  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.
