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Let $J^{65}$ be the Jacobian of the Shimura curve attached to the indefinitequaternion algebra over $\mathbb{Q}$ of discriminant $65$. We study theisogenies $J_0(65)\rightarrow J^{65}$ defined over $\mathbb{Q}$, whoseexistence was proved by Ribet. We prove that there is an isogeny whose kernelis 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 cuspidaldivisor of order $7$, as is predicted by a conjecture of Ogg.

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