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On the torsion of rational elliptic curves over sextic fields


Authors: Harris B. Daniels and Enrique González-Jiménez
Journal: Math. Comp. 89 (2020), 411-435
MSC (2010): Primary 11G05; Secondary 14H52, 14G05
DOI: https://doi.org/10.1090/mcom/3440
Published electronically: April 30, 2019
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Abstract:

Given an elliptic curve $ E/\mathbb{Q}$ with torsion subgroup $ G = E(\mathbb{Q})_{\rm {tors}}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $ E$ base-extended to $ K$, a degree 6 extension of $ \mathbb{Q}$. We also determine which groups $ H = E(K)_{\rm {tors}}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth over sextic fields.


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Additional Information

Harris B. Daniels
Affiliation: Department of Mathematics and Statistics, Amherst College, Massachusetts 01002
Email: hdaniels@amherst.edu

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

DOI: https://doi.org/10.1090/mcom/3440
Keywords: Elliptic curves, torsion subgroup, rationals, sextic fields.
Received by editor(s): October 8, 2018
Received by editor(s) in revised form: February 27, 2019
Published electronically: April 30, 2019
Additional Notes: The first author was partially supported by the grant MTM2015–68524–P
Article copyright: © Copyright 2019 American Mathematical Society