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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Torsion subgroups of elliptic curves over quintic and sextic number fields
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by Maarten Derickx and Andrew V. Sutherland PDF
Proc. Amer. Math. Soc. 145 (2017), 4233-4245 Request permission


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 $\Phi ^\infty (6)$.
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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:
  • MathSciNet review: 3690609