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We prove that, for $p>37$, the residual mod $p$ Galois representation $\\bar{\\rho}_{E,p}:G_{\\mathbb{Q}}\\rightarrow\\mathrm{GL}_2(\\mathbb{F}_p)$ is surjective."},"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":"1702.01985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"abd2dd269e9a10eace1bf6cb68a0519e28fc4ee28aa20965bf62a43c9612a07b","abstract_canon_sha256":"ec83e633dd401d1f0880ed0c7260f81390e1f7439ea35d16f6e12465d2679c09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:06.268034Z","signature_b64":"fXGxQh6UEYKAlVZMBHi8n2k4+Om0LOmID+aLA1apJE0LGRRW14o/3FS96v5EOIj7MUCYmdPg7uOxZKASAwF4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","last_reissued_at":"2026-05-18T00:49:06.267610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:06.267610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic Isogenies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pedro Lemos","submitted_at":"2017-02-07T12:42:24Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ such that $\\mathrm{End}_{\\bar{\\mathbb{Q}}}(E)=\\mathbb{Z}$ and which admits a non-trivial cyclic $\\mathbb{Q}$-isogeny. 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