A criterion to rule out torsion groups for elliptic curves over number fields
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40993_2015_Article_31.pdf
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511.48 KB
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Author(s)
Bruin, Peter
Najman, Filip
Date Issued
January 2016
Journal
Research in Number Theory
Publisher
Springer International Publishing
Citation
Bruin, Peter, and Filip Najman. “A Criterion to Rule out Torsion Groups for Elliptic Curves over Number Fields.” Research in Number Theory 2.1 (2016): n. pag.
Version
Final published version
Abstract
We present a criterion for proving that certain groups of the form \(\mathbb {Z}/m\mathbb {Z}\oplus \mathbb {Z}/n\mathbb {Z}\) do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups of elliptic curves over cubic and quartic fields. We also use this criterion to give the list of all torsion groups of elliptic curves occurring over a specific cubic field and over a specific quartic field.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s40993-015-0031-5
