Generalizing Vélu’s formulas and some applications

Vélu’s formulas allow to compute an isogeny between elliptic curves from the coordinates of the points in the kernel. In this talk, I describe an algorithm using theta functions to compute an isogeny from its kernel on any abelian variety. I will give specific timings of a genus 2 implementation, and describe some applications.

This is a joint work with Romain Cosset and David Lubicz.