Tamagawa numbers of elliptic curves with torsion points

2022/02/13 by Mentzelos Melistas, Melistas, Mentzelos · 1 citation
Arts and Humanities · Mathematics · Social Sciences · #11G05 #11G07 #11G10 #Algebraic Geometry and Number Theory #FOS: Mathematics #French Historical and Cultural Studies #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2202.06235

openalex publication_date 2022/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a global field and let E/K be an elliptic curve with a K-rational point of prime order p. In this paper we are interested in how often the (global) Tamagawa number c(E/K) of E/K is divisible by p. This is a natural question to consider in view of the fact that the fraction c(E/K)/ |E(K)_tors| appears in the second part of the Birch and Swinnerton-Dyer Conjecture. We focus on elliptic curves defined over global fields, but we also prove a result for higher dimensional abelian varieties defined over ℚ.

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• Small Tamagawa numbers of elliptic curves with isogenies or torsion

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