Small Tamagawa numbers of elliptic curves with isogenies or torsion

Mentzelos Melistas

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arXiv · 2505.20479

Small Tamagawa numbers of elliptic curves with isogenies or torsion

Mentzelos Melistas

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Abstract

In this article with study Tamagawa numbers of elliptic curves defined over $\mathbb{Q}$ that have isogenies or torsion points. More precisely, our aim is either to bound the set of primes primes that can divide their Tamagawa numbers or, when such a bound is not possible, to find infinite subfamilies whose Tamagawa numbers are as small as possible. Finally, we also investigate Tamagawa numbers of specializations of elliptic surfaces.

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Mentzelos Melistas. 2025-05-26. Small Tamagawa numbers of elliptic curves with isogenies or torsion. https://arxiv.org/abs/2505.20479

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