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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics