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arXiv · 2512.05023

On inertial types of elliptic curves

Jose Castro-Moreno·Enric Florit·Nuno Freitas
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Abstract

We classify the inertial Weil-Deligne types arising from elliptic curves over all finite extensions $F/\mathbb Q_p$. Based on this classification, we give a fully explicit description of the types and implement an algorithm that computes all inertial types of elliptic curves defined over a given $F$. As an application, we determine all inertial types arising from elliptic curves over any extension $F/\mathbb Q_p$ of degree at most 3.

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Jose Castro-Moreno, Enric Florit, Nuno Freitas. 2025-12-04. On inertial types of elliptic curves. https://arxiv.org/abs/2512.05023

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