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December 2020 Modular Degrees of Elliptic Curves and Some Quotient of $L$-values
Hiro-aki NARITA, Kousuke SUGIMOTO
Tokyo J. Math. 43(2): 279-293 (December 2020). DOI: 10.3836/tjm/1502179331

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 $E_f$ 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.

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Hiro-aki NARITA. Kousuke SUGIMOTO. "Modular Degrees of Elliptic Curves and Some Quotient of $L$-values." Tokyo J. Math. 43 (2) 279 - 293, December 2020. https://doi.org/10.3836/tjm/1502179331

Information

Published: December 2020
First available in Project Euclid: 9 November 2020

MathSciNet: MR4185840
Digital Object Identifier: 10.3836/tjm/1502179331

Subjects:
Primary: 11F67
Secondary: 11G05

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 2 • December 2020
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