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We find that the only such curves with exceptional rational points are of levels $137$ and $311$. In particular there are no exceptional rational points on those curves of genus five and six. More precisely, we determine the rational points on the curves $X_0^+(N)$ for $N=137,173,199,251,311,157,181,227,263,163,197,211,223,269,271,359$."},"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":"2105.04811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-05-11T06:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"0c115d245ef413491f1da85a4ff51df748eb304d6afb2037da73d5345405bd6b","abstract_canon_sha256":"3c765817b893839bdb59b5b095587633b8321a9b850f741fa5dbdf993e7b33ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:24.526012Z","signature_b64":"dZJsr2X52V0ed2JnAAMuwV85ByEuKuDBUtVvwCq0Y1oMb9BXkQC5QRCz5+CjHqtAT60+dinYJBJuGLNUa0iFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db721bda6851a7224b6024e68ea830f5f794202a8ac75f2c8c5d82fb48ea7c4c","last_reissued_at":"2026-07-05T02:39:24.525557Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:24.525557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Boya Wen, Lea Beneish, Mingjie Chen, Nikola Ad\\v{z}aga, Shiva Chidambaram, Timo Keller, Vishal Arul","submitted_at":"2021-05-11T06:51:42Z","abstract_excerpt":"We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the only such curves with exceptional rational points are of levels $137$ and $311$. In particular there are no exceptional rational points on those curves of genus five and six. 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