Torsion groups of Mordell curves over number fields of higher degree

Abstract

Mordell curves over a number field $K$ are elliptic curves of the form $y^2=x^3+c$, where $c\in K\setminus \{0\}$. Let $p\ge 5$ be a prime number, $K$ a number field such that $[K:\mathbb{Q}]\in \{2p,3p\}$ and let $E$ be a Mordell curve defined over $K$. We classify all the possible torsion subgroups $E(K{)}_{\text{tors}}$ for all Mordell curves $E$ defined over $\mathbb{Q}$ when $[K:\mathbb{Q}]\in \{2p,3p\}$.

11 pages