On the torsion of rational elliptic curves over sextic fields

Daniels, Harris; González-Jiménez, Enrique

doi:10.1090/mcom/3440

On the torsion of rational elliptic curves over sextic fields
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Math. Comp. 89 (2020), 411-435 Request permission

Abstract:

Given an elliptic curve $E/\mathbb {Q}$ with torsion subgroup $G = E(\mathbb {Q})_\textrm {{tors}}$ 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 $H = E(K)_\textrm {{tors}}$ 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 over sextic fields.

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