Torsion groups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt{d}),$ $0<d<100$

Antonela Trbović

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arXiv · 1806.05993

Torsion groups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt{d}),$ $0<d<100$

Antonela Trbović

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Abstract

We prove results towards classifying the possible torsion subgroups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt{d})$, where $0<d<100$ 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 a torsion group of an elliptic curve.

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Antonela Trbović. 2018-06-15. Torsion groups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt{d}),$ $0<d<100$. https://arxiv.org/abs/1806.05993

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