Torsion points on elliptic curves over number fields of small degree

Derickx, Maarten; Kamienny, Sheldon; Stein, William; Stoll, Michael

doi:10.2140/ant.2023.17.267

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Torsion points on elliptic curves over number fields of small degree

Maarten Derickx, Sheldon Kamienny, William Stein and Michael Stoll

Vol. 17 (2023), No. 2, 267–308

DOI: 10.2140/ant.2023.17.267

Abstract

We determine the set $S (d)$ of possible prime orders of $K$ -rational points on elliptic curves over number fields $K$ of degree $d$ for $d = 4$ , $5$ , $6$ , and $7$ .

Dedicated to the memory of Bas Edixhoven

Keywords

elliptic curve, torsion point, torsion subgroup, number fields of small degree

Mathematical Subject Classification 2010

Primary: 11G05

Secondary: 14G05, 14G25, 14H52

Supplementary material

Magma code verifying computational claims

Milestones

Received: 18 July 2017

Revised: 5 February 2021

Accepted: 1 February 2022

Published: 24 March 2023

Authors

Maarten Derickx
Mathematisch Instituut Universiteit Leiden Leiden Netherlands

Sheldon Kamienny
Department of Mathematics USC Dornsife Los Angeles, CA United States

William Stein
SageMath, Inc. Renton, WA United States

Michael Stoll
Mathematisches Institut Universität Bayreuth Bayreuth Germany

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Vol. 17, No. 2, 2023