English

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 jj-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.

Keywords

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

R2 v1 2026-06-23T15:21:29.695Z