Tamagawa numbers of elliptic curves with torsion points

Mentzelos Melistas*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)155-165
Number of pages11
JournalArchiv der Mathematik
Volume119
Early online date22 Apr 2022
DOIs
Publication statusPublished - Aug 2022
Externally publishedYes

Keywords

  • Elliptic curve
  • Torsion point
  • Tamagawa number
  • n/a OA procedure

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