{"paper":{"title":"The Manin-Stevens constant in the semistable case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kestutis Cesnavicius","submitted_at":"2016-04-07T20:17:07Z","abstract_excerpt":"Stevens conjectured that for every optimal parametrization $\\phi\\colon X_1(n) \\rightarrow E$ of an elliptic curve $E$ over $\\mathbb{Q}$ of conductor $n$, the pullback of some N\\'eron differential on $E$ is the differential associated to the normalized new eigenform that corresponds to the isogeny class of $E$. We prove this conjecture under the assumption that $E$ is semistable, the key novelty lying in the $2$-primary analysis when $n$ is even. For this analysis, we first relate the general case of the conjecture to a divisibility relation between $\\mathrm{deg}\\, \\phi$ and a certain congruenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02165","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"}