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I have the hyperelliptic curve y^2=x^4+81473/1024x^2-1. How do I convert this curve to an elliptic curve in a short weierstrass form? Also, how can I convert the point (x,y,z)=(1,i,0) on the y^2=x^4+81473/1024x^2z^2-1z^4 curve to the point on the elliptic curve? Thanks.

I have the hyperelliptic curve y^2=x^4+81473/1024$y^2=x^4+81473/1024x^2-1. x^2-1$. How do I convert this curve to an elliptic curve in a short weierstrass form? Also, how can I convert the point (x,y,z)=(1,i,0) $(x,y,z)=(1,i,0)$ on the y^2=x^4+81473/1024$y^2=x^4+81473/1024x^2z^2-1z^4 z^4$ curve to the point on the elliptic curve? Thanks.

I have the hyperelliptic curve $y^2=x^4+81473/1024x^2-1$. $y^2=x^4+81473/1024x^2-1$. How do I convert this curve to an elliptic curve in a short weierstrass Weierstrass form? Also, how can I convert the point $(x,y,z)=(1,i,0)$ on the $y^2=x^4+81473/1024x^2z^2-1$y^2=x^4+81473/1024x^2z^2- z^4$ curve to the point on the elliptic curve? Thanks.