Average Cyclicity for Elliptic Curves in Torsion Families

2021/01/15 by Luke Fredericks, Fredericks, Luke
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2101.06202

Abstract

We prove asymptotic formulas for cyclicity of reductions of elliptic curves over the rationals in a family of curves having specified torsion. These results agree with established conditional results and with average results taken over larger families. As a key tool, we prove an analogue of a result of Vlăduţ that estimates the number of elliptic curves over a finite field with a specified torsion point and cyclic group structure.

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