Torsion of elliptic curves with rational $j$-invariant over quartic number fields

Abstract

Let $E$ be an elliptic curve, defined over a quartic extension $K$ of $\mathbb{Q}$, with $j(E) \in \mathbb{Q}$. In this paper, we classify the possible group structure of the torsion subgroup $E(K)_{\text{tors}}$.