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Much work has been done in recent years to study the image of $\\rho_E$ (up to conjugation) as part of Mazur's so called ``Program B.'' In this paper, we describe and implement an efficient algorithm to compute the image of $\\rho_E$ in $\\operatorname{GL}(2, \\widehat{\\mathbb{Z}})$ (up to conjugation) for an elliptic curve $E/\\mathbb{Q}$ with complex multiplication (CM) and $j$-invar"},"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":"2603.08545","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-09T16:13:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e755eb41811cb6a609c3d111b806b689dbf33101396d5cd94410c2ca9332e5c7","abstract_canon_sha256":"6e638b784ecb05682c6c2e31048aa43d035d17986753834f8839053f0effa965"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:19.393307Z","signature_b64":"XlEj454FUTh3OdkQ/K+jZ2b8tRoSzmkGam3PBcdhe7+Tejg/cTQAQPWVKu3Jv4W3vtpRiYFjTQRQE1h3ZJhhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71ce8425752bc9d679ca40e188ffff13a2cfb40acde0cc31fb473d49bca2c554","last_reissued_at":"2026-06-19T16:12:19.392966Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:19.392966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The image of the adelic Galois representation of an elliptic curve with complex multiplication","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"\\'Alvaro Lozano-Robledo, Benjamin York","submitted_at":"2026-03-09T16:13:10Z","abstract_excerpt":"Let $E/\\mathbb{Q}$ be an elliptic curve and let $\\rho_E \\colon \\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q}) \\to \\operatorname{GL}(2, \\widehat{\\mathbb{Z}})$ be the adelic Galois representation attached to $E$. Much work has been done in recent years to study the image of $\\rho_E$ (up to conjugation) as part of Mazur's so called ``Program B.'' In this paper, we describe and implement an efficient algorithm to compute the image of $\\rho_E$ in $\\operatorname{GL}(2, \\widehat{\\mathbb{Z}})$ (up to conjugation) for an elliptic curve $E/\\mathbb{Q}$ with complex multiplication (CM) and $j$-invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.08545","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.08545/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2603.08545","created_at":"2026-06-19T16:12:19.393021+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.08545v2","created_at":"2026-06-19T16:12:19.393021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.08545","created_at":"2026-06-19T16:12:19.393021+00:00"},{"alias_kind":"pith_short_12","alias_value":"OHHIIJLVFPE5","created_at":"2026-06-19T16:12:19.393021+00:00"},{"alias_kind":"pith_short_16","alias_value":"OHHIIJLVFPE5M6OK","created_at":"2026-06-19T16:12:19.393021+00:00"},{"alias_kind":"pith_short_8","alias_value":"OHHIIJLV","created_at":"2026-06-19T16:12:19.393021+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/OHHIIJLVFPE5M6OKIDQYR777CO","json":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO.json","graph_json":"https://pith.science/api/pith-number/OHHIIJLVFPE5M6OKIDQYR777CO/graph.json","events_json":"https://pith.science/api/pith-number/OHHIIJLVFPE5M6OKIDQYR777CO/events.json","paper":"https://pith.science/paper/OHHIIJLV"},"agent_actions":{"view_html":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO","download_json":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO.json","view_paper":"https://pith.science/paper/OHHIIJLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.08545&json=true","fetch_graph":"https://pith.science/api/pith-number/OHHIIJLVFPE5M6OKIDQYR777CO/graph.json","fetch_events":"https://pith.science/api/pith-number/OHHIIJLVFPE5M6OKIDQYR777CO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO/action/storage_attestation","attest_author":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO/action/author_attestation","sign_citation":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO/action/citation_signature","submit_replication":"https://pith.science/pith/OHHIIJLVFPE5M6OKIDQYR777CO/action/replication_record"}},"created_at":"2026-06-19T16:12:19.393021+00:00","updated_at":"2026-06-19T16:12:19.393021+00:00"}