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arXiv:1912.07159 [math.NT]AbstractReferencesReviewsResources

Torsion of rational elliptic curves over different types of cubic fields

Daeyeol Jeon, Andreas Schweizer

Published 2019-12-16Version 1

Let $E$ be an elliptic curve defined over $\Q$, and let $G$ be the torsion group $E(K)_{tors}$ for some cubic field $K$ which does not occur over $\Q$. In this paper, we determine over which types of cubic number fields (cyclic cubic, non-Galois totally real cubic, complex cubic or pure cubic) $G$ can occur, and if so, whether it can occur infinitely often or not. Moreover, if it occurs, we provide elliptic curves $E/\Q$ together with cubic fields $K$ so that $G= E(K)_{tors}$.

Comments: 15 pages
Categories: math.NT
Subjects: 11G05, 11G18
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