1) In the published version the expression for v^2 in equation (6) should be replaced by 

v^2=-2(j+1)(5j^2-2j+13) 

[This is correct in the accompanying computer file on the arxiv however---see Remark 4---as is the solution defined on the smooth quartic (7), modulo 2) below]

---Thanks to O. Lisovyy and Y. Tykhyy for finding this.

2) "s" should replaced by "j" in the displayed equation after (7), and in the paragraph just before (7); "(Eliminating j from (6) yields a singular plane sextic...)".  

3) In the fourth paragraph of the introduction add "Aut" before the finite set {1,2,...,deg(t)}