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A generalisation of a conjecture of Andr\\'e and Pink predicts that Z is a weakly special subvariety. We prove this when dim Z = 1 using the Pila--Zannier method and the Masser--W\\\"ustholz isogeny theorem. This generalises results of Edixhoven and Yafaev when the Hecke orbit consists of CM points and of Pink when it consists of Galois generic points."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.3653","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-17T13:55:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bf2e5bb0ef7c066b0f2fe8610256fdec21c8f2583982d03028c818c5bcc79fcc","abstract_canon_sha256":"17cd3237c01fbf6391153a0ea36b64e85f63b6d22d269043b5a00aeea1cecac0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:46.166524Z","signature_b64":"P2GoCJqXKXM2J78WlWEdR/NCVLPfBqHZuEzNgE2ehZwmXp8AIBNg5gvKrqxgh4PkDozdKT8hTuvyRuf0BKEXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c7eba302422d7e9dd4b2154e449cf25568e5b5af9724620d95faaa6112b695b","last_reissued_at":"2026-05-18T01:04:46.166031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:46.166031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Families of abelian varieties with many isogenous fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Martin Orr","submitted_at":"2012-09-17T13:55:51Z","abstract_excerpt":"Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. 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