{"paper":{"title":"Equations and Rational Points of the Modular Curves $X^+_0(p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pietro Mercuri","submitted_at":"2016-07-15T15:38:35Z","abstract_excerpt":"Let $p$ be an odd prime number and let $X_0^+(p)$ be the quotient of the classical modular curve $X_0(p)$ by the action of the Atkin-Lehner operator $w_p$. In this paper we show how to compute explicit equations for the canonical model of $X_0^+(p)$. Then we show how to compute the modular parametrization, when it exists, from $X_0^+(p)$ to an isogeny factor $E$ of dimension 1 of its jacobian $J_0^+(p)$. Finally we show how use this map to determine the rational points on $X_0^+(p)$ up to a large fixed height."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04558","kind":"arxiv","version":1},"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"}