Statistics for 3-isogeny induced Selmer groups of elliptic curves

2024/06/05 by Shingavekar, Pratiksha
#11G05 #11R32 #11R45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.03066

Abstract

Given a sixth power free integer a, let E_a be the elliptic curve defined by y²=x³+a. We prove explicit results for the lower density of sixth power free integers a for which the 3-isogeny induced Selmer group of E_a over ℚ(μ₃) has dimension ≤ 1. The results are proven by refining the strategy of Davenport--Heilbronn, by relating the statistics for integral binary cubic forms to the statistics for 3-isogeny induced Selmer groups.

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