Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny

Alexander Barrios; John Cullinan

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arXiv · 2408.03419

Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny

Alexander Barrios·John Cullinan

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Abstract

Let $\ell$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\ell$-torsion point, then there has been significant work done on characterizing the $\ell$-divisibility of the global Tamagawa number of $E$. In this paper, we consider elliptic curves that are $\ell$-isogenous to elliptic curves with an $\ell$-torsion point and study the $\ell$-divisibility of their global Tamagawa numbers.

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Alexander Barrios, John Cullinan. 2024-08-06. Tamagawa Numbers of Elliptic Curves with an $\ell$-isogeny. https://arxiv.org/abs/2408.03419

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