Torsion of elliptic curves with rational $j$-invariant defined over number fields of prime degree

Abstract

Let $[K:\mathbb{Q}]=p$ be a prime number and let $E/K$ be an elliptic curve with $j(E)\in \mathbb{Q}$. We determine the all possibilities for $E(K{)}_{tors}$. We obtain these results by studying Galois representations of $E$ and of it's quadratic twists.

MAGMA code used in this paper can be found on the auther's webpage ( https://web.math.pmf.unizg.hr/~tguzvic/ )

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