{"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. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01985","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"}