Torsion groups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt d)$, $0 < d < 100$
Volume 192 / 2020
Acta Arithmetica 192 (2020), 141-153
MSC: Primary 11G05.
DOI: 10.4064/aa180725-8-1
Published online: 25 October 2019
Abstract
We prove results towards classifying the possible torsion subgroups of elliptic curves over quadratic fields $\mathbb {Q}(\sqrt {d})$, where $0 \lt d \lt 100$ is a square-free integer, and obtain a complete classification for 49 out of 60 such fields. Over the remaining 11 quadratic fields, we cannot rule out the possibility of the group $\mathbb {Z}/16\mathbb {Z}$ appearing as the torsion group of an elliptic curve.
