Isogenies of elliptic curves over function fields
Number Theory
2021-02-04 v2 Algebraic Geometry
Abstract
We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the -invariant in an isogeny class. The second one is an "isogeny estimate", providing an explicit bound on the degree of a minimal isogeny between two isogenous elliptic curves. We also give several corollaries of these two results.
Cite
@article{arxiv.2005.02920,
title = {Isogenies of elliptic curves over function fields},
author = {Richard Griffon and Fabien Pazuki},
journal= {arXiv preprint arXiv:2005.02920},
year = {2021}
}
Comments
24 pages. Minor corrections and changes following referee reports. Accepted at IMRN