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arXiv · 2406.03066

Statistics for 3-isogeny induced Selmer groups of elliptic curves

Pratiksha Shingavekar
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Abstract

Given a sixth power free integer $a$, let $E_a$ be the elliptic curve defined by $y^2=x^3+a$. 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 $\mathbb{Q}(μ_3)$ has dimension $\leq 1$. 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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Pratiksha Shingavekar. 2024-06-05. Statistics for 3-isogeny induced Selmer groups of elliptic curves. https://arxiv.org/abs/2406.03066

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