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 $p \geq 5$ 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 $[K: \mathbb{Q}] \in {2p, 3p }$.