Torsion points on elliptic curves over number fields of small degree

Maarten Derickx; Sheldon Kamienny; William Stein; Michael Stoll

doi:10.2140/ant.2023.17.267

Torsion points on elliptic curves over number fields of small degree

Number Theory 2023-03-29 v2 Algebraic Geometry

Authors: Maarten Derickx , Sheldon Kamienny , William Stein , Michael Stoll

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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 $7$ .

Keywords

elliptic curves torsion points number fields rational points prime orders Diophantine geometry

Cite

@article{arxiv.1707.00364,
  title  = {Torsion points on elliptic curves over number fields of small degree},
  author = {Maarten Derickx and Sheldon Kamienny and William Stein and Michael Stoll},
  journal= {arXiv preprint arXiv:1707.00364},
  year   = {2023}
}

Comments

v2: Paper almost completely rewritten; exact determination of S(7) is new; added classification of elliptic curves over sextic fields with a point of order 37

Torsion points on elliptic curves over number fields of small degree

Abstract

Keywords

Cite

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