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arXiv · 2505.04149

Torsion of Rational Elliptic Curves over the $\mathbb{Z}_p$-Extensions of Quadratic Fields

Omer Avci
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Abstract

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. For a quadratic number field $K$ and an odd prime number $p$, let $L$ be a $\mathbb{Z}_p$-extension of $K$. We prove that $E(L)_{\text{tors}}=E(K)_{\text{tors}}$ when $p>5$. It enables us to classify the groups that can be realized as the torsion subgroup $E(L)_{\text{tors}}$, by using the classification of torsion subgroups over the quadratic fields.

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Omer Avci. 2025-05-07. Torsion of Rational Elliptic Curves over the $\mathbb{Z}_p$-Extensions of Quadratic Fields. https://arxiv.org/abs/2505.04149

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