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Optimal curves differing by a 3-isogeny

Volume 158 / 2013

Dongho Byeon, Donggeon Yhee Acta Arithmetica 158 (2013), 219-227 MSC: Primary 11G05; Secondary 14K02. DOI: 10.4064/aa158-3-2

Abstract

Stein and Watkins conjectured that for a certain family of elliptic curves $E$, the $X_0(N)$-optimal curve and the $X_1(N)$-optimal curve of the isogeny class $\mathcal {C}$ containing $E$ of conductor $N$ differ by a 3-isogeny. In this paper, we show that this conjecture is true.

Authors

  • Dongho ByeonDepartment of Mathematics
    Seoul National University
    Seoul, Korea
    e-mail
  • Donggeon YheeDepartment of Mathematics
    Seoul National University
    Seoul, Korea
    e-mail

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