@article{f2ce0281d42849a986444c92d24e376e,
title = "On Ribet{\textquoteright}s isogeny for J0 (65)",
abstract = "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.",
author = "Krzysztof Klosin and Mihran Papikian",
note = "Funding Information: Received by the editors July 19, 2017, and, in revised form, November 13, 2017. 2010 Mathematics Subject Classification. Primary 11G18. Key words and phrases. Modular curves, Ribet{\textquoteright}s isogeny, Eisenstein ideal, cuspidal divisor group. The first author was supported by the Young Investigator Grant #H98230-16-1-0129 from the National Security Agency, and by a PSC-CUNY award jointly funded by the Professional Staff Congress and the City University of New York. The second author was partially supported by grants from the Simons Foundation (245676) and the National Security Agency (H98230-15-1-0008). Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/proc/14019",
language = "English (US)",
volume = "146",
pages = "3307--3320",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "8",
}