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arXiv · 1608.07549

Torsion subgroups of elliptic curves over quintic and sextic number fields

Maarten Derickx·Andrew V. Sutherland
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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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Maarten Derickx, Andrew V. Sutherland. 2016-08-26. Torsion subgroups of elliptic curves over quintic and sextic number fields. https://doi.org/10.1090/proc/13605

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