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Let $[K:\mathbb{Q}]=p$ be a prime number and let $E/K$ be an elliptic curvewith $j(E) \in \mathbb{Q}$. 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.

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