On the torsion of rational elliptic curves over quartic fields

González-Jiménez, Enrique; Lozano-Robledo, Álvaro

doi:10.1090/mcom/3235

On the torsion of rational elliptic curves over quartic fields
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by Enrique González-Jiménez and Álvaro Lozano-Robledo;

Math. Comp. 87 (2018), 1457-1478

DOI: https://doi.org/10.1090/mcom/3235

Published electronically: August 3, 2017

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Abstract:

Let $E$ be an elliptic curve defined over $\mathbb {Q}$ and let $G = E(\mathbb {Q})_{\mathrm {tors}}$ be the associated torsion subgroup. We study, for a given $G$, which possible groups $G \subseteq H$ could appear such that $H=E(K)_{\mathrm {tors}}$, for $[K:\mathbb {Q}]=4$ and $H$ is one of the possible torsion structures that occur infinitely often as torsion structures of elliptic curves defined over quartic number fields.

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