Isogenies of elliptic curves over function fields

2020/05/06 by Griffon, Richard, Pazuki, Fabien · 2 citations
#11G05 #11G50 #11R58 #14G17 #14G25 #14G40 #14H52 #14K02 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/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 j-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.

Cited by

• A parallelogram height inequality for Drinfeld modules
• Effective surjectivity of Galois representations of products of elliptic curves over function fields

Related

• Isogenies over quadratic fields of elliptic curves with rational j-invariant
• Local invariants of isogenous elliptic curves
• Families of isogenous elliptic curves ordered by height
• Fast computation of elliptic curve isogenies in characteristic two
• Integrality properties in the Moduli Space of Elliptic Curves: Isogeny Case