### 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) |
---|---|

Pages (from-to) | 3307-3320 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

_{0}(65).

*Proceedings of the American Mathematical Society*,

*146*(8), 3307-3320. https://doi.org/10.1090/proc/14019

}

_{0}(65)',

*Proceedings of the American Mathematical Society*, vol. 146, no. 8, pp. 3307-3320. https://doi.org/10.1090/proc/14019

**On Ribet’s isogeny for J _{0} (65).** / Klosin, Krzysztof; Papikian, Mihran.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Ribet’s isogeny for J0 (65)

AU - Klosin, Krzysztof

AU - Papikian, Mihran

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let J65 be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over ℚ of discriminant 65. We study the isogenies J0 (65) → J65 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 J0 (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.

AB - Let J65 be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over ℚ of discriminant 65. We study the isogenies J0 (65) → J65 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 J0 (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.

UR - http://www.scopus.com/inward/record.url?scp=85047667579&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047667579&partnerID=8YFLogxK

U2 - 10.1090/proc/14019

DO - 10.1090/proc/14019

M3 - Article

AN - SCOPUS:85047667579

VL - 146

SP - 3307

EP - 3320

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -

_{0}(65). Proceedings of the American Mathematical Society. 2018 Jan 1;146(8):3307-3320. https://doi.org/10.1090/proc/14019