Application: Weierstrass form
C : y3
+ 2x3
y − x7
= 0 has genus g = 2, so it is hyperelliptic
⇝ has model H : w2
= F(u).
Ω1
(H) = ⟨du
w
, u du
w
⟩ ⇝ our basis of Ω1
(C) is (au+b) du
w
, (cu+d) du
w
⇝ Their quotient is au+b
cu+d
.
C[7] \\ yx/(2x^3+3y^2) dx, x^3/(2x^3+3y^2) dx
u = C[7][1][1]/C[7][1][2]
w = x
factor(MorImg(y^3+2*x^3*y-x^7,u,w))
poldisc(%[2,1],y)
DivPrint(FnDiv(C,u-2/3))
Nicolas Mascot Algebraic curves