Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $K$ be a number field of degree four that is Galois over $\mathbb{Q}$. The goal of this article is to classify the different isomorphism types of $E(K)_{\text{tors}}$.
On the torsion of rational elliptic curves over sextic fields
Torsion of Rational Elliptic Curves over the $\mathbb{Z}_p$-Extensions of Quadratic Fields
Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of $\mathbb{Q}$
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