## Abstract

Let J^{65} be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over ℚ of discriminant 65. We study the isogenies J_{0} (65) → J^{65} defined over ℚ, whose existence was proved by Ribet. We prove that there is an isogeny whose kernel is supported on the Eisenstein maximal ideals of the Hecke algebra acting on J_{0} (65), and, moreover, the odd part of the kernel is generated by a cuspidal divisor of order 7, as is predicted by a conjecture of Ogg.

Original language | English (US) |
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Pages (from-to) | 3307-3320 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 8 |

DOIs | |

State | Published - 2018 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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