change of variable from hyperellictic curve to Weierstrass form

asked 2017-02-15 21:31:48 -0600

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I have the hyperelliptic curve v^2 = p^4-2*p^3+5*p^2+8*p+4 which I wish to change it to an elliptic curve in Weierstrass form where it returns the change of variable v=[u,r,s,t]. I got the following from Maple. Was wondering if I could get a similar thing using Sage.

-(y^2) = x^3-(121/3)*x-(1690/27)

x = -(1/3)*(5*p^2+24*p-12*v+24)/p^2    
y = (-4*p^3 + 20*p^2 + (-8*v + 48)*p + (-16*v + 32))/p^3   

p = (-72*x-264+36*y)/(9*x^2+30*x-119) 
v = (-162*x^4+540*x^3-648*x^2*y+13176*x^2-4752*x*y+62340*x-16488*y+153994)/(81*x^4+540*x^3-1242*x^2-7140*x+14161)
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