Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

Compose Affine/Projective Curve morphism with Elliptic Curve isogeny

When I tried to do this, I got TypeError: ... must be a map to multiply it by Isogeny ...

And when I tried to dehomogenize projective curve morphism in x,y,z by z-coordinate, the remaining variables become x0 and x1. Can I keep them as x and y instead?

Compose Affine/Projective Curve morphism with Elliptic Curve isogeny

When I tried to do this, I got TypeError: ... must be a map to multiply it by Isogeny ...

And when I tried to dehomogenize projective curve morphism in x,y,z by z-coordinate, the remaining variables become x0 and x1. Can I keep them as x and y instead?

EDIT: Example code:

k = GF(23)
x,y,z = k['x,y,z'].gens()
d = k(2)
C = Curve([x^3+y^3+z^3-3*d*x*y*z]) #domain curve
a = d+2
b = 4*(d^2+d+1)/3
E = EllipticCurve(y^2-x^3-(a*x+b)^2) #codomain curve
m = b
n = 4*(d^3 -1)/3
X = m*(x+y+z)
Y = n*(z-y)
Z = -z-y-d*x   
f = C.Hom(E)([X,Y,Z]) #map from C to E
Q = E(2,9,1) #a point on E
g = E.isogeny(Q) #isogeny
g*f #TypeError here