Torsion groups of elliptic curves over $\mathbb{Q}(\mu_{p^{\infty}})$

Tomislav Gužvić; Borna Vukorepa

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arXiv · 2206.15208

Torsion groups of elliptic curves over $\mathbb{Q}(\mu_{p^{\infty}})$

Tomislav Gužvić·Borna Vukorepa

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Abstract

Let $E/\mathbb{Q}$ be an elliptic curve and $p \in \{5,7,11 \}$ be a prime. We determine the possibilities for $E(\mathbb{Q}(\zeta_{p}))_{tors}$. Additionally, we determine all the possibilities for $E(\mathbb{Q}(\zeta_{16}))_{tors}$ and $E(\mathbb{Q}(\zeta_{27}))_{tors}$. Using these results we are able to determine the possibilities for $E(\mathbb{Q}(\mu_{p^{\infty}}))_{tors}$.

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Tomislav Gužvić, Borna Vukorepa. 2022-06-30. Torsion groups of elliptic curves over $\mathbb{Q}(\mu_{p^{\infty}})$. https://arxiv.org/abs/2206.15208

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