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Let $A$ be favorable and let $B$ be any semistable abelian variety of dimension $2d$ and conductor $N^d$ such that $B[2]$ is filtered by copies of $A[2]$. We give a sufficient class field theoretic criterion on $F$ to guarantee that $B$ is isogenous to $A^d$.\n  As expected from our paramodular conjecture, we conclude that there is one isogeny class of abelian surfaces for each conductor in $\\{277, 349,461,797,971\\"},"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":"1510.06249","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-21T13:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"0e9db31302ea03eb66213d2fd8b79f80e5ed771c1f2f03da81e3d71dbdc521b3","abstract_canon_sha256":"ddf7a317861bb99ce434481f0c96249d3ddf7515ab66370e85d34ad2fb015fce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:46.626225Z","signature_b64":"+e0HRIQJ+4QFaIOJaW14D9OzRn3sTdcDi/RrGJ+ckt2RKJJO9d3ERATe9kyh2T669jneKV/2ar0GVhSFLFxABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cad9264c35459e0e44bc01e54a25f40205e64276df8c5dd1013ff4d0ae3c81d","last_reissued_at":"2026-05-18T00:08:46.625622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:46.625622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certain Abelian varieties bad at only one prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Armand Brumer, Kenneth Kramer","submitted_at":"2015-10-21T13:43:50Z","abstract_excerpt":"An abelian surface $A_{/{\\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\\mathcal S}_5$-extension with ramification index 5 over ${\\mathbb Q}_2$. Let $A$ be favorable and let $B$ be any semistable abelian variety of dimension $2d$ and conductor $N^d$ such that $B[2]$ is filtered by copies of $A[2]$. We give a sufficient class field theoretic criterion on $F$ to guarantee that $B$ is isogenous to $A^d$.\n  As expected from our paramodular conjecture, we conclude that there is one isogeny class of abelian surfaces for each conductor in $\\{277, 349,461,797,971\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06249","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":"1510.06249","created_at":"2026-05-18T00:08:46.625701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06249v3","created_at":"2026-05-18T00:08:46.625701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06249","created_at":"2026-05-18T00:08:46.625701+00:00"},{"alias_kind":"pith_short_12","alias_value":"DSWZEZGDKRM6","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DSWZEZGDKRM6BZCL","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DSWZEZGD","created_at":"2026-05-18T12:29:17.054201+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/DSWZEZGDKRM6BZCLYAPFJIS7IA","json":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA.json","graph_json":"https://pith.science/api/pith-number/DSWZEZGDKRM6BZCLYAPFJIS7IA/graph.json","events_json":"https://pith.science/api/pith-number/DSWZEZGDKRM6BZCLYAPFJIS7IA/events.json","paper":"https://pith.science/paper/DSWZEZGD"},"agent_actions":{"view_html":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA","download_json":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA.json","view_paper":"https://pith.science/paper/DSWZEZGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06249&json=true","fetch_graph":"https://pith.science/api/pith-number/DSWZEZGDKRM6BZCLYAPFJIS7IA/graph.json","fetch_events":"https://pith.science/api/pith-number/DSWZEZGDKRM6BZCLYAPFJIS7IA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA/action/storage_attestation","attest_author":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA/action/author_attestation","sign_citation":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA/action/citation_signature","submit_replication":"https://pith.science/pith/DSWZEZGDKRM6BZCLYAPFJIS7IA/action/replication_record"}},"created_at":"2026-05-18T00:08:46.625701+00:00","updated_at":"2026-05-18T00:08:46.625701+00:00"}