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arXiv · 1706.08228

On Ribet's isogeny for $J_0(65)$

Krzysztof Klosin·Mihran Papikian
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Abstract

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 $J_0(65)\rightarrow J^{65}$ 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.

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Krzysztof Klosin, Mihran Papikian. 2017-06-26. On Ribet's isogeny for $J_0(65)$. https://arxiv.org/abs/1706.08228

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