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

Volume 192 / 2020

Antonela Trbović 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.

Authors

  • Antonela TrbovićDepartment of Mathematics
    University of Zagreb
    Bijenička cesta 30
    10000 Zagreb, Croatia
    e-mail

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