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Torsion subgroups of elliptic curves over quintic and sextic number fields


Authors: Maarten Derickx and Andrew V. Sutherland
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
Published electronically: April 12, 2017
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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)$.


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Additional Information

Maarten Derickx
Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands

Andrew V. Sutherland
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachsuetts Avenue, Cambridge, Massachusetts 02139

DOI: https://doi.org/10.1090/proc/13605
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
Article copyright: © Copyright 2017 American Mathematical Society