# Lexicographic degrees of two-bridge knots

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 $b+c=3N$.
We list here the degree $b$ corresponding to the lexicographic degree $(3,b,3N-b)$.
For every knot, we list all simple diagrams (see [BKP1]) for which there is a construction (T-reduction) with the minimal degree. If not, we give at least one diagram. We also list all (simple) diagrams with at most $b-1$ crossings. For each diagram $D$ we give a lower bound for a polynomial trigonal curve $\mathcal{C}$ that could be $\mathcal{L}$-isotopic to it, using the fact that the associated braid $\mathfrak{b}$ must be quasipositivite, must be a link with 3 components and the linking number of any two strings of $\mathfrak{b}$ must be non-negative, see [BKP2, Prop. 3.4]).

Example. The knot $10_{40}=C(2,1,1,2,2,2)$ has lexicographic degree $(3,13,17)$.
3 simple diagrams (with 11 crossings) have this algebraic degree: $C(2,2,1,1,-2,-1,-2)$, $C(2,1,1,1,1,-3,-2)$, $C(2,1,1,2,1,1,-3)$.
The only diagram that might have a better algebraic degree would be the alternating diagram $C(2,1,1,2,2,2)$ (or equivalently $C(2,2,2,1,1,2)$). Its plane projection $D(2,2,2,1,1,2)$ has algebraic degree at least $(3,13)$ because we have checked that any polynomial trigonal curve of degree $(3,11)$ would not satisfy the braid condition.

We obtain similar results for two-bridge knots with crossing number 12 and 13.

NameSchub.Conway Not.Lex. Deg.Details
$3_{ 1}$ 3 $C(3)$ 4
 Chebyshev parametrisation of degree $(3,4,5)$ 1 simple diagrams with 3 crossings or fewer, of degree $b=4$ $\quad C(3)$ 3 crossings
$4_{ 1}$ 5/2 $C(2,2)$ 5
 Chebyshev parametrisation of degree $(3,5,7)$ 1 simple diagrams with 4 crossings or fewer, of degree $b=5$ $\quad C(2,2)$ 4 crossings
$5_{ 1}$ 5 $C(5)$ 7
 Chebyshev parametrisation of degree $(3,7,8)$ 1 simple diagrams with 6 crossings or fewer, of degree $b=7$ $\quad C(5)$ 5 crossings
$5_{ 2}$ 7/2 $C(3,2)$ 7
 Chebyshev parametrisation of degree $(3,7,8)$ 1 simple diagrams with 6 crossings or fewer, of degree $b=7$ $\quad C(3,2)$ 5 crossings
$6_{ 1}$ 9/2 $C(4,2)$ 8
 Chebyshev parametrisation of degree $(3,8,10)$ 1 simple diagrams with 7 crossings or fewer, of degree $b=8$ $\quad C(4,2)$ 6 crossings Braid condition for simple diagrams with 6 crossings or fewer $\quad D(4,2)$ $b \geq8$
$6_{ 2}$ 11/3 $C(3,1,2)$ 7
 Chebyshev parametrisation of degree $(3,8,10)$ 1 simple diagrams with 6 crossings or fewer, of degree $b=7$ $\quad C(3,1,2)$ 6 crossings
$6_{ 3}$ 13/5 $C(2,1,1,2)$ 7
 Chebyshev parametrisation of degree $(3,7,11)$ 1 simple diagrams with 6 crossings or fewer, of degree $b=7$ $\quad C(2,1,1,2)$ 6 crossings
$7_{ 1}$ 7 $C(7)$ 10
 Chebyshev parametrisation of degree $(3,10,11)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(7)$ 7 crossings Braid condition for simple diagrams with 7 crossings or fewer $\quad D(7)$ $b \geq10$
$7_{ 2}$ 11/2 $C(5,2)$ 10
 Chebyshev parametrisation of degree $(3,10,11)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(5,2)$ 7 crossings Braid condition for simple diagrams with 7 crossings or fewer $\quad D(5,2)$ $b \geq10$
$7_{ 3}$ 13/3 $C(4,3)$ 10
 Chebyshev parametrisation of degree $(3,10,11)$ 20 non simple diagrams with 9 crossings or fewer, of degree $b=10$. For example: $\quad C(3,1,-2,-1,2)$ 9 crossings Braid condition for simple diagrams with 7 crossings or fewer $\quad D(4,3)$ $b \geq10$
$7_{ 4}$ 15/4 $C(3,1,3)$ 8
 Chebyshev parametrisation of degree $(3,10,11)$ 1 simple diagrams with 7 crossings or fewer, of degree $b=8$ $\quad C(3,1,3)$ 7 crossings
$7_{ 5}$ 17/5 $C(3,2,2)$ 10
 Chebyshev parametrisation of degree $(3,10,11)$ 2 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,1,1,-3)$ 8 crossings $\quad C(2,1,1,-4)$ 8 crossings Braid condition for simple diagrams with 7 crossings or fewer $\quad D(3,2,2)$ $b \geq10$
$7_{ 6}$ 19/7 $C(2,1,2,2)$ 8
 Chebyshev parametrisation of degree $(3,10,11)$ 1 simple diagrams with 7 crossings or fewer, of degree $b=8$ $\quad C(2,2,1,2)$ 7 crossings
$7_{ 7}$ 21/8 $C(2,1,1,1,2)$ 8
 Chebyshev parametrisation of degree $(3,8,13)$ 1 simple diagrams with 7 crossings or fewer, of degree $b=8$ $\quad C(2,1,1,1,2)$ 7 crossings
$8_{ 1}$ 13/2 $C(6,2)$ 11
 Chebyshev parametrisation of degree $(3,11,13)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(6,2)$ 8 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(6,2)$ $b \geq11$
$8_{ 2}$ 17/3 $C(5,1,2)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 8 non simple diagrams with 9 crossings or fewer, of degree $b=10$. For example: $\quad C(2,1,2,1,-1,-2)$ 9 crossings
$8_{ 3}$ 17/4 $C(4,4)$ 11
 Chebyshev parametrisation of degree $(3,11,13)$ 15 non simple diagrams with 10 crossings or fewer, of degree $b=11$. For example: $\quad C(3,1,-1,-1,1,3)$ 10 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(4,4)$ $b \geq11$
$8_{ 4}$ 19/4 $C(4,1,3)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(4,1,3)$ 8 crossings
$8_{ 6}$ 23/7 $C(3,3,2)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 2 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,2,1,-3)$ 9 crossings $\quad C(2,2,1,-4)$ 9 crossings
$8_{ 7}$ 23/5 $C(4,1,1,2)$ 10
 Chebyshev parametrisation of degree $(3,10,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(4,1,1,2)$ 8 crossings
$8_{ 8}$ 25/9 $C(2,1,3,2)$ 10
 Chebyshev parametrisation of degree $(3,10,14)$ 3 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,2,1,-2,-2)$ 9 crossings $\quad C(2,3,1,2)$ 8 crossings $\quad C(2,1,2,1,-3)$ 9 crossings
$8_{ 9}$ 25/7 $C(3,1,1,3)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,1,1,3)$ 8 crossings
$8_{ 11}$ 27/8 $C(3,2,1,2)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,2,1,2)$ 8 crossings
$8_{ 12}$ 29/12 $C(2,2,2,2)$ 11
 Chebyshev parametrisation of degree $(3,11,13)$ 3 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,2,1,1,-3)$ 9 crossings $\quad C(2,1,1,-3,-2)$ 9 crossings $\quad C(2,2,2,2)$ 8 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(2,2,1,1,3)$ $b \geq11$ $\quad D(2,1,1,3,2)$ $b \geq11$ $\quad D(2,2,2,2)$ $b \geq11$
$8_{ 13}$ 29/8 $C(3,1,1,1,2)$ 10
 Chebyshev parametrisation of degree $(3,10,14)$ 4 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,1,2,-3)$ 9 crossings $\quad C(3,1,1,1,2)$ 8 crossings $\quad C(3,-2,-1,-3)$ 9 crossings $\quad C(2,1,1,1,3)$ 8 crossings
$8_{ 14}$ 31/12 $C(2,1,1,2,2)$ 10
 Chebyshev parametrisation of degree $(3,11,13)$ 3 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,2,1,1,2)$ 8 crossings $\quad C(2,1,1,1,1,-3)$ 9 crossings $\quad C(2,1,1,-2,-1,-2)$ 9 crossings
$9_{ 1}$ 9 $C(9)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 53 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(4,1,-2,2,-1,-2)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(9)$ $b \geq13$
$9_{ 2}$ 15/2 $C(7,2)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(7,2)$ 9 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(7,2)$ $b \geq13$
$9_{ 3}$ 19/3 $C(6,3)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 73 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(4,1,-2,2,1,-2)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(6,3)$ $b \geq13$
$9_{ 4}$ 21/4 $C(5,4)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 72 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(3,1,-1,-1,1,2,1,-2)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,4)$ $b \geq13$
$9_{ 5}$ 23/4 $C(5,1,3)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(5,1,3)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(5,1,3)$ $b \geq11$
$9_{ 6}$ 27/5 $C(5,2,2)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,1,1,-3)$ 10 crossings $\quad C(2,1,1,-6)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,1,1,3)$ $b \geq13$ $\quad D(2,1,1,6)$ $b \geq13$ $\quad D(5,2,2)$ $b \geq13$
$9_{ 7}$ 29/9 $C(3,4,2)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,-2,3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,3,1,3)$ $b \geq13$ $\quad D(2,3,1,4)$ $b \geq13$ $\quad D(3,4,2)$ $b \geq13$
$9_{ 8}$ 31/11 $C(2,1,4,2)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 3 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,3,1,-2,-2)$ 10 crossings $\quad C(2,1,3,1,-3)$ 10 crossings $\quad C(2,4,1,2)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(2,4,1,2)$ $b \geq11$
$9_{ 9}$ 31/7 $C(4,2,3)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,1,-4)$ 10 crossings $\quad C(3,1,1,-5)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,1,1,4)$ $b \geq13$ $\quad D(3,1,1,5)$ $b \geq13$ $\quad D(4,2,3)$ $b \geq13$
$9_{ 10}$ 33/10 $C(3,3,3)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,2,1,-4)$ 10 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(3,3,3)$ $b \geq13$
$9_{ 11}$ 33/7 $C(4,1,2,2)$ 10
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(4,1,2,2)$ 9 crossings
$9_{ 12}$ 35/8 $C(4,2,1,2)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(4,2,1,2)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(4,2,1,2)$ $b \geq11$
$9_{ 13}$ 37/10 $C(3,1,2,3)$ 10
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,2,1,3)$ 9 crossings
$9_{ 14}$ 37/8 $C(4,1,1,1,2)$ 11
 Chebyshev parametrisation of degree $(3,11,16)$ 2 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(4,1,2,-3)$ 10 crossings $\quad C(4,1,1,1,2)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(4,1,1,1,2)$ $b \geq11$
$9_{ 15}$ 39/16 $C(2,2,3,2)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 2 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,2,2,1,-3)$ 10 crossings $\quad C(2,2,1,-3,-2)$ 10 crossings
$9_{ 17}$ 39/14 $C(2,1,3,1,2)$ 10
 Chebyshev parametrisation of degree $(3,11,16)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,1,3,1,2)$ 9 crossings
$9_{ 18}$ 41/12 $C(3,2,2,2)$ 13
 Chebyshev parametrisation of degree $(3,13,14)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,1,-3,-2)$ 10 crossings $\quad C(2,2,1,1,-4)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,1,1,3,2)$ $b \geq13$ $\quad D(2,2,1,1,4)$ $b \geq13$ $\quad D(3,2,1,1,3)$ $b \geq13$ $\quad D(2,1,1,3,3)$ $b \geq13$ $\quad D(3,2,2,2)$ $b \geq13$
$9_{ 19}$ 41/16 $C(2,1,1,3,2)$ 11
 Chebyshev parametrisation of degree $(3,11,16)$ 3 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,2,1,-2,-1,-2)$ 10 crossings $\quad C(2,1,1,2,1,-3)$ 10 crossings $\quad C(2,3,1,1,2)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(2,3,1,1,2)$ $b \geq11$
$9_{ 20}$ 41/11 $C(3,1,2,1,2)$ 10
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,1,2,1,2)$ 9 crossings
$9_{ 21}$ 43/12 $C(3,1,1,2,2)$ 11
 Chebyshev parametrisation of degree $(3,13,14)$ 3 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,1,1,1,1,-3)$ 10 crossings $\quad C(2,1,1,-2,-1,-3)$ 10 crossings $\quad C(3,1,1,2,2)$ 9 crossings Braid condition for simple diagrams with 9 crossings or fewer $\quad D(3,1,1,2,2)$ $b \geq11$
$9_{ 23}$ 45/19 $C(2,2,1,2,2)$ 10
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,2,1,2,2)$ 9 crossings
$9_{ 26}$ 47/13 $C(3,1,1,1,1,2)$ 10
 Chebyshev parametrisation of degree $(3,11,16)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(3,1,1,1,1,2)$ 9 crossings
$9_{ 27}$ 49/18 $C(2,1,2,1,1,2)$ 10
 Chebyshev parametrisation of degree $(3,13,14)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,1,2,1,1,2)$ 9 crossings
$9_{ 31}$ 55/21 $C(2,1,1,1,1,1,2)$ 10
 Chebyshev parametrisation of degree $(3,10,17)$ 1 simple diagrams with 9 crossings or fewer, of degree $b=10$ $\quad C(2,1,1,1,1,1,2)$ 9 crossings
$10_{ 1}$ 17/2 $C(8,2)$ 14
 Chebyshev parametrisation of degree $(3,14,16)$ 126 non simple diagrams with 13 crossings or fewer, of degree $b=14$. For example: $\quad C(2,1,-2,1,2,1,-1,-1,-2)$ 13 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(8,2)$ $b \geq14$
$10_{ 2}$ 23/3 $C(7,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 40 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(2,2,-1,-3,-1,1,2)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(7,1,2)$ $b \geq13$
$10_{ 3}$ 25/4 $C(6,4)$ 14
 Chebyshev parametrisation of degree $(3,14,16)$ 116 non simple diagrams with 13 crossings or fewer, of degree $b=14$. For example: $\quad C(2,1,-2,1,2,1,1,-1,-2)$ 13 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(6,4)$ $b \geq14$
$10_{ 4}$ 27/4 $C(6,1,3)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(6,1,3)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(6,1,3)$ $b \geq13$
$10_{ 5}$ 33/5 $C(6,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(6,1,1,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(6,1,1,2)$ $b \geq13$
$10_{ 6}$ 37/7 $C(5,3,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,2,1,-3)$ 11 crossings $\quad C(2,2,1,-6)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,3,2)$ $b \geq13$
$10_{ 7}$ 43/8 $C(5,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,2,1,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,2,1,2)$ $b \geq13$
$10_{ 8}$ 29/5 $C(5,1,4)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 37 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(4,1,-2,-2,-1,2)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,1,4)$ $b \geq13$
$10_{ 9}$ 39/7 $C(5,1,1,3)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,1,1,3)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,1,1,3)$ $b \geq13$
$10_{ 10}$ 45/8 $C(5,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,1,2,-3)$ 11 crossings $\quad C(5,1,1,1,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(5,1,1,1,2)$ $b \geq13$
$10_{ 11}$ 43/10 $C(4,3,3)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,2,1,-4)$ 11 crossings $\quad C(3,2,1,-5)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,3,3)$ $b \geq13$
$10_{ 12}$ 47/11 $C(4,3,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,1,-5)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,3,1,2)$ $b \geq13$
$10_{ 13}$ 53/12 $C(4,2,2,2)$ 14
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,1,1,-3,-2)$ 11 crossings $\quad C(2,2,1,1,-5)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,3,2,3)$ $b \geq16$ $\quad D(4,1,1,3,2)$ $b \geq14$ $\quad D(2,2,1,1,5)$ $b \geq14$ $\quad D(4,2,1,1,3)$ $b \geq14$ $\quad D(2,1,1,3,4)$ $b \geq14$ $\quad D(4,2,2,2)$ $b \geq14$
$10_{ 14}$ 57/13 $C(4,2,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,1,-2,-1,-2)$ 11 crossings $\quad C(2,1,1,1,1,-5)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,2,1,1,2)$ $b \geq13$
$10_{ 15}$ 43/9 $C(4,1,3,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,1,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,1,3,2)$ $b \geq13$
$10_{ 16}$ 47/10 $C(4,1,2,3)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(4,1,2,3)$ 10 crossings
$10_{ 17}$ 41/9 $C(4,1,1,4)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,1,4)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,1,1,4)$ $b \geq13$
$10_{ 18}$ 55/12 $C(4,1,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,-2,3)$ 12 crossings $\quad C(4,1,1,1,1,-3)$ 11 crossings $\quad C(3,-2,2,1,4)$ 12 crossings $\quad C(2,1,1,-2,-1,-4)$ 11 crossings $\quad C(4,1,1,2,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,1,1,2,2)$ $b \geq13$
$10_{ 19}$ 51/11 $C(4,1,1,1,3)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,-4)$ 11 crossings $\quad C(5,-2,-1,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(4,1,1,1,3)$ $b \geq13$
$10_{ 20}$ 35/11 $C(3,5,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,3,1,-2,3)$ 12 crossings $\quad C(2,3,1,-2,4)$ 12 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,5,2)$ $b \geq13$
$10_{ 21}$ 45/14 $C(3,4,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,3,1,-2,-2)$ 11 crossings $\quad C(2,1,3,1,-4)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,4,1,2)$ $b \geq13$
$10_{ 22}$ 49/13 $C(3,1,3,3)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,-2,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,3,1,3)$ $b \geq13$
$10_{ 23}$ 59/18 $C(3,3,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,-2,-1,-2)$ 11 crossings $\quad C(3,2,1,-3,3)$ 12 crossings $\quad C(3,-2,-2,-1,4)$ 12 crossings $\quad C(2,1,1,2,1,-4)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,3,1,1,2)$ $b \geq13$
$10_{ 24}$ 55/16 $C(3,2,3,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,2,1,-3)$ 11 crossings $\quad C(2,2,1,-3,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,2,3,2)$ $b \geq14$
$10_{ 25}$ 65/19 $C(3,2,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,1,-3,-1,-2)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,2,2,1,2)$ $b \geq13$
$10_{ 26}$ 61/17 $C(3,1,1,2,3)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,1,1,1,-4)$ 11 crossings $\quad C(3,1,1,-2,-1,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,2,1,1,3)$ $b \geq13$
$10_{ 27}$ 71/21 $C(3,2,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,2,-3)$ 11 crossings $\quad C(3,-2,-1,-2,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,2,1,1,1,2)$ $b \geq13$
$10_{ 28}$ 53/14 $C(3,1,3,1,2)$ 11
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,1,3,1,2)$ 10 crossings
$10_{ 29}$ 63/17 $C(3,1,2,2,2)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,1,2,2,2)$ 10 crossings
$10_{ 30}$ 67/18 $C(3,1,2,1,1,2)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,1,2,1,1,2)$ 10 crossings
$10_{ 31}$ 57/16 $C(3,1,1,3,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,1,2,1,-3)$ 11 crossings $\quad C(3,1,1,1,1,-2,3)$ 12 crossings $\quad C(2,2,1,-2,-1,-3)$ 11 crossings $\quad C(2,1,1,-2,2,1,3)$ 12 crossings $\quad C(3,1,1,3,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,1,1,3,2)$ $b \geq13$
$10_{ 32}$ 69/19 $C(3,1,1,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,-3,-2)$ 11 crossings $\quad C(3,1,1,1,1,1,-3)$ 11 crossings $\quad C(2,1,1,-2,-1,-1,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(3,1,1,1,2,2)$ $b \geq13$
$10_{ 33}$ 65/18 $C(3,1,1,1,1,3)$ 11
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(3,1,1,1,1,3)$ 10 crossings
$10_{ 34}$ 37/13 $C(2,1,5,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,3,1,-2,2,2)$ 12 crossings $\quad C(2,4,1,-2,-2)$ 11 crossings $\quad C(2,1,4,1,-3)$ 11 crossings $\quad C(2,1,3,1,-2,3)$ 12 crossings $\quad C(2,5,1,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(2,5,1,2)$ $b \geq13$
$10_{ 35}$ 49/20 $C(2,2,4,2)$ 14
 Chebyshev parametrisation of degree $(3,14,16)$ 7 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,2,2,1,-2,3)$ 12 crossings $\quad C(2,2,1,-2,3,2)$ 12 crossings $\quad C(2,3,1,-3,-2)$ 11 crossings $\quad C(2,2,3,1,-3)$ 11 crossings $\quad C(2,4,1,1,-3)$ 11 crossings $\quad C(2,1,1,-5,-2)$ 11 crossings $\quad C(2,4,2,2)$ 10 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,2,2,1,2,3)$ $b \geq14$ $\quad D(2,2,1,2,3,2)$ $b \geq14$ $\quad D(2,3,1,3,2)$ $b \geq14$ $\quad D(2,2,3,1,3)$ $b \geq14$ $\quad D(2,4,1,1,3)$ $b \geq14$ $\quad D(2,1,1,5,2)$ $b \geq14$ $\quad D(2,4,2,2)$ $b \geq14$
$10_{ 36}$ 51/20 $C(2,1,1,4,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,3,1,-2,-1,-2)$ 11 crossings $\quad C(2,2,1,-2,2,1,2)$ 12 crossings $\quad C(2,1,1,3,1,-3)$ 11 crossings $\quad C(2,1,1,2,1,-2,3)$ 12 crossings $\quad C(2,4,1,1,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(2,4,1,1,2)$ $b \geq13$
$10_{ 37}$ 53/23 $C(2,3,3,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,3,2,1,-3)$ 11 crossings $\quad C(2,2,1,-4,-2)$ 11 crossings $\quad C(2,3,3,2)$ 10 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(2,3,3,2)$ $b \geq13$
$10_{ 38}$ 59/25 $C(2,2,1,3,2)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,3,1,2,2)$ 10 crossings
$10_{ 39}$ 61/22 $C(2,1,3,2,2)$ 13
 Chebyshev parametrisation of degree $(3,14,16)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,2,1,-2,-2)$ 11 crossings $\quad C(2,1,2,1,-3,-2)$ 11 crossings $\quad C(2,1,3,1,1,-3)$ 11 crossings $\quad C(2,1,1,-4,-1,-2)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(2,2,3,1,2)$ $b \geq13$
$10_{ 40}$ 75/29 $C(2,1,1,2,2,2)$ 13
 Chebyshev parametrisation of degree $(3,13,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,1,1,-2,-1,-2)$ 11 crossings $\quad C(2,1,1,1,1,-3,-2)$ 11 crossings $\quad C(2,1,1,2,1,1,-3)$ 11 crossings Braid condition for simple diagrams with 10 crossings or fewer $\quad D(2,2,2,1,1,2)$ $b \geq13$
$10_{ 41}$ 71/26 $C(2,1,2,1,2,2)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,2,1,2,1,2)$ 10 crossings
$10_{ 42}$ 81/31 $C(2,1,1,1,1,2,2)$ 11
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,2,1,1,1,1,2)$ 10 crossings
$10_{ 43}$ 73/27 $C(2,1,2,2,1,2)$ 11
 Chebyshev parametrisation of degree $(3,13,17)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,1,2,2,1,2)$ 10 crossings
$10_{ 44}$ 79/29 $C(2,1,2,1,1,1,2)$ 11
 Chebyshev parametrisation of degree $(3,14,16)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,1,2,1,1,1,2)$ 10 crossings
$10_{ 45}$ 89/34 $C(2,1,1,1,1,1,1,2)$ 11
 Chebyshev parametrisation of degree $(3,11,19)$ 1 simple diagrams with 10 crossings or fewer, of degree $b=11$ $\quad C(2,1,1,1,1,1,1,2)$ 10 crossings
$11a_{ 13}$ 61/24 $C(2,1,1,5,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,3,1,-2,2,1,2)$ 13 crossings $\quad C(2,1,1,3,1,-2,3)$ 13 crossings $\quad C(2,4,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,4,1,-3)$ 12 crossings $\quad C(2,5,1,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,4,1,2,1,2)$ $b \geq14$ $\quad D(2,1,1,4,1,3)$ $b \geq14$ $\quad D(2,5,1,1,2)$ $b \geq14$
$11a_{ 59}$ 43/15 $C(2,1,6,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,4,1,-2,2,2)$ 13 crossings $\quad C(2,1,4,1,-2,3)$ 13 crossings $\quad C(2,5,1,-2,-2)$ 12 crossings $\quad C(2,1,5,1,-3)$ 12 crossings $\quad C(2,6,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,5,1,2,2)$ $b \geq14$ $\quad D(2,1,5,1,3)$ $b \geq14$ $\quad D(2,6,1,2)$ $b \geq14$
$11a_{ 65}$ 59/24 $C(2,2,5,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,3,1,-2,3,2)$ 13 crossings $\quad C(2,2,3,1,-2,3)$ 13 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,5,2,2)$ $b \geq14$
$11a_{ 75}$ 83/30 $C(2,1,3,3,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,1,-4,-1,-2)$ 12 crossings $\quad C(2,1,3,2,1,-3)$ 12 crossings
$11a_{ 77}$ 131/50 $C(2,1,1,1,1,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,-2,-1,-2,-2)$ 12 crossings $\quad C(2,2,1,1,1,1,1,2)$ 11 crossings $\quad C(2,1,1,1,1,1,1,1,-3)$ 12 crossings $\quad C(2,1,1,-2,-1,-1,-1,-1,-2)$ 12 crossings
$11a_{ 84}$ 101/39 $C(2,1,1,2,3,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,1,-3,-1,-1,-2)$ 12 crossings $\quad C(2,1,1,2,2,1,-3)$ 12 crossings
$11a_{ 85}$ 107/41 $C(2,1,1,1,1,3,2)$ 13
 Chebyshev parametrisation of degree $(3,13,20)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,3,1,2,-2,-2)$ 12 crossings $\quad C(2,2,1,-2,-1,-1,-1,-2)$ 12 crossings $\quad C(2,2,-2,-1,-3,-2)$ 12 crossings $\quad C(2,1,1,1,1,2,1,-3)$ 12 crossings $\quad C(2,3,1,1,1,1,2)$ 11 crossings
$11a_{ 89}$ 119/44 $C(2,1,2,2,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,2,1,1,2)$ 11 crossings $\quad C(2,1,2,1,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,2,2,1,2)$ 11 crossings $\quad C(2,1,1,1,1,-3,-1,-2)$ 12 crossings
$11a_{ 90}$ 87/23 $C(3,1,3,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,3,1,1,2)$ 11 crossings $\quad C(3,1,2,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,3,1,3)$ 11 crossings $\quad C(2,1,1,2,1,-2,-3)$ 12 crossings
$11a_{ 91}$ 129/49 $C(2,1,1,1,2,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,1,1,1,-2,-1,-1,-2)$ 12 crossings $\quad C(3,-2,-1,-2,-1,-1,-2)$ 12 crossings $\quad C(2,1,1,2,1,1,1,2)$ 11 crossings $\quad C(2,1,1,1,1,1,-2,-1,-2)$ 12 crossings
$11a_{ 93}$ 93/34 $C(2,1,2,1,3,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,1,2,1,-3)$ 12 crossings $\quad C(2,3,1,2,1,2)$ 11 crossings $\quad C(2,2,1,-2,-2,-1,-2)$ 12 crossings $\quad C(2,1,2,1,3,2)$ 11 crossings
$11a_{ 95}$ 73/31 $C(2,2,1,4,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,3,1,-2,-2,-2)$ 12 crossings $\quad C(2,2,1,3,1,-3)$ 12 crossings $\quad C(2,4,1,2,2)$ 11 crossings
$11a_{ 96}$ 121/46 $C(2,1,1,1,2,2,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 8 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(3,-2,-1,-2,-1,-1,3)$ 13 crossings $\quad C(2,1,1,-3,-1,-2,3)$ 13 crossings $\quad C(3,-2,-1,-2,-2,-2)$ 12 crossings $\quad C(2,2,1,1,-2,-1,-1,-2)$ 12 crossings $\quad C(2,1,1,1,2,1,1,-3)$ 12 crossings $\quad C(2,1,1,1,1,1,-3,-2)$ 12 crossings $\quad C(2,1,1,-3,-1,-1,-1,-2)$ 12 crossings $\quad C(2,2,2,1,1,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(3,2,1,2,2,2)$ $b \geq14$ $\quad D(2,2,1,1,2,1,1,2)$ $b \geq14$ $\quad D(2,1,1,1,2,1,1,3)$ $b \geq14$ $\quad D(2,1,1,1,1,1,3,2)$ $b \geq14$ $\quad D(2,1,1,3,1,1,1,2)$ $b \geq14$ $\quad D(2,2,2,1,1,1,2)$ $b \geq14$
$11a_{ 98}$ 77/18 $C(4,3,1,1,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,2,1,-3,3)$ 13 crossings $\quad C(3,-2,-2,-1,5)$ 13 crossings $\quad C(4,2,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,2,1,-5)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,3,2,3)$ $b \geq16$ $\quad D(4,2,1,2,1,2)$ $b \geq14$ $\quad D(2,1,1,2,1,5)$ $b \geq14$ $\quad D(4,3,1,1,2)$ $b \geq14$
$11a_{110}$ 97/35 $C(2,1,3,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,2,1,-2,-2)$ 12 crossings $\quad C(2,1,3,2,1,2)$ 11 crossings $\quad C(2,1,2,1,-3,-1,-2)$ 12 crossings
$11a_{111}$ 103/37 $C(2,1,3,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,20)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,-2,-1,-3,-1,-2)$ 12 crossings $\quad C(2,1,2,1,-2,-1,-1,-2)$ 12 crossings $\quad C(2,1,1,1,2,1,-2,-2)$ 12 crossings $\quad C(2,1,3,1,2,-3)$ 12 crossings $\quad C(2,1,3,1,1,1,2)$ 11 crossings
$11a_{117}$ 117/43 $C(2,1,2,1,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,1,1,1,1,-2,-2)$ 12 crossings $\quad C(2,1,1,1,-2,-1,-2,-2)$ 12 crossings $\quad C(2,1,1,-2,-1,-2,-1,-2)$ 12 crossings $\quad C(2,2,1,1,2,1,2)$ 11 crossings $\quad C(2,1,2,1,1,1,1,-3)$ 12 crossings
$11a_{119}$ 77/34 $C(2,3,1,3,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,2,1,-2,-2,-1,3)$ 13 crossings $\quad C(2,3,1,2,1,-3)$ 12 crossings $\quad C(2,2,1,-2,-3,-2)$ 12 crossings $\quad C(2,3,1,3,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,3,1,2,1,3)$ $b \geq14$ $\quad D(2,2,1,2,3,2)$ $b \geq14$ $\quad D(2,3,1,3,2)$ $b \geq14$
$11a_{120}$ 109/45 $C(2,2,2,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,2,1,2,2)$ 11 crossings $\quad C(2,2,1,2,1,1,-3)$ 12 crossings $\quad C(2,1,1,-3,-1,-2,-2)$ 12 crossings
$11a_{121}$ 119/50 $C(2,2,1,1,1,2,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,1,1,-2,-1,-1,-1,-1,3)$ 13 crossings $\quad C(2,3,-2,-1,-2,-2)$ 12 crossings $\quad C(2,2,1,1,1,1,1,-3)$ 12 crossings $\quad C(2,1,1,-2,-1,-1,-2,-2)$ 12 crossings $\quad C(2,2,1,1,1,2,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,3,2,1,2,2)$ $b \geq14$ $\quad D(2,2,1,1,1,1,1,3)$ $b \geq14$ $\quad D(2,1,1,2,1,1,2,2)$ $b \geq14$ $\quad D(2,2,1,1,1,2,2)$ $b \geq14$
$11a_{140}$ 65/17 $C(3,1,4,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,3,1,-2,-2)$ 12 crossings $\quad C(3,1,4,1,2)$ 11 crossings $\quad C(2,1,3,1,-2,-3)$ 12 crossings
$11a_{144}$ 73/17 $C(4,3,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,2,1,-3,-2)$ 12 crossings $\quad C(2,2,2,1,-5)$ 12 crossings
$11a_{145}$ 83/22 $C(3,1,3,2,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(3,1,3,1,1,-3)$ 12 crossings $\quad C(3,1,2,1,-3,-2)$ 12 crossings $\quad C(2,2,2,1,-2,-3)$ 12 crossings $\quad C(2,1,1,-4,-1,-3)$ 12 crossings $\quad C(3,1,3,2,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(3,1,3,1,1,3)$ $b \geq14$ $\quad D(3,1,2,1,3,2)$ $b \geq14$ $\quad D(2,2,2,1,2,3)$ $b \geq14$ $\quad D(2,1,1,4,1,3)$ $b \geq14$ $\quad D(3,1,3,2,2)$ $b \geq14$
$11a_{154}$ 67/29 $C(2,3,4,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,4,2,1,-3)$ 12 crossings $\quad C(2,2,1,-5,-2)$ 12 crossings $\quad C(2,4,3,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,4,2,1,3)$ $b \geq14$ $\quad D(2,2,1,5,2)$ $b \geq14$ $\quad D(2,4,3,2)$ $b \geq14$
$11a_{159}$ 111/41 $C(2,1,2,2,2,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(2,2,1,1,-3,-1,-2)$ 12 crossings $\quad C(2,1,2,2,1,1,-3)$ 12 crossings $\quad C(2,1,2,1,1,-3,-2)$ 12 crossings $\quad C(2,1,1,-3,-2,-1,-2)$ 12 crossings $\quad C(2,2,2,2,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(2,2,1,1,3,1,2)$ $b \geq14$ $\quad D(2,1,2,2,1,1,3)$ $b \geq14$ $\quad D(2,1,2,1,1,3,2)$ $b \geq14$ $\quad D(2,1,1,3,2,1,2)$ $b \geq14$ $\quad D(2,2,2,2,1,2)$ $b \geq14$
$11a_{166}$ 59/14 $C(4,4,1,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,3,1,-2,-2)$ 12 crossings $\quad C(2,1,3,1,-5)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,5,3)$ $b \geq16$ $\quad D(4,3,1,2,2)$ $b \geq14$ $\quad D(2,1,3,1,5)$ $b \geq14$ $\quad D(4,4,1,2)$ $b \geq14$
$11a_{174}$ 79/28 $C(2,1,4,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,3,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,3,1,-2,-2)$ 12 crossings $\quad C(2,1,1,4,1,2)$ 11 crossings
$11a_{175}$ 105/41 $C(2,1,1,3,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,20)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,1,2,1,-2,-1,-2)$ 12 crossings
$11a_{176}$ 111/31 $C(3,1,1,2,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,1,1,1,-2,-1,-2)$ 12 crossings $\quad C(2,1,1,1,1,-2,-1,-3)$ 12 crossings $\quad C(2,1,1,2,1,1,3)$ 11 crossings
$11a_{177}$ 97/21 $C(4,1,1,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,20)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,-2,-1,-2)$ 12 crossings
$11a_{178}$ 123/34 $C(3,1,1,1,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,13,20)$ 6 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,-2,-1,-1,-2)$ 12 crossings $\quad C(3,1,1,1,1,2,-3)$ 12 crossings $\quad C(3,1,1,1,1,1,1,2)$ 11 crossings $\quad C(3,-2,-1,-1,-1,-1,-3)$ 12 crossings $\quad C(2,1,1,2,-2,-1,-3)$ 12 crossings $\quad C(2,1,1,1,1,1,1,3)$ 11 crossings
$11a_{179}$ 57/20 $C(2,1,5,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,4,1,-2,-2)$ 12 crossings $\quad C(2,1,5,1,2)$ 11 crossings
$11a_{180}$ 89/25 $C(3,1,1,3,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,1,-2,-1,-3)$ 12 crossings $\quad C(3,1,1,2,1,-2,-2)$ 12 crossings $\quad C(3,1,1,3,1,2)$ 11 crossings
$11a_{182}$ 73/13 $C(5,1,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,1,2,-2,-2)$ 12 crossings $\quad C(5,1,1,1,1,2)$ 11 crossings
$11a_{183}$ 115/34 $C(3,2,1,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,1,1,1,2)$ 11 crossings
$11a_{184}$ 87/19 $C(4,1,1,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,1,1,1,-2,-2)$ 12 crossings $\quad C(2,1,1,1,-2,-1,-4)$ 12 crossings $\quad C(4,1,1,2,1,2)$ 11 crossings
$11a_{185}$ 109/30 $C(3,1,1,1,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,-3,-1,-2)$ 12 crossings $\quad C(3,1,1,1,2,1,2)$ 11 crossings $\quad C(2,1,3,-2,-1,-3)$ 12 crossings $\quad C(2,1,2,1,1,1,3)$ 11 crossings
$11a_{186}$ 95/39 $C(2,2,3,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,2,2,1,-3,-2)$ 12 crossings
$11a_{188}$ 67/14 $C(4,1,3,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,3,1,2)$ 11 crossings
$11a_{190}$ 85/18 $C(4,1,2,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,2,-3)$ 12 crossings $\quad C(4,1,2,1,1,2)$ 11 crossings $\quad C(3,-2,-2,-1,-4)$ 12 crossings $\quad C(2,1,1,2,1,4)$ 11 crossings
$11a_{191}$ 83/19 $C(4,2,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 8 non simple diagrams with 12 crossings or fewer, of degree $b=13$. For example: $\quad C(3,1,-3,-1,-2,-2)$ 12 crossings
$11a_{192}$ 97/26 $C(3,1,2,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,1,2,2)$ 11 crossings $\quad C(3,1,2,1,1,1,-3)$ 12 crossings $\quad C(2,2,1,2,1,3)$ 11 crossings $\quad C(2,1,1,-2,-2,-1,-3)$ 12 crossings
$11a_{193}$ 95/29 $C(3,3,1,1,1,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,3,1,2,-3)$ 12 crossings $\quad C(3,2,1,-2,-1,-1,-2)$ 12 crossings $\quad C(3,-2,-1,-3,-3)$ 12 crossings $\quad C(2,1,1,1,2,1,-4)$ 12 crossings
$11a_{195}$ 53/8 $C(6,1,1,1,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(6,1,2,-3)$ 12 crossings $\quad C(6,1,1,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(6,1,2,3)$ $b \geq14$ $\quad D(6,1,1,1,2)$ $b \geq14$
$11a_{203}$ 63/11 $C(5,1,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(2,1,2,1,5)$ 11 crossings
$11a_{204}$ 101/30 $C(3,2,1,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,3,-3)$ 12 crossings $\quad C(3,2,1,2,1,2)$ 11 crossings $\quad C(3,-3,-1,-2,-3)$ 12 crossings $\quad C(2,1,2,1,2,3)$ 11 crossings
$11a_{205}$ 91/25 $C(3,1,1,1,3,2)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,-2,-1,-3,-2)$ 12 crossings $\quad C(3,1,1,1,2,1,-3)$ 12 crossings $\quad C(2,3,1,2,-4)$ 12 crossings $\quad C(2,2,1,-2,-1,-1,-3)$ 12 crossings
$11a_{206}$ 47/7 $C(6,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(6,1,2,2)$ 11 crossings
$11a_{207}$ 85/26 $C(3,3,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,3,1,2,2)$ 11 crossings
$11a_{208}$ 105/31 $C(3,2,1,1,2,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,1,1,1,-3)$ 12 crossings $\quad C(3,1,1,-2,-1,-2,-2)$ 12 crossings $\quad C(2,2,1,1,1,1,-4)$ 12 crossings $\quad C(2,1,1,-2,-1,-2,-3)$ 12 crossings
$11a_{210}$ 73/16 $C(4,1,1,3,2)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,1,1,1,1,-2,3)$ 13 crossings $\quad C(2,1,1,-2,2,1,4)$ 13 crossings $\quad C(4,1,1,2,1,-3)$ 12 crossings $\quad C(2,2,1,-2,-1,-4)$ 12 crossings $\quad C(4,1,1,3,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,1,1,2,1,3)$ $b \geq14$ $\quad D(2,2,1,2,1,4)$ $b \geq14$ $\quad D(4,1,1,3,2)$ $b \geq14$
$11a_{211}$ 67/12 $C(5,1,1,2,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 4 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(5,1,2,-2,3)$ 13 crossings $\quad C(5,1,1,1,1,-3)$ 12 crossings $\quad C(2,1,1,-2,-1,-5)$ 12 crossings $\quad C(5,1,1,2,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(5,1,1,1,1,3)$ $b \geq14$ $\quad D(2,1,1,2,1,5)$ $b \geq14$ $\quad D(5,1,1,2,2)$ $b \geq14$
$11a_{220}$ 85/23 $C(3,1,2,3,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,2,1,-3)$ 12 crossings $\quad C(2,2,1,-3,-1,-3)$ 12 crossings $\quad C(3,1,2,3,2)$ 11 crossings
$11a_{224}$ 89/27 $C(3,3,2,1,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,-3,-1,-2)$ 12 crossings $\quad C(2,1,2,2,1,-4)$ 12 crossings
$11a_{225}$ 53/11 $C(4,1,4,2)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,3,1,-3)$ 12 crossings $\quad C(2,3,1,-2,-4)$ 12 crossings
$11a_{226}$ 71/20 $C(3,1,1,4,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 5 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(3,1,1,2,1,-2,3)$ 13 crossings $\quad C(2,2,1,-2,2,1,3)$ 13 crossings $\quad C(3,1,1,3,1,-3)$ 12 crossings $\quad C(2,3,1,-2,-1,-3)$ 12 crossings $\quad C(3,1,1,4,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(3,1,1,3,1,3)$ $b \geq14$ $\quad D(2,3,1,2,1,3)$ $b \geq14$ $\quad D(3,1,1,4,2)$ $b \geq14$
$11a_{229}$ 71/16 $C(4,2,3,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,2,2,1,-3)$ 12 crossings $\quad C(2,2,1,-3,-4)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,2,2,1,3)$ $b \geq14$ $\quad D(2,2,1,3,4)$ $b \geq14$ $\quad D(4,2,3,2)$ $b \geq16$
$11a_{230}$ 51/8 $C(6,2,1,2)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(6,2,1,2)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(6,3,3)$ $b \geq16$ $\quad D(6,2,1,2)$ $b \geq14$
$11a_{234}$ 37/5 $C(7,2,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 249 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,2,-1,-1,1,1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(7,1,1,3)$ $b \geq16$ $\quad D(2,1,1,8)$ $b \geq16$ $\quad D(7,2,2)$ $b \geq16$
$11a_{235}$ 71/22 $C(3,4,2,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(3,2,1,-2,3,2)$ 13 crossings $\quad C(2,2,2,1,-2,4)$ 13 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(3,5,2,3)$ $b \geq16$ $\quad D(3,2,1,2,3,2)$ $b \geq16$ $\quad D(2,2,2,1,2,4)$ $b \geq16$ $\quad D(3,3,1,3,2)$ $b \geq16$ $\quad D(2,2,3,1,4)$ $b \geq16$ $\quad D(3,4,1,1,3)$ $b \geq16$ $\quad D(2,1,1,5,3)$ $b \geq16$ $\quad D(3,4,2,2)$ $b \geq16$
$11a_{236}$ 99/29 $C(3,2,2,2,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(3,1,1,-3,-1,-1,3)$ 13 crossings $\quad C(2,1,1,-3,-1,-1,4)$ 13 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(3,1,1,3,1,1,3)$ $b \geq16$ $\quad D(2,1,1,3,1,1,4)$ $b \geq16$ $\quad D(3,2,1,1,3,2)$ $b \geq16$ $\quad D(3,1,1,3,2,2)$ $b \geq16$ $\quad D(2,2,2,1,1,4)$ $b \geq16$ $\quad D(2,2,1,1,3,3)$ $b \geq16$ $\quad D(3,2,2,1,1,3)$ $b \geq16$ $\quad D(2,1,1,3,2,3)$ $b \geq16$ $\quad D(3,2,2,2,2)$ $b \geq16$ $\quad D(4,2,3,2,2)$ $b \geq16$ $\quad D(3,3,2,3,2)$ $b \geq16$ $\quad D(2,2,3,2,4)$ $b \geq16$ $\quad D(3,2,3,2,3)$ $b \geq16$ $\quad D(3,2,3,2,3)$ $b \geq16$
$11a_{238}$ 65/12 $C(5,2,2,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(5,1,1,-3,-2)$ 12 crossings $\quad C(2,2,1,1,-6)$ 12 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(5,3,2,3)$ $b \geq16$ $\quad D(5,1,1,3,2)$ $b \geq16$ $\quad D(2,2,1,1,6)$ $b \geq16$ $\quad D(5,2,1,1,3)$ $b \geq16$ $\quad D(2,1,1,3,5)$ $b \geq16$ $\quad D(5,2,2,2)$ $b \geq16$
$11a_{242}$ 47/9 $C(5,4,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(5,2,1,-2,3)$ 13 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(5,2,1,2,3)$ $b \geq16$ $\quad D(5,3,1,3)$ $b \geq16$ $\quad D(2,3,1,6)$ $b \geq16$ $\quad D(2,2,1,2,6)$ $b \geq16$ $\quad D(5,4,2)$ $b \geq16$
$11a_{243}$ 69/20 $C(3,2,4,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(3,1,1,-5,-2)$ 12 crossings $\quad C(2,4,1,1,-4)$ 12 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(3,1,1,5,2)$ $b \geq16$ $\quad D(2,4,1,1,4)$ $b \geq16$ $\quad D(3,2,2,1,2,3)$ $b \geq16$ $\quad D(2,2,1,2,3,3)$ $b \geq16$ $\quad D(3,2,3,1,3)$ $b \geq16$ $\quad D(2,3,1,3,3)$ $b \geq16$ $\quad D(3,2,4,2)$ $b \geq16$
$11a_{246}$ 41/13 $C(3,6,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(3,3,1,-2,2,-3)$ 14 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(3,4,1,2,3)$ $b \geq16$ $\quad D(2,4,1,2,4)$ $b \geq16$ $\quad D(3,5,1,3)$ $b \geq16$ $\quad D(2,5,1,4)$ $b \geq16$ $\quad D(3,6,2)$ $b \geq16$
$11a_{247}$ 19/2 $C(9,2)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 324 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(3,1,-2,2,-1,-1,-1,1,1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(9,2)$ $b \geq16$
$11a_{306}$ 105/29 $C(3,1,1,1,1,1,3)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,-2,-1,-3)$ 12 crossings $\quad C(3,1,1,1,1,1,3)$ 11 crossings
$11a_{307}$ 83/18 $C(4,1,1,1,1,3)$ 13
 Chebyshev parametrisation of degree $(3,14,19)$ 4 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,-2,-3)$ 12 crossings $\quad C(4,1,1,1,1,3)$ 11 crossings $\quad C(3,2,-2,-1,-4)$ 12 crossings $\quad C(3,1,1,1,1,4)$ 11 crossings
$11a_{308}$ 71/15 $C(4,1,2,1,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,1,2,1,3)$ 11 crossings
$11a_{309}$ 93/25 $C(3,1,2,1,1,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 3 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,1,2,1,1,3)$ 11 crossings $\quad C(3,1,1,1,1,-2,-3)$ 12 crossings $\quad C(3,1,1,1,-2,-1,-3)$ 12 crossings
$11a_{310}$ 61/13 $C(4,1,2,4)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(4,2,1,4)$ 11 crossings
$11a_{311}$ 79/18 $C(4,2,1,1,3)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(4,1,1,-2,-1,-3)$ 12 crossings $\quad C(3,1,1,1,1,-5)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(4,3,2,3)$ $b \geq16$ $\quad D(4,1,1,2,1,3)$ $b \geq14$ $\quad D(3,1,1,1,1,5)$ $b \geq14$ $\quad D(4,2,1,1,3)$ $b \geq14$
$11a_{333}$ 65/14 $C(4,1,1,1,4)$ 14
 Chebyshev parametrisation of degree $(3,14,19)$ 1 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(5,-2,-1,-4)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(5,2,1,4)$ $b \geq14$ $\quad D(4,1,1,1,4)$ $b \geq14$
$11a_{334}$ 49/9 $C(5,2,4)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 246 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,-1,1,1,-2,1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(5,1,1,5)$ $b \geq16$ $\quad D(4,1,1,6)$ $b \geq16$ $\quad D(5,2,4)$ $b \geq16$
$11a_{335}$ 75/17 $C(4,2,2,3)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 210 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(3,1,-1,-1,1,2,-1,-1,-1,-1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(5,2,3,3)$ $b \geq17$ $\quad D(4,3,2,4)$ $b \geq17$ $\quad D(3,3,2,5)$ $b \geq17$ $\quad D(4,2,1,1,4)$ $b \geq16$ $\quad D(4,1,1,3,3)$ $b \geq16$ $\quad D(3,2,1,1,5)$ $b \geq16$ $\quad D(3,1,1,3,4)$ $b \geq16$ $\quad D(4,2,2,3)$ $b \geq16$
$11a_{336}$ 59/11 $C(5,2,1,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,2,1,3)$ 11 crossings
$11a_{337}$ 89/24 $C(3,1,2,2,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,2,1,3)$ 11 crossings
$11a_{339}$ 55/13 $C(4,4,3)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 15 crossings or fewer, of degree $b=16$ $\quad C(4,2,1,-2,4)$ 13 crossings $\quad C(3,2,1,-2,5)$ 13 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(4,2,1,2,4)$ $b \geq16$ $\quad D(3,2,1,2,5)$ $b \geq16$ $\quad D(4,3,1,4)$ $b \geq16$ $\quad D(3,3,1,5)$ $b \geq16$ $\quad D(4,4,3)$ $b \geq16$
$11a_{341}$ 61/16 $C(3,1,4,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,3,1,-2,-3)$ 12 crossings $\quad C(3,1,3,1,-4)$ 12 crossings
$11a_{342}$ 29/4 $C(7,4)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 269 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(3,1,-1,-1,1,3,1,-2,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(7,4)$ $b \geq16$
$11a_{343}$ 31/4 $C(7,1,3)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(7,1,3)$ 11 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(7,1,3)$ $b \geq14$
$11a_{355}$ 45/7 $C(6,2,3)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 248 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,2,1,-1,-1,1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(6,1,1,4)$ $b \geq16$ $\quad D(3,1,1,7)$ $b \geq16$ $\quad D(6,2,3)$ $b \geq16$
$11a_{356}$ 79/23 $C(3,2,3,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,2,1,-4)$ 12 crossings $\quad C(3,2,1,-3,-3)$ 12 crossings
$11a_{357}$ 91/27 $C(3,2,1,2,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(3,2,1,2,3)$ 11 crossings
$11a_{358}$ 31/5 $C(6,5)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 256 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,3,1,-2,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(6,5)$ $b \geq16$
$11a_{359}$ 53/10 $C(5,3,3)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 2 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(5,2,1,-4)$ 12 crossings $\quad C(3,2,1,-6)$ 12 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(5,3,3)$ $b \geq14$ $\quad D(5,2,1,4)$ $b \geq14$ $\quad D(3,2,1,6)$ $b \geq14$
$11a_{360}$ 57/10 $C(5,1,2,3)$ 13
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 12 crossings or fewer, of degree $b=13$ $\quad C(5,1,2,3)$ 11 crossings
$11a_{363}$ 35/6 $C(5,1,5)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 24 non simple diagrams with 13 crossings or fewer, of degree $b=14$. For example: $\quad C(4,1,-2,-1,-1,1,3)$ 13 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(5,1,5)$ $b \geq14$
$11a_{364}$ 25/3 $C(8,3)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 272 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,2,-1,-1,-1,-1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(8,3)$ $b \geq16$
$11a_{365}$ 51/16 $C(3,5,3)$ 14
 Chebyshev parametrisation of degree $(3,16,17)$ 1 simple diagrams with 13 crossings or fewer, of degree $b=14$ $\quad C(3,3,1,-2,4)$ 13 crossings Braid condition for simple diagrams with 12 crossings or fewer $\quad D(3,4,1,4)$ $b \geq16$ $\quad D(3,5,3)$ $b \geq14$
$11a_{367}$ 11 $C(11)$ 16
 Chebyshev parametrisation of degree $(3,16,17)$ 202 non simple diagrams with 15 crossings or fewer, of degree $b=16$. For example: $\quad C(4,1,-2,2,-1,-1,-1,1,2)$ 15 crossings Braid condition for simple diagrams with 13 crossings or fewer $\quad D(11)$ $b \geq16$