{"id": "card_chain_coates_wiles_1977", "kind": "reference", "title": "Coates 1977 — On the conjecture of Birch and Swinnerton-Dyer", "body": "J. Coates, A. Wiles (1977). On the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977) 223–251. DOI 10.1007/BF01402975. Canonical: https://doi.org/10.1007/BF01402975. Cited by its record. License as found: Springer TDM license — publisher's copyright, cited. What it gave the chain: for curves with complex multiplication, L(E, 1) != 0 forces rank zero - the first theorem toward the conjecture.", "source": {"label": "J. Coates, A. Wiles (1977), Invent. Math. 39 (1977) 223–251", "url": "https://doi.org/10.1007/BF01402975", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "1977", "coates", "mathematics"], "subject": "On the conjecture of Birch and Swinnerton-Dyer", "connections": [{"to_card_id": "card_chain_birch_swinnerton_dyer_1965", "relationship": "builds_on", "evidence": "for curves with complex multiplication, L(E, 1) != 0 forces rank zero - the first theorem toward the conjecture"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.chain", "facets": {"subject": ["1977", "coates", "mathematics", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "J. Coates, A. Wiles (1977), Invent. Math. 39 (1977) 223–251", "authority": "reference", "posted": "", "standing": "", "link": {"url": "https://doi.org/10.1007/BF01402975", "host": "doi.org", "provider": "", "titled": "Coates 1977 — On the conjecture of Birch and Swinnerton-Dyer", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_chain_birch_swinnerton_dyer_1965", "title": "Birch 1965 — Notes on elliptic curves. II", "relationship": "builds on", "why": "for curves with complex multiplication, L(E, 1) != 0 forces rank zero - the first theorem toward the conjecture", "href": "/card/card_chain_birch_swinnerton_dyer_1965", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_coates_wiles_1977", "next_step": {"do": "read the source itself", "door": "FIND", "web": "/reader.html?card=card_chain_coates_wiles_1977"}, "ends": "a verdict or a card · the trail · a seal · one next step"}}