Average Cyclicity for Elliptic Curves in Torsion Families

Luke Fredericks

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arXiv · 2101.06202

Average Cyclicity for Elliptic Curves in Torsion Families

Luke Fredericks

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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 Vl\u{a}du\c{t} that estimates the number of elliptic curves over a finite field with a specified torsion point and cyclic group structure.

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Luke Fredericks. 2021-01-15. Average Cyclicity for Elliptic Curves in Torsion Families. https://arxiv.org/abs/2101.06202

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