Torsion subgroups of elliptic curves over quintic and sextic number fields
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- by Maarten Derickx and Andrew V. Sutherland PDF
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Abstract:
Let $\Phi ^\infty (d)$ denote the set of finite abelian groups that occur infinitely often as the torsion subgroup of an elliptic curve over a number field of degree $d$. The sets $\Phi ^\infty (d)$ are known for $d\le 4$. In this article we determine $\Phi ^\infty (5)$ and $\Phi ^\infty (6)$.References
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Additional Information
- Maarten Derickx
- Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands
- MR Author ID: 1040992
- Andrew V. Sutherland
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachsuetts Avenue, Cambridge, Massachusetts 02139
- MR Author ID: 852273
- ORCID: 0000-0001-7739-2792
- Received by editor(s): September 16, 2016
- Received by editor(s) in revised form: November 21, 2016
- Published electronically: April 12, 2017
- Additional Notes: The second author was supported by NSF grant DMS-1522526.
- Communicated by: Romyar T. Sharifi
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4233-4245
- MSC (2010): Primary 11G05; Secondary 11G18, 14G35, 14H51
- DOI: https://doi.org/10.1090/proc/13605
- MathSciNet review: 3690609