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Mathematics of Computation

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On the torsion of rational elliptic curves over quartic fields


Authors: Enrique González-Jiménez and Álvaro Lozano-Robledo
Journal: Math. Comp. 87 (2018), 1457-1478
MSC (2010): Primary 11G05; Secondary 14H52, 14G05, 11R16
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})_{\textup {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)_{\textup {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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Additional Information

Enrique González-Jiménez
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
Email: enrique.gonzalez.jimenez@uam.es

Álvaro Lozano-Robledo
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: alvaro.lozano-robledo@uconn.edu

DOI: https://doi.org/10.1090/mcom/3235
Keywords: Elliptic curves, torsion subgroup, rationals, quartic fields.
Received by editor(s): April 4, 2016
Received by editor(s) in revised form: November 1, 2016
Published electronically: August 3, 2017
Additional Notes: The first author was partially supported by the grant MTM2015–68524–P
Article copyright: © Copyright 2017 American Mathematical Society

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