{"paper":{"title":"Integral Models of $X_0(N)$ and Their Degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Goran Mui\\'c","submitted_at":"2013-05-10T20:15:13Z","abstract_excerpt":"In this paper we compute the degree of a curve which is the image of a mapping $z\\longmapsto (f(z): g(z): h(z))$ constructed out of three linearly independent modular forms of the same even weight $\\ge 4$ into $\\mathbb P^2$. We prove that in most cases this map is a birational equivalence and defined over $\\mathbb Z$. We use this to construct models of $X_0(N)$, $N\\ge 2$, using modular forms in $M_{12}(\\Gamma_0(N))$ with integral $q$--expansion. The models have degree equal to $\\psi(N)$ (a classical Dedekind psi function). When genus is at least one, we show the existence of models constructed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2428","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"}