Computing isogenies from modular equations in genus two
Algebraic Geometry
2024-12-24 v3 Number Theory
Abstract
We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2.
Cite
@article{arxiv.2001.04137,
title = {Computing isogenies from modular equations in genus two},
author = {Jean Kieffer and Aurel Page and Damien Robert},
journal= {arXiv preprint arXiv:2001.04137},
year = {2024}
}