paper

Isogenies of elliptic curves over function fields

arXiv:2005.02920

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.

24 pages. Minor corrections and changes following referee reports. Accepted at IMRN

Isogenies of elliptic curves over function fields · wovepaper