For Mordell curves over cubic fields the torsion subgroup is one of five cyclic groups; over sextic fields the rational-coefficient list gains five product groups, and arbitrary sextic coefficients add Z/19, Z/7 and Z/14 + Z/2.
On the torsion of rational elliptic curves over sextic fields
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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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Torsion groups of Mordell curves over cubic and sextic fields
For Mordell curves over cubic fields the torsion subgroup is one of five cyclic groups; over sextic fields the rational-coefficient list gains five product groups, and arbitrary sextic coefficients add Z/19, Z/7 and Z/14 + Z/2.