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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
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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