Contents Online
Mathematical Research Letters
Volume 23 (2016)
Number 1
Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$
Pages: 245 – 272
DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n1.a12
Author
Abstract
We classify the possible torsion structures of rational elliptic curves over cubic fields. Along the way we find a previously unknown torsion structure over a cubic field, $\mathbb{Z} / 21 \mathbb{Z}$, which corresponds to a sporadic point on $X_1(21)$ of degree 3, which is the lowest possible degree of a sporadic point on a modular curve $X_1(n)$.
Keywords
elliptic curves, torsion subgroups, cubic fields, modular curves
2010 Mathematics Subject Classification
11G05, 11G18, 11G25
Accepted 1 September 2014
Published 25 May 2016