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

Gužvić, Tomislav

doi:10.1090/proc/15500

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

Proc. Amer. Math. Soc. 149 (2021), 3261-3275

DOI: https://doi.org/10.1090/proc/15500

Published electronically: May 18, 2021

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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 its quadratic twists.

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