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For example, we have $#X_1(17)(\\mathbb{F}_{10^{1000}+1357})\\textrm{mod} 17=3$."},"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":"1305.4505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-20T11:53:38Z","cross_cats_sorted":[],"title_canon_sha256":"9b8747322c0fb2a06dcad0d7b8f78e2f3b492e20cee0e6eb79b71e07e1ff24e3","abstract_canon_sha256":"e5c8f98441ad34f1f3fe1465901fa8d83bf5484a592ffc0d0aa9e81b1618fc3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:23.535928Z","signature_b64":"am3QnR0IUQLPkYb7u7irOjnQnsfuV9wU7U3faoYeLIbfFCTwbE6qlaLnMZsqF/NdMP0U/nGyN7aNrL3bavTRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ead96d591aa1a29013bb85be7eebcd4de2cb38f69a5eb0e1d268765af962ae15","last_reissued_at":"2026-05-18T03:25:23.535434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:23.535434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing points on modular curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinxiang Zeng","submitted_at":"2013-05-20T11:53:38Z","abstract_excerpt":"In this paper, we present a probabilistic algorithm to compute the number of $\\mathbb{F}_p$-points of modular curve $X_1(n)$. 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