Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method
Number Theory
2013-05-30 v2
Abstract
Let ell be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ell. If S is a maximal Weil-isotropic subgroup of Jac(H)[ell], then Jac(H)/S is isomorphic to the Jacobian of some (possibly reducible) curve X. We investigate the Dolgachev--Lehavi method for constructing the curve X, simplifying their approach and making it more explicit. The result, at least for ell=3, is an efficient and easily programmable algorithm suitable for number-theoretic calculations.
Cite
@article{arxiv.1110.2963,
title = {Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method},
author = {Benjamin Smith},
journal= {arXiv preprint arXiv:1110.2963},
year = {2013}
}