Revision history [back]

Let $E: y^2 = x^3 + x$ be an elliptic curve over a field $K$ of characteristic $p\neq 2, 3$. It is well known that the map $[i]$ defined as below is an endomorphism on $E$ and $[i]^2=-1$

$[i]:(x,y)\mapsto(-x, iy)$

I'm wondering how to construct this isogeny on sage when $K$ is a finite field. If I can define an isogeny by giving its rational maps then I can simply compute a fourth root of unity $i$ in $K$ and let $\phi = (-x, iy)$, but as I know of sage doesn't let you define an isogeny from rational maps?