On the torsion of rational elliptic curves over sextic fields
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- Math. Comp. 89 (2020), 411-435 Request permission
Abstract:
Given an elliptic curve $E/\mathbb {Q}$ with torsion subgroup $G = E(\mathbb {Q})_\textrm {{tors}}$ 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 $H = E(K)_\textrm {{tors}}$ 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.References
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Additional Information
- Harris B. Daniels
- Affiliation: Department of Mathematics and Statistics, Amherst College, Massachusetts 01002
- MR Author ID: 1105200
- Email: hdaniels@amherst.edu
- Enrique González-Jiménez
- Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
- MR Author ID: 703386
- Email: enrique.gonzalez.jimenez@uam.es
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 411-435
- MSC (2010): Primary 11G05; Secondary 14H52, 14G05
- DOI: https://doi.org/10.1090/mcom/3440
- MathSciNet review: 4011550