{"id":"https://openalex.org/W7225450283","doi":"https://doi.org/10.5281/zenodo.24029195","title":"Elliptic Curve over \u211a Achieves Rank \u2265 29, Breaking Record \u2014 E8 Intelligence Research","display_name":"Elliptic Curve over \u211a Achieves Rank \u2265 29, Breaking Record \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225450283","doi":"https://doi.org/10.5281/zenodo.24029195"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24029195","doi":"https://doi.org/10.5281/zenodo.24029195","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24029195","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153285007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/elliptic-curves-over-the-rationals","display_name":"elliptic curves over the rationals","score":0.9440000057220459},{"id":"https://openalex.org/keywords/mordell-weil-rank","display_name":"Mordell-Weil rank","score":0.9570000171661377},{"id":"https://openalex.org/keywords/mordell-weil-lattice","display_name":"Mordell-Weil lattice","score":0.8970000147819519},{"id":"https://openalex.org/keywords/height-pairing","display_name":"height pairing","score":0.7329999804496765},{"id":"https://openalex.org/keywords/birch-swinnerton-dyer-conjecture","display_name":"Birch and Swinnerton-Dyer conjecture","score":0.8870000243186951},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.46399998664855957}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7537000179290771},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6859999895095825},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6427000164985657},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6331999897956848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5357000231742859},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.5309000015258789},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.5295000076293945},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.49059998989105225},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4415999948978424},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3174999952316284},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31700000166893005},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29910001158714294},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.2906999886035919},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.267300009727478}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24029195","doi":"https://doi.org/10.5281/zenodo.24029195","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24029196","doi":"https://doi.org/10.5281/zenodo.24029196","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24029195","doi":"https://doi.org/10.5281/zenodo.24029195","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7220998194","https://openalex.org/W7206216391","https://openalex.org/W7214943236","https://openalex.org/W7210267431","https://openalex.org/W7207557645","https://openalex.org/W7210285622","https://openalex.org/W7206204904","https://openalex.org/W7221343996","https://openalex.org/W7208822036","https://openalex.org/W7221060877"],"abstract_inverted_index":{"FINDING:":[0,84],"Elliptic":[1],"curve":[2,88],"over":[3],"\u211a":[4],"with":[5,26],"rank":[6,27],"\u2265":[7,29],"29":[8,42,56],"discovered,":[9],"breaking":[10],"previous":[11],"record":[12],"of":[13,41,55,86,93,103,119],"28":[14],"(Elkies":[15],"2006)":[16],"|":[17,51,81,96],"MATH:":[18,97],"y\u00b2":[19],"=":[20,49,64,101],"x\u00b3":[21],"+":[22,24],"ax":[23],"b":[25],"r":[28],"29;":[30],"Mordell-Weil":[31,60],"group":[32],"E(\u211a)":[33],"\u2245":[34],"\u2124\u00b2\u2079":[35],"\u2295":[36],"Torsion;":[37],"height":[38,68],"pairing":[39],"matrix":[40],"independent":[43,57],"points;":[44],"BSD":[45],"conjecture":[46],"predicts":[47],"L\u207d\u02b3\u207e(E,1)/r!":[48],"\u03a9\u00b7Reg\u00b7\u220fc\u209a\u00b7|\u0428|/|Tors|\u00b2":[50],"CONNECTION:":[52],"Lattice":[53],"basis":[54],"points":[58],"in":[59],"lattice;":[61],"regulator":[62],"Reg":[63],"det(\u27e8P\u1d62,P\u2c7c\u27e9)":[65],"encodes":[66],"geometric":[67],"pairing;":[69],"no":[70],"golden":[71],"ratio/CM":[72],"structure":[73],"\u2014":[74],"generic":[75],"high-rank":[76],"construction":[77],"via":[78],"Mestre-Nagao":[79],"method":[80],"DEPTH:":[82],"9":[83],"Classification":[85],"elliptic":[87],"configurations":[89],"on":[90,105],"Fano":[91,98],"surface":[92,99],"cubic":[94,106],"threefold":[95,107],"S":[100],"F(X)":[102],"lines":[104],"X":[108],"\u2282":[109],"\u2119":[110],"Author:":[111],"Andrew":[112],"Stewart":[113],"Caldin,":[114],"Independent":[115],"Researcher,":[116],"UK.":[117],"Part":[118],"the":[120],"E8":[121],"Intelligence":[122],"Research":[123],"series.":[124],"Platform:":[125],"e8intelligence.com":[126]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}