On Ribet's isogeny for J_0(65)

Let J^{65} be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over \mathbb{Q} of discriminant 65. We study the isogenies J_0(65)\to J^{65} defined over \mathbb{Q}, whose existence was proved by Ribet. We prove that there is an isogeny whose kernel is supported on the...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2018-08, Vol.146 (8), p.3307-3320
Main Authors: Klosin, Krzysztof, Papikian, Mihran
Format: Article
Language:English
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Summary:Let J^{65} be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over \mathbb{Q} of discriminant 65. We study the isogenies J_0(65)\to J^{65} defined over \mathbb{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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14019