{"paper":{"title":"On Ribet's isogeny for $J_0(65)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Krzysztof Klosin, Mihran Papikian","submitted_at":"2017-06-26T04:34:38Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08228","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}