{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:H7P5C7JBXFOGJ57JPS5DP2U4WZ","short_pith_number":"pith:H7P5C7JB","schema_version":"1.0","canonical_sha256":"3fdfd17d21b95c64f7e97cba37ea9cb640734322a284caaaf81539105bc2e735","source":{"kind":"arxiv","id":"1802.07290","version":2},"attestation_state":"computed","paper":{"title":"Growth of the analytic rank of modular elliptic curves over quintic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michele Fornea","submitted_at":"2018-02-20T19:15:15Z","abstract_excerpt":"Given $F$ a totally real field and $E_{/F}$ a modular elliptic curve, we denote by $G_5(E_{/F};X)$ the number of quintic extensions $K$ of $F$ such that the norm of the relative discriminant is at most $X$ and the analytic rank of $E$ grows over $K$, i.e., $r_\\mathrm{an}(E/K)>r_\\mathrm{an}(E/F)$. We show that $G_5(E_{/F};X)\\asymp_{+\\infty} X$ when the elliptic curve $E_{/F}$ has odd conductor and at least one prime of multiplicative reduction. As Bhargava, Shankar and Wang \\cite{BSW} showed that the number of quintic extensions of $F$ with norm of the relative discriminant at most $X$ is asymp"},"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":"1802.07290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-20T19:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"54f39686a4f16e57f04c0bbd5f91c4a1df34ab6d80629be72d7ed8e2b7f3118e","abstract_canon_sha256":"9e69ad51079c4980c4106f6867067b8f1a09655ed79875112acbab3734880761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:26.315260Z","signature_b64":"sQjQHkIuRVTNv7rIgb3hQS7tgumup0lE/0D1jIyCwaU6Q/uV0Gi2QQaBLg7JgllEC8eyvLYPabn+VrULwHuEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fdfd17d21b95c64f7e97cba37ea9cb640734322a284caaaf81539105bc2e735","last_reissued_at":"2026-05-17T23:54:26.314706Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:26.314706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth of the analytic rank of modular elliptic curves over quintic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michele Fornea","submitted_at":"2018-02-20T19:15:15Z","abstract_excerpt":"Given $F$ a totally real field and $E_{/F}$ a modular elliptic curve, we denote by $G_5(E_{/F};X)$ the number of quintic extensions $K$ of $F$ such that the norm of the relative discriminant is at most $X$ and the analytic rank of $E$ grows over $K$, i.e., $r_\\mathrm{an}(E/K)>r_\\mathrm{an}(E/F)$. We show that $G_5(E_{/F};X)\\asymp_{+\\infty} X$ when the elliptic curve $E_{/F}$ has odd conductor and at least one prime of multiplicative reduction. As Bhargava, Shankar and Wang \\cite{BSW} showed that the number of quintic extensions of $F$ with norm of the relative discriminant at most $X$ is asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07290","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":""},"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":"1802.07290","created_at":"2026-05-17T23:54:26.314790+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.07290v2","created_at":"2026-05-17T23:54:26.314790+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07290","created_at":"2026-05-17T23:54:26.314790+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7P5C7JBXFOG","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7P5C7JBXFOGJ57J","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7P5C7JB","created_at":"2026-05-18T12:32:28.185984+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/H7P5C7JBXFOGJ57JPS5DP2U4WZ","json":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ.json","graph_json":"https://pith.science/api/pith-number/H7P5C7JBXFOGJ57JPS5DP2U4WZ/graph.json","events_json":"https://pith.science/api/pith-number/H7P5C7JBXFOGJ57JPS5DP2U4WZ/events.json","paper":"https://pith.science/paper/H7P5C7JB"},"agent_actions":{"view_html":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ","download_json":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ.json","view_paper":"https://pith.science/paper/H7P5C7JB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.07290&json=true","fetch_graph":"https://pith.science/api/pith-number/H7P5C7JBXFOGJ57JPS5DP2U4WZ/graph.json","fetch_events":"https://pith.science/api/pith-number/H7P5C7JBXFOGJ57JPS5DP2U4WZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ/action/storage_attestation","attest_author":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ/action/author_attestation","sign_citation":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ/action/citation_signature","submit_replication":"https://pith.science/pith/H7P5C7JBXFOGJ57JPS5DP2U4WZ/action/replication_record"}},"created_at":"2026-05-17T23:54:26.314790+00:00","updated_at":"2026-05-17T23:54:26.314790+00:00"}