I have the hyperelliptic curve y^2=x^4+81473/1024*x^2-1. How do I convert this curve to an elliptic curve in a short weierstrass form?

asked 2020-03-21 07:52:10 -0500

Gamzeee gravatar image

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.

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The point $(1,i,0)$ does not lie on the curve, though $(i,1,0)$ does; but the equation in $x,y,z$ is not homogeneous, and if you homogenize w.r.t. $z$ then the point is no longer on the curve. So are you sure about this data?

rburing gravatar imagerburing ( 2020-03-22 14:27:41 -0500 )edit