 $C(4,1,2,1,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(4,1,2,1,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,1,2,1,2,2)$ $b \geq 14$
$12a_{600}$ 109/25 $C(4,2,1,3,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,2,1,3,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{601}$ 127/34 $C(3,1,2,1,3,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,2,1,3,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,2,1,3,2)$ $b \geq 14$
$12a_{643}$ 99/23 $C(4,3,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
63 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-4,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(4,3,3,2)$ $b \geq 16$
$\quad D(4,2,1,4,2)$ $b \geq 16$
$\quad D(4,3,2,1,3)$ $b \geq 16$
$12a_{644}$ 113/30 $C(3,1,3,3,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,3,2,1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,3,3,2)$ $b \geq 16$
$12a_{649}$ 127/27 $C(4,1,2,2,1,2)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,1,2,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{650}$ 165/46 $C(3,1,1,2,2,1,2)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,1,2,2,1,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,1,2,2,1,2)$ $b \geq 14$
$12a_{651}$ 97/17 $C(5,1,2,2,2)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(5,1,2,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{652}$ 155/46 $C(3,2,1,2,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(3,2,1,2,2,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,2,1,2,2,2)$ $b \geq 14$
$12a_{682}$ 107/29 $C(3,1,2,4,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,2,4,2)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,2,4,2)$ $b \geq 14$
$12a_{684}$ 135/41 $C(3,3,2,2,2)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(3,2,1,-3,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,3,2,2,2)$ $b \geq 16$
$12a_{690}$ 89/20 $C(4,2,4,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
155 diagrams of degree $(3,17,19) $. For example
$\quad C(3,-1,-3,-3,1,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 6 simple diagrams with 15 crossings or fewer
$\quad D(4,2,4,2)$ $b \geq 17$
$\quad D(4,1,1,5,2)$ $b \geq 17$
$\quad D(4,2,3,1,3)$ $b \geq 17$
$\quad D(5,2,5,2)$ $b \geq 19$
$\quad D(4,2,2,1,2,3)$ $b \geq 17$
$\quad D(4,2,1,1,2,2,3)$ $b \geq 19$
$12a_{691}$ 77/12 $C(6,2,2,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
161 diagrams of degree $(3,17,19) $. For example
$\quad C(6,3,-1,-2,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 5 simple diagrams with 15 crossings or fewer
$\quad D(6,2,2,2)$ $b \geq 17$
$\quad D(6,1,1,3,2)$ $b \geq 17$
$\quad D(6,2,1,1,3)$ $b \geq 17$
$\quad D(6,3,2,3)$ $b \geq 17$
$\quad D(7,2,3,2)$ $b \geq 19$
$12a_{713}$ 139/39 $C(3,1,1,3,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
58 diagrams of degree $(3,16,20) $. For example
$\quad C(3,-1,-1,-3,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,1,1,3,2,2)$ $b \geq 16$
$\quad D(3,2,4,2,2)$ $b \geq 19$
$\quad D(4,2,3,2,2)$ $b \geq 16$
$\quad D(3,1,1,2,1,3,2)$ $b \geq 16$
$12a_{714}$ 107/19 $C(5,1,1,1,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(6,-2,-1,-3,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(5,1,1,1,2,2)$ $b \geq 16$
$\quad D(5,1,2,3,2)$ $b \geq 16$
$\quad D(5,2,2,2,2)$ $b \geq 19$
$\quad D(6,2,1,2,2)$ $b \geq 16$
$\quad D(5,1,1,1,1,1,3)$ $b \geq 16$
$12a_{715}$ 169/50 $C(3,2,1,1,1,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(3,2,1,2,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 6 simple diagrams with 13 crossings or fewer
$\quad D(3,2,1,1,1,2,2)$ $b \geq 16$
$\quad D(3,2,1,2,3,2)$ $b \geq 16$
$\quad D(3,2,2,2,2,2)$ $b \geq 19$
$\quad D(3,3,2,1,2,2)$ $b \geq 16$
$\quad D(3,1,1,2,1,1,2,2)$ $b \geq 16$
$\quad D(3,2,1,1,1,1,1,3)$ $b \geq 16$
$12a_{716}$ 43/5 $C(8,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
62 diagrams of degree $(3,16,20) $. For example
$\quad C(8,1,2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(8,1,1,2)$ $b \geq 16$
$\quad D(8,2,3)$ $b \geq 19$
$\quad D(9,2,2)$ $b \geq 19$
$12a_{717}$ 89/28 $C(3,5,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(2,-2,-1,-6,1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,5,1,1,2)$ $b \geq 16$
$\quad D(3,5,2,3)$ $b \geq 16$
$\quad D(3,6,2,2)$ $b \geq 19$
$\quad D(3,4,1,2,1,2)$ $b \geq 16$
$12a_{718}$ 141/41 $C(3,2,3,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(3,3,-1,-2,-2,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,2,3,1,1,2)$ $b \geq 16$
$\quad D(3,2,4,2,2)$ $b \geq 19$
$\quad D(3,1,1,4,1,1,2)$ $b \geq 16$
$\quad D(3,2,2,1,2,1,2)$ $b \geq 16$
$12a_{720}$ 113/21 $C(5,2,1,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
51 diagrams of degree $(3,16,20) $. For example
$\quad C(5,2,1,2,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(5,2,1,1,1,2)$ $b \geq 16$
$\quad D(5,2,1,2,3)$ $b \geq 16$
$\quad D(5,2,2,2,2)$ $b \geq 19$
$\quad D(5,3,2,1,2)$ $b \geq 16$
$\quad D(5,1,1,2,1,1,2)$ $b \geq 16$
$12a_{721}$ 171/50 $C(3,2,2,1,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
51 diagrams of degree $(3,16,20) $. For example
$\quad C(3,-3,2,1,-3,-3)$,15 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 6 simple diagrams with 13 crossings or fewer
$\quad D(3,2,2,1,1,1,2)$ $b \geq 16$
$\quad D(3,2,2,1,2,3)$ $b \geq 16$
$\quad D(3,2,2,2,2,2)$ $b \geq 19$
$\quad D(3,2,3,2,1,2)$ $b \geq 17$
$\quad D(3,1,1,3,1,1,1,2)$ $b \geq 16$
$\quad D(3,2,1,1,2,1,1,2)$ $b \geq 16$
$12a_{722}$ 29/3 $C(9,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
79 diagrams of degree $(3,16,20) $. For example
$\quad C(8,1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(9,1,2)$ $b \geq 16$
$\quad D(10,3)$ $b \geq 19$
$12a_{723}$ 63/20 $C(3,6,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
52 diagrams of degree $(3,16,20) $. For example
$\quad C(2,1,-7,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(3,6,1,2)$ $b \geq 16$
$\quad D(3,5,1,2,2)$ $b \geq 16$
$12a_{724}$ 107/31 $C(3,2,4,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,1,-5,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,5,2,3)$ $b \geq 16$
$\quad D(3,2,4,1,2)$ $b \geq 16$
$\quad D(3,1,1,5,1,2)$ $b \geq 16$
$\quad D(3,2,3,1,2,2)$ $b \geq 16$
$12a_{726}$ 103/19 $C(5,2,2,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,1,-3,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,2,2,1,2)$ $b \geq 16$
$\quad D(5,2,3,3)$ $b \geq 17$
$\quad D(5,1,1,3,1,2)$ $b \geq 16$
$\quad D(5,2,1,1,2,2)$ $b \geq 16$
$12a_{727}$ 157/46 $C(3,2,2,2,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
43 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,1,-3,-2,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(3,3,2,2,3)$ $b \geq 16$
$\quad D(3,2,2,2,1,2)$ $b \geq 16$
$\quad D(3,1,1,3,2,1,2)$ $b \geq 16$
$\quad D(3,2,1,1,3,1,2)$ $b \geq 16$
$\quad D(3,2,2,1,1,2,2)$ $b \geq 17$
$12a_{728}$ 133/29 $C(4,1,1,2,2,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,1,2,1,1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(4,1,1,2,2,2)$ $b \geq 16$
$\quad D(4,2,3,2,2)$ $b \geq 16$
$\quad D(5,2,2,2,2)$ $b \geq 19$
$\quad D(4,1,1,1,1,3,2)$ $b \geq 16$
$\quad D(4,1,1,2,1,1,3)$ $b \geq 16$
$12a_{729}$ 167/46 $C(3,1,1,1,2,2,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(4,-2,-1,-2,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(3,1,1,1,2,2,2)$ $b \geq 16$
$\quad D(3,1,2,3,2,2)$ $b \geq 16$
$\quad D(3,2,2,2,2,2)$ $b \geq 19$
$\quad D(4,2,1,2,2,2)$ $b \geq 16$
$\quad D(3,1,1,1,1,1,3,2)$ $b \geq 16$
$12a_{731}$ 105/22 $C(4,1,3,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
59 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,2,1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,1,3,2,2)$ $b \geq 16$
$\quad D(5,4,2,2)$ $b \geq 19$
$\quad D(4,1,2,1,3,2)$ $b \geq 16$
$\quad D(4,1,3,1,1,3)$ $b \geq 16$
$12a_{732}$ 95/18 $C(5,3,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
61 diagrams of degree $(3,16,20) $. For example
$\quad C(5,3,1,2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,3,1,1,2)$ $b \geq 16$
$\quad D(5,3,2,3)$ $b \geq 16$
$\quad D(5,4,2,2)$ $b \geq 19$
$\quad D(5,2,1,2,1,2)$ $b \geq 16$
$12a_{733}$ 73/14 $C(5,4,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
47 diagrams of degree $(3,16,20) $. For example
$\quad C(5,3,1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(5,4,1,2)$ $b \geq 16$
$\quad D(5,5,3)$ $b \geq 16$
$\quad D(5,3,1,2,2)$ $b \geq 16$
$12a_{736}$ 141/43 $C(3,3,1,1,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(2,2,1,1,4,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(3,3,1,1,2,2)$ $b \geq 16$
$\quad D(3,3,2,3,2)$ $b \geq 16$
$\quad D(3,4,2,2,2)$ $b \geq 19$
$\quad D(3,2,1,2,1,2,2)$ $b \geq 16$
$\quad D(3,3,1,1,1,1,3)$ $b \geq 16$
$12a_{738}$ 119/37 $C(3,4,1,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
55 diagrams of degree $(3,16,20) $. For example
$\quad C(2,1,-5,-1,-1,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(3,4,1,1,1,2)$ $b \geq 16$
$\quad D(3,4,1,2,3)$ $b \geq 16$
$\quad D(3,4,2,2,2)$ $b \geq 19$
$\quad D(3,5,2,1,2)$ $b \geq 16$
$\quad D(3,3,1,2,1,1,2)$ $b \geq 16$
$12a_{740}$ 113/35 $C(3,4,2,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
47 diagrams of degree $(3,16,20) $. For example
$\quad C(2,1,-5,-2,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,4,2,1,2)$ $b \geq 16$
$\quad D(3,4,3,3)$ $b \geq 16$
$\quad D(3,3,1,3,1,2)$ $b \geq 16$
$\quad D(3,4,1,1,2,2)$ $b \geq 16$
$12a_{743}$ 79/12 $C(6,1,1,2,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,-2,-1,-2,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(6,1,1,2,2)$ $b \geq 16$
$\quad D(6,2,3,2)$ $b \geq 17$
$\quad D(7,2,2,2)$ $b \geq 19$
$\quad D(6,1,1,1,1,3)$ $b \geq 16$
$12a_{744}$ 61/8 $C(7,1,1,1,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
56 diagrams of degree $(3,16,20) $. For example
$\quad C(7,1,2,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(7,1,1,1,2)$ $b \geq 16$
$\quad D(7,1,2,3)$ $b \geq 16$
$\quad D(7,2,2,2)$ $b \geq 19$
$\quad D(8,2,1,2)$ $b \geq 17$
$12a_{745}$ 59/8 $C(7,2,1,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
33 diagrams of degree $(3,16,20) $. For example
$\quad C(6,1,-3,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(7,2,1,2)$ $b \geq 16$
$\quad D(7,3,3)$ $b \geq 17$
$\quad D(7,1,1,2,2)$ $b \geq 17$
$12a_{758}$ 113/31 $C(3,1,1,1,4,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
59 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,2,-5,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,1,1,1,4,2)$ $b \geq 16$
$\quad D(3,1,2,5,2)$ $b \geq 16$
$\quad D(3,2,2,4,2)$ $b \geq 19$
$\quad D(4,2,1,4,2)$ $b \geq 16$
$12a_{759}$ 61/9 $C(6,1,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
61 diagrams of degree $(3,16,20) $. For example
$\quad C(6,1,2,1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(6,1,3,2)$ $b \geq 16$
$\quad D(7,4,2)$ $b \geq 19$
$\quad D(6,1,2,1,3)$ $b \geq 16$
$12a_{760}$ 111/34 $C(3,3,1,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
58 diagrams of degree $(3,16,20) $. For example
$\quad C(3,2,1,-2,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,3,1,3,2)$ $b \geq 16$
$\quad D(3,4,4,2)$ $b \geq 19$
$\quad D(3,2,1,2,3,2)$ $b \geq 16$
$\quad D(3,3,1,2,1,3)$ $b \geq 16$
$12a_{761}$ 139/41 $C(3,2,1,1,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(2,3,1,1,3,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 5 simple diagrams with 13 crossings or fewer
$\quad D(3,2,1,1,3,2)$ $b \geq 16$
$\quad D(3,2,2,4,2)$ $b \geq 19$
$\quad D(3,3,2,3,2)$ $b \geq 16$
$\quad D(3,1,1,2,1,3,2)$ $b \geq 16$
$\quad D(3,2,1,1,2,1,3)$ $b \geq 16$
$12a_{762}$ 51/7 $C(7,3,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
66 diagrams of degree $(3,16,20) $. For example
$\quad C(7,2,1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(7,3,2)$ $b \geq 16$
$\quad D(7,2,1,3)$ $b \geq 16$
$12a_{763}$ 97/30 $C(3,4,3,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
40 diagrams of degree $(3,16,20) $. For example
$\quad C(3,-1,-2,-5,1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,4,3,2)$ $b \geq 16$
$\quad D(3,3,1,4,2)$ $b \geq 17$
$\quad D(3,4,2,1,3)$ $b \geq 16$
$12a_{764}$ 133/39 $C(3,2,2,3,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
44 diagrams of degree $(3,16,20) $. For example
$\quad C(2,2,1,-3,-3,1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,2,2,3,2)$ $b \geq 16$
$\quad D(3,1,1,3,3,2)$ $b \geq 16$
$\quad D(3,2,1,1,4,2)$ $b \geq 16$
$\quad D(3,2,2,2,1,3)$ $b \geq 16$
$12a_{773}$ 91/20 $C(4,1,1,4,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-2,-1,-4,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,1,1,4,2)$ $b \geq 16$
$\quad D(4,2,5,2)$ $b \geq 17$
$\quad D(5,2,4,2)$ $b \geq 19$
$\quad D(4,1,1,3,1,3)$ $b \geq 16$
$12a_{774}$ 89/16 $C(5,1,1,3,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,-2,-1,-3,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,1,1,3,2)$ $b \geq 16$
$\quad D(5,2,4,2)$ $b \geq 19$
$\quad D(6,2,3,2)$ $b \geq 17$
$\quad D(5,1,1,2,1,3)$ $b \geq 16$
$12a_{775}$ 87/16 $C(5,2,3,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
33 diagrams of degree $(3,16,20) $. For example
$\quad C(5,2,2,1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(5,2,3,2)$ $b \geq 16$
$\quad D(5,1,1,4,2)$ $b \geq 17$
$\quad D(5,2,2,1,3)$ $b \geq 16$
$12a_{791}$ 63/13 $C(4,1,5,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
63 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-2,-5,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(4,1,5,2)$ $b \geq 16$
$\quad D(5,6,2)$ $b \geq 19$
$\quad D(4,1,4,1,3)$ $b \geq 16$
$12a_{792}$ 85/24 $C(3,1,1,5,2)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(2,5,1,2,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,1,1,5,2)$ $b \geq 16$
$\quad D(3,2,6,2)$ $b \geq 19$
$\quad D(4,2,5,2)$ $b \geq 17$
$12a_{796}$ 57/11 $C(5,5,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
46 diagrams of degree $(3,16,20) $. For example
$\quad C(6,-1,-3,-1,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(5,5,2)$ $b \geq 16$
$\quad D(5,4,1,3)$ $b \geq 16$
$12a_{797}$ 83/24 $C(3,2,5,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
25 diagrams of degree $(3,16,20) $. For example
$\quad C(3,3,-1,-3,-1,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,2,5,2)$ $b \geq 16$
$\quad D(3,1,1,6,2)$ $b \geq 17$
$\quad D(3,2,4,1,3)$ $b \geq 17$
$12a_{802}$ 47/15 $C(3,7,2)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
30 diagrams of degree $(3,16,20) $. For example
$\quad C(4,-2,1,4,1,-3)$,15 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(3,7,2)$ $b \geq 16$
$\quad D(3,6,1,3)$ $b \geq 16$
$12a_{803}$ 21/2 $C(10,2)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
142 diagrams of degree $(3,17,19) $. For example
$\quad C(3,-1,-7,-1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 1 simple diagrams with 15 crossings or fewer
$\quad D(10,2)$ $b \geq 17$
$12a_{1023}$ 127/29 $C(4,2,1,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
67 diagrams of degree $(3,16,20) $. For example
$\quad C(4,-2,-1,-2,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,2,1,1,1,3)$ $b \geq 16$
$\quad D(4,2,2,2,3)$ $b \geq 19$
$\quad D(4,3,2,1,3)$ $b \geq 16$
$\quad D(4,1,1,2,1,1,3)$ $b \geq 16$
$12a_{1024}$ 149/40 $C(3,1,2,1,1,1,3)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,1,1,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1029}$ 81/19 $C(4,3,1,4)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
75 diagrams of degree $(3,16,20) $. For example
$\quad C(4,2,-1,-2,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(4,3,1,4)$ $b \geq 16$
$\quad D(5,4,4)$ $b \geq 19$
$12a_{1030}$ 91/19 $C(4,1,3,1,3)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,1,3,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1033}$ 107/25 $C(4,3,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
64 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,-4,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,3,1,1,3)$ $b \geq 16$
$\quad D(4,3,2,4)$ $b \geq 17$
$\quad D(4,4,2,3)$ $b \geq 19$
$\quad D(4,2,1,2,1,3)$ $b \geq 16$
$12a_{1034}$ 121/32 $C(3,1,3,1,1,3)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
8 diagrams of degree $(3,14,22) $. For example
$\quad C(3,1,3,1,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,1,3,1,1,3)$ $b \geq 14$
$12a_{1039}$ 137/37 $C(3,1,2,2,1,3)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,1,2,2,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1040}$ 115/26 $C(4,2,2,1,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
4 diagrams of degree $(3,14,22) $. For example
$\quad C(4,2,2,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,2,2,1,3)$ $b \geq 14$
$12a_{1125}$ 101/23 $C(4,2,1,1,4)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
62 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,1,3,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(4,2,1,1,4)$ $b \geq 16$
$\quad D(4,3,2,4)$ $b \geq 17$
$\quad D(5,2,2,4)$ $b \geq 19$
$12a_{1126}$ 119/26 $C(4,1,1,2,1,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(4,1,1,2,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,1,1,2,1,3)$ $b \geq 14$
$12a_{1127}$ 97/22 $C(4,2,2,4)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
83 diagrams of degree $(3,17,19) $. For example
$\quad C(3,1,-3,-3,1,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 2 simple diagrams with 15 crossings or fewer
$\quad D(4,2,2,4)$ $b \geq 17$
$\quad D(5,2,3,4)$ $b \geq 19$
$12a_{1128}$ 59/9 $C(6,1,1,4)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
75 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,-2,-1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(6,1,1,4)$ $b \geq 16$
$\quad D(6,2,5)$ $b \geq 19$
$\quad D(7,2,4)$ $b \geq 19$
$12a_{1129}$ 105/23 $C(4,1,1,3,3)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
60 diagrams of degree $(3,16,20) $. For example
$\quad C(4,1,1,4,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(4,1,1,3,3)$ $b \geq 16$
$\quad D(4,2,4,3)$ $b \geq 19$
$\quad D(5,2,3,3)$ $b \geq 17$
$12a_{1130}$ 125/27 $C(4,1,1,1,2,3)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
63 diagrams of degree $(3,16,20) $. For example
$\quad C(5,-2,-1,-2,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(4,1,1,1,2,3)$ $b \geq 16$
$\quad D(4,1,2,3,3)$ $b \geq 16$
$\quad D(4,2,2,2,3)$ $b \geq 19$
$\quad D(5,2,1,2,3)$ $b \geq 16$
$12a_{1131}$ 73/11 $C(6,1,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
64 diagrams of degree $(3,16,20) $. For example
$\quad C(7,-2,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(6,1,1,1,3)$ $b \geq 16$
$\quad D(6,1,2,4)$ $b \geq 16$
$\quad D(6,2,2,3)$ $b \geq 19$
$\quad D(7,2,1,3)$ $b \geq 16$
$12a_{1132}$ 131/40 $C(3,3,1,1,1,3)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(4,-2,-1,-3,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,3,1,1,1,3)$ $b \geq 16$
$12a_{1133}$ 159/47 $C(3,2,1,1,1,1,3)$ 13
Chebyshev parametrisation of degree $(3,16,20)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,2,1,1,1,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1134}$ 53/7 $C(7,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
76 diagrams of degree $(3,16,20) $. For example
$\quad C(6,1,-2,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(7,1,1,3)$ $b \geq 16$
$\quad D(7,2,4)$ $b \geq 19$
$\quad D(8,2,3)$ $b \geq 19$
$12a_{1135}$ 103/32 $C(3,4,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
56 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,1,5,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(3,4,1,1,3)$ $b \geq 16$
$\quad D(3,5,2,3)$ $b \geq 16$
$\quad D(4,2,4,3)$ $b \geq 19$
$\quad D(3,3,1,2,1,3)$ $b \geq 16$
$12a_{1136}$ 147/43 $C(3,2,2,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
62 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,1,-3,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,2,2,1,1,3)$ $b \geq 16$
$\quad D(4,2,2,2,3)$ $b \geq 19$
$\quad D(3,2,1,1,2,1,3)$ $b \geq 16$
$12a_{1138}$ 79/14 $C(5,1,1,1,4)$ 16
Chebyshev parametrisation of degree $(3,16,20)$
65 diagrams of degree $(3,16,20) $. For example
$\quad C(6,-2,-1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,2,1,5)$ $b \geq 16$
$\quad D(5,1,1,1,4)$ $b \geq 16$
$\quad D(5,2,2,4)$ $b \geq 19$
$\quad D(6,2,1,4)$ $b \geq 16$
$12a_{1139}$ 101/18 $C(5,1,1,1,1,3)$ 14
Chebyshev parametrisation of degree $(3,16,20)$
7 diagrams of degree $(3,14,22) $. For example
$\quad C(5,1,1,1,1,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(5,1,1,1,1,3)$ $b \geq 14$
$12a_{1140}$ 97/18 $C(5,2,1,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
57 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,1,-2,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,2,1,1,3)$ $b \geq 16$
$\quad D(5,2,2,4)$ $b \geq 19$
$\quad D(5,3,2,3)$ $b \geq 16$
$\quad D(5,1,1,2,1,3)$ $b \geq 16$
$12a_{1145}$ 79/15 $C(5,3,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
64 diagrams of degree $(3,16,20) $. For example
$\quad C(5,2,1,-2,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(5,3,1,3)$ $b \geq 16$
$\quad D(5,4,4)$ $b \geq 19$
$\quad D(5,2,1,2,3)$ $b \geq 16$
$12a_{1146}$ 117/34 $C(3,2,3,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
51 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,4,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,2,3,1,3)$ $b \geq 16$
$\quad D(4,4,2,3)$ $b \geq 19$
$\quad D(3,2,2,1,2,3)$ $b \geq 16$
$12a_{1148}$ 73/23 $C(3,5,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
59 diagrams of degree $(3,16,20) $. For example
$\quad C(3,1,6,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(3,5,1,3)$ $b \geq 16$
$\quad D(4,6,3)$ $b \geq 19$
$\quad D(3,4,1,2,3)$ $b \geq 16$
$12a_{1149}$ 35/4 $C(8,1,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
52 diagrams of degree $(3,16,20) $. For example
$\quad C(7,1,-2,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(8,1,3)$ $b \geq 16$
$\quad D(9,4)$ $b \geq 19$
$12a_{1157}$ 39/5 $C(7,1,4)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
68 diagrams of degree $(3,16,20) $. For example
$\quad C(7,2,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(7,1,4)$ $b \geq 16$
$\quad D(8,5)$ $b \geq 19$
$12a_{1158}$ 77/16 $C(4,1,4,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
5 diagrams of degree $(3,14,22) $. For example
$\quad C(4,-1,-3,-1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,1,4,3)$ $b \geq 16$
$12a_{1159}$ 113/24 $C(4,1,2,2,3)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(4,1,2,2,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1161}$ 75/14 $C(5,2,1,4)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(5,2,1,4)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(5,2,1,4)$ $b \geq 14$
$12a_{1162}$ 69/13 $C(5,3,4)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
54 diagrams of degree $(3,16,20) $. For example
$\quad C(5,-1,-3,1,4)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(5,3,4)$ $b \geq 16$
$\quad D(5,2,1,5)$ $b \geq 16$
$12a_{1163}$ 103/24 $C(4,3,2,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
3 diagrams of degree $(3,14,22) $. For example
$\quad C(4,2,1,-3,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(4,3,2,3)$ $b \geq 16$
$12a_{1165}$ 67/16 $C(4,5,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
36 diagrams of degree $(3,16,20) $. For example
$\quad C(5,-1,-3,-1,4)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(4,5,3)$ $b \geq 16$
$\quad D(4,4,1,4)$ $b \geq 16$
$12a_{1166}$ 33/4 $C(8,4)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
172 diagrams of degree $(3,17,19) $. For example
$\quad C(3,1,-7,-1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 1 simple diagrams with 15 crossings or fewer
$\quad D(8,4)$ $b \geq 17$
$12a_{1273}$ 61/11 $C(5,1,1,5)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
36 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,2,-1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(5,1,1,5)$ $b \geq 16$
$\quad D(6,2,5)$ $b \geq 19$
$12a_{1274}$ 95/17 $C(5,1,1,2,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
58 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,1,3,-1,-2)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 4 simple diagrams with 13 crossings or fewer
$\quad D(5,1,1,2,3)$ $b \geq 16$
$\quad D(5,2,3,3)$ $b \geq 17$
$\quad D(6,2,2,3)$ $b \geq 19$
$\quad D(5,1,1,1,1,4)$ $b \geq 16$
$12a_{1275}$ 149/44 $C(3,2,1,1,2,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
2 diagrams of degree $(3,14,22) $. For example
$\quad C(3,2,1,2,-1,-1,-3)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(3,2,1,1,2,3)$ $b \geq 16$
$12a_{1276}$ 75/13 $C(5,1,3,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
66 diagrams of degree $(3,16,20) $. For example
$\quad C(5,1,2,1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 3 simple diagrams with 13 crossings or fewer
$\quad D(5,1,3,3)$ $b \geq 16$
$\quad D(6,4,3)$ $b \geq 19$
$\quad D(5,1,2,1,4)$ $b \geq 16$
$12a_{1277}$ 121/37 $C(3,3,1,2,3)$ 13
Chebyshev parametrisation of degree $(3,17,19)$
1 diagrams of degree $(3,13,23) $. For example
$\quad C(3,3,1,2,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 23$
$12a_{1278}$ 41/6 $C(6,1,5)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
65 diagrams of degree $(3,16,20) $. For example
$\quad C(6,2,-1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(6,1,5)$ $b \geq 16$
$\quad D(7,6)$ $b \geq 19$
$12a_{1279}$ 67/10 $C(6,1,2,3)$ 14
Chebyshev parametrisation of degree $(3,17,19)$
6 diagrams of degree $(3,14,22) $. For example
$\quad C(6,1,2,3)$,12 crossings,23 sign changes in the Gauss sequence, ie $c \leq 22$
Braid condition for 1 simple diagrams with 12 crossings or fewer
$\quad D(6,1,2,3)$ $b \geq 14$
$12a_{1281}$ 109/33 $C(3,3,3,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
28 diagrams of degree $(3,16,20) $. For example
$\quad C(4,-1,-3,1,2,3)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 1 simple diagrams with 13 crossings or fewer
$\quad D(3,3,3,3)$ $b \geq 16$
$12a_{1282}$ 63/10 $C(6,3,3)$ 16
Chebyshev parametrisation of degree $(3,17,19)$
48 diagrams of degree $(3,16,20) $. For example
$\quad C(6,2,1,-4)$,13 crossings,22 sign changes in the Gauss sequence, ie $c \leq 20$
Braid condition for 2 simple diagrams with 13 crossings or fewer
$\quad D(6,3,3)$ $b \geq 16$
$\quad D(6,2,1,4)$ $b \geq 16$
$12a_{1287}$ 37/6 $C(6,6)$ 17
Chebyshev parametrisation of degree $(3,17,19)$
81 diagrams of degree $(3,17,19) $. For example
$\quad C(7,-1,-3,-1,2)$,14 crossings,21 sign changes in the Gauss sequence, ie $c \leq 19$
Braid condition for 1 simple diagrams with 15 crossings or fewer
$\quad D(6,6)$ $b \geq 17$