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Modular parametrizations of certain elliptic curves

Volume 163 / 2014

Matija Kazalicki, Yuichi Sakai, Koji Tasaka Acta Arithmetica 163 (2014), 33-43 MSC: Primary 11G05; Secondary 11F11, 11F30. DOI: 10.4064/aa163-1-3

Abstract

Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan–Serre differential operator.

In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over $\mathbb {Q}$, and as a consequence we generalize and explain some of their findings.

Authors

  • Matija KazalickiDepartment of Mathematics
    University of Zagreb
    Bijenicka cesta 30
    Zagreb, Croatia
    e-mail
  • Yuichi Sakai
    e-mail
  • Koji TasakaGraduate School of Mathematics
    Kyushu University
    744 Motooka Nishiku
    Fukuoka-city
    Fukuoka, 819-0395, Japan
    e-mail

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