Modular Degrees of Elliptic Curves and Some Quotient of L-values

Hiro Aki Narita, Kousuke Sugimoto

Research output: Contribution to journalArticlepeer-review

Abstract

By the modular degree we mean the degree of a modular parametrization of an elliptic curve, namely the mapping degree of the surjection from a modular curve to an elliptic curve. Its arithmetic significance is discussed by Zagier and Agashe-Ribet-Stein et al. in terms of the congruence of modular forms. Given an elliptic curve Ef attached to a rational newform f , we explicitly relate its modular degree to a quotient of special values of some two L-functions attached to f . We also provide several numerical examples of the formula.

Original languageEnglish
Pages (from-to)279-293
Number of pages15
JournalTokyo Journal of Mathematics
Volume43
Issue number2
DOIs
Publication statusPublished - 2020 Dec

Keywords

  • Elliptic curves
  • L-functions
  • Modular degrees
  • Newforms
  • Periods

ASJC Scopus subject areas

  • Mathematics(all)

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