{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:22VXNUPLIOLKDZOOKQ7R5GXTTV","short_pith_number":"pith:22VXNUPL","canonical_record":{"source":{"id":"math/0301370","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2003-01-31T14:29:07Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"487f6c2672881550bb71de2df04950a5be796e238fab45b545e70efa2d4d7591","abstract_canon_sha256":"8b76eb958e5f41747f3ee60574760be9a9c12e79f6d2ed8935d612deed2ef6f0"},"schema_version":"1.0"},"canonical_sha256":"d6ab76d1eb4396a1e5ce543f1e9af39d47b492d1312d60809d2c6b458597b284","source":{"kind":"arxiv","id":"math/0301370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301370","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301370v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301370","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"22VXNUPLIOLK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"22VXNUPLIOLKDZOO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"22VXNUPL","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:22VXNUPLIOLKDZOOKQ7R5GXTTV","target":"record","payload":{"canonical_record":{"source":{"id":"math/0301370","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2003-01-31T14:29:07Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"487f6c2672881550bb71de2df04950a5be796e238fab45b545e70efa2d4d7591","abstract_canon_sha256":"8b76eb958e5f41747f3ee60574760be9a9c12e79f6d2ed8935d612deed2ef6f0"},"schema_version":"1.0"},"canonical_sha256":"d6ab76d1eb4396a1e5ce543f1e9af39d47b492d1312d60809d2c6b458597b284","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.220829Z","signature_b64":"8p3s5u1j/3ax4JiR3eYzaGunKutVLntnvaNOi0v1S6skt717VWJ72VPeqeL8gwebxF8GvO4Q5+qiDGmu6psQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6ab76d1eb4396a1e5ce543f1e9af39d47b492d1312d60809d2c6b458597b284","last_reissued_at":"2026-05-18T01:38:29.220100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.220100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0301370","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQBP3rfonUGcJYjPF6P5vBV52AfVb0gzWDwRdxScyOlL6OSYn5a7COmUFHaNaeJw8PWO6voRx7p1FiQeuQDMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:10:26.371253Z"},"content_sha256":"cd79209db379dc77d06fa185e140e3b5641d6dc4202304fbcc34e14627a7426c","schema_version":"1.0","event_id":"sha256:cd79209db379dc77d06fa185e140e3b5641d6dc4202304fbcc34e14627a7426c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:22VXNUPLIOLKDZOOKQ7R5GXTTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Familles de polynomes liees aux courbes modulaires X_1(l) unicursales et points rationnels non-triviaux de courbes elliptiques quotient","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Andreas M. Schoepp, Franck Leprevost, Michael E. Pohst","submitted_at":"2003-01-31T14:29:07Z","abstract_excerpt":"Soit l un entier et E_{c,l} la famille de Kubert des courbes elliptiques definies sur Q munies d'un point rationnel A d'ordre l. On note F_{c,l} la courbe elliptique quotient de E_{c,l} par le groupe engendre' par A, et f_l l'isogenie de E_{c,l} sur F_{c,l}. Pour l = 3, 4, 5 et 6, nous construisons explicitement, pour des parametrisations convenables de c, des elements non-triviaux de F_{c,l}(Q) / (f_l(E_{c,l}(Q))), autrement dit, des points explicites de F_{c,l}(Q) qui ne sont l'image par f_l d'aucun element de E_{c,l}(Q). Ces points sont en general d'ordre infini. Nous donnons des applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301370","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7t9Z95vLzzK7oY8KzQDeQ5ITZSPC25mDNtBjoAQFPtCx/fzphJu/2nEmasd0j9eG3PQI+mfzNr/r3pVLiJkWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:10:26.371600Z"},"content_sha256":"b978ef1ca185011f2f393c9d21ee10f501090c9df219031afed2d8690108161a","schema_version":"1.0","event_id":"sha256:b978ef1ca185011f2f393c9d21ee10f501090c9df219031afed2d8690108161a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/bundle.json","state_url":"https://pith.science/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T20:10:26Z","links":{"resolver":"https://pith.science/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV","bundle":"https://pith.science/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/bundle.json","state":"https://pith.science/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22VXNUPLIOLKDZOOKQ7R5GXTTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:22VXNUPLIOLKDZOOKQ7R5GXTTV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8b76eb958e5f41747f3ee60574760be9a9c12e79f6d2ed8935d612deed2ef6f0","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2003-01-31T14:29:07Z","title_canon_sha256":"487f6c2672881550bb71de2df04950a5be796e238fab45b545e70efa2d4d7591"},"schema_version":"1.0","source":{"id":"math/0301370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301370","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301370v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301370","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"22VXNUPLIOLK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"22VXNUPLIOLKDZOO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"22VXNUPL","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:b978ef1ca185011f2f393c9d21ee10f501090c9df219031afed2d8690108161a","target":"graph","created_at":"2026-05-18T01:38:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Soit l un entier et E_{c,l} la famille de Kubert des courbes elliptiques definies sur Q munies d'un point rationnel A d'ordre l. On note F_{c,l} la courbe elliptique quotient de E_{c,l} par le groupe engendre' par A, et f_l l'isogenie de E_{c,l} sur F_{c,l}. Pour l = 3, 4, 5 et 6, nous construisons explicitement, pour des parametrisations convenables de c, des elements non-triviaux de F_{c,l}(Q) / (f_l(E_{c,l}(Q))), autrement dit, des points explicites de F_{c,l}(Q) qui ne sont l'image par f_l d'aucun element de E_{c,l}(Q). Ces points sont en general d'ordre infini. Nous donnons des applicatio","authors_text":"Andreas M. Schoepp, Franck Leprevost, Michael E. Pohst","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2003-01-31T14:29:07Z","title":"Familles de polynomes liees aux courbes modulaires X_1(l) unicursales et points rationnels non-triviaux de courbes elliptiques quotient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301370","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cd79209db379dc77d06fa185e140e3b5641d6dc4202304fbcc34e14627a7426c","target":"record","created_at":"2026-05-18T01:38:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8b76eb958e5f41747f3ee60574760be9a9c12e79f6d2ed8935d612deed2ef6f0","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2003-01-31T14:29:07Z","title_canon_sha256":"487f6c2672881550bb71de2df04950a5be796e238fab45b545e70efa2d4d7591"},"schema_version":"1.0","source":{"id":"math/0301370","kind":"arxiv","version":1}},"canonical_sha256":"d6ab76d1eb4396a1e5ce543f1e9af39d47b492d1312d60809d2c6b458597b284","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ab76d1eb4396a1e5ce543f1e9af39d47b492d1312d60809d2c6b458597b284","first_computed_at":"2026-05-18T01:38:29.220100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.220100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8p3s5u1j/3ax4JiR3eYzaGunKutVLntnvaNOi0v1S6skt717VWJ72VPeqeL8gwebxF8GvO4Q5+qiDGmu6psQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.220829Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0301370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd79209db379dc77d06fa185e140e3b5641d6dc4202304fbcc34e14627a7426c","sha256:b978ef1ca185011f2f393c9d21ee10f501090c9df219031afed2d8690108161a"],"state_sha256":"d44c00407d2ae68abf19b311781aee485a21400ce8fc94c75216d989f7b009b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZjWn9VMHL0+/moPJtyIHXWdGn9d4r5VVLPb4FncAlf2tky2AznP1Fgudm7VrT32VkVyCAhLEJ2cBAgtWxVRRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:10:26.373487Z","bundle_sha256":"c29db59a956be6cbcb14d74760d4e9487f93fab54c6dbf3363eecb87574cdf45"}}