{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FT4R5B22Z7BDUUQSAJU5IYWHNN","short_pith_number":"pith:FT4R5B22","schema_version":"1.0","canonical_sha256":"2cf91e875acfc23a52120269d462c76b466a8a20daa15507317f25fc77b5ae7f","source":{"kind":"arxiv","id":"1007.4617","version":3},"attestation_state":"computed","paper":{"title":"On elliptic curves with an isogeny of degree 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Silverberg, K. Rubin, M. Stoll, R. Greenberg","submitted_at":"2010-07-27T04:27:05Z","abstract_excerpt":"We show that if $E$ is an elliptic curve over $\\mathbf{Q}$ with a $\\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\\mathbf{Q}(\\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the"},"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":"1007.4617","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T04:27:05Z","cross_cats_sorted":[],"title_canon_sha256":"19f577fa6c406b28c23af3cb171c13419e20822a4e95b5af6025b122f5e4b6c8","abstract_canon_sha256":"7effac4192194680df233c1ba41fec44eea17a28368ae7994260282cfa938a49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:07.799114Z","signature_b64":"JdPWsjSUnWRU9BMbs5WHvZhdvCOo+6JmY6gF7UBohm3rlkVinjeDlV3DsH/kZwdwLW/ALt8fx8Q+3DASHjipBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cf91e875acfc23a52120269d462c76b466a8a20daa15507317f25fc77b5ae7f","last_reissued_at":"2026-05-18T03:43:07.798299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:07.798299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On elliptic curves with an isogeny of degree 7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Silverberg, K. Rubin, M. Stoll, R. Greenberg","submitted_at":"2010-07-27T04:27:05Z","abstract_excerpt":"We show that if $E$ is an elliptic curve over $\\mathbf{Q}$ with a $\\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\\mathbf{Q}(\\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4617","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.4617","created_at":"2026-05-18T03:43:07.798450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.4617v3","created_at":"2026-05-18T03:43:07.798450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4617","created_at":"2026-05-18T03:43:07.798450+00:00"},{"alias_kind":"pith_short_12","alias_value":"FT4R5B22Z7BD","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"FT4R5B22Z7BDUUQS","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"FT4R5B22","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN","json":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN.json","graph_json":"https://pith.science/api/pith-number/FT4R5B22Z7BDUUQSAJU5IYWHNN/graph.json","events_json":"https://pith.science/api/pith-number/FT4R5B22Z7BDUUQSAJU5IYWHNN/events.json","paper":"https://pith.science/paper/FT4R5B22"},"agent_actions":{"view_html":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN","download_json":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN.json","view_paper":"https://pith.science/paper/FT4R5B22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.4617&json=true","fetch_graph":"https://pith.science/api/pith-number/FT4R5B22Z7BDUUQSAJU5IYWHNN/graph.json","fetch_events":"https://pith.science/api/pith-number/FT4R5B22Z7BDUUQSAJU5IYWHNN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN/action/storage_attestation","attest_author":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN/action/author_attestation","sign_citation":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN/action/citation_signature","submit_replication":"https://pith.science/pith/FT4R5B22Z7BDUUQSAJU5IYWHNN/action/replication_record"}},"created_at":"2026-05-18T03:43:07.798450+00:00","updated_at":"2026-05-18T03:43:07.798450+00:00"}