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arXiv · 2502.01351

Constructing families of 3-Selmer companions

Harry Spencer
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Abstract

Mazur and Rubin introduced the notion of $n$-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by $t\in\ZZ$, such that the two curves in a pair corresponding to a given $t$ are non-isogenous $3$-Selmer companions, possibly provided that $t$ satisfies a simple congruence condition.

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Harry Spencer. 2025-02-03. Constructing families of 3-Selmer companions. https://arxiv.org/abs/2502.01351

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