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arXiv · 1808.02887

On the torsion of rational elliptic curves over sextic fields

Harris B. Daniels·Enrique González-Jiménez
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Abstract

Given an elliptic curve $E/\mathbb{Q}$ with torsion subgroup $G = E(\mathbb{Q})_{\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\mathbb{Q}$. We also determine which groups $H = E(K)_{\rm tors}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields.

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Harris B. Daniels, Enrique González-Jiménez. 2018-08-08. On the torsion of rational elliptic curves over sextic fields. https://doi.org/10.1090/mcom/3440

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