{"id":"https://openalex.org/W1986401942","doi":"https://doi.org/10.1112/s1461157000000668","title":"Computing the Rank of Elliptic Curves over Number Fields","display_name":"Computing the Rank of Elliptic Curves over Number Fields","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1986401942","doi":"https://doi.org/10.1112/s1461157000000668","mag":"1986401942"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000000668","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000668","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8FAFF26D93D01A154C51CF897E4BE6CD/S1461157000000668a.pdf/div-class-title-computing-the-rank-of-elliptic-curves-over-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8FAFF26D93D01A154C51CF897E4BE6CD/S1461157000000668a.pdf/div-class-title-computing-the-rank-of-elliptic-curves-over-number-fields-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Denis Simon","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110254","display_name":"Laboratoire de Physique Corpusculaire de Caen","ror":"https://ror.org/022txr781","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210110254","https://openalex.org/I4210133362","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Denis Simon","raw_affiliation_strings":["Universit\u00e9 de Caen \u2013 France, Campus II \u2013 Boulevard Mar\u00e9chal Juin, BP 5186, 14032 Caen cedex, France","Universit\u00e9 de Caen \u2013 France, Campus II \u2013 Boulevard Mar\u00e9chal Juin, BP 5186, 14032 Caen cedex, France, Denis.Simon@math.unicaen.fr"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Caen \u2013 France, Campus II \u2013 Boulevard Mar\u00e9chal Juin, BP 5186, 14032 Caen cedex, France","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I4210110254"]},{"raw_affiliation_string":"Universit\u00e9 de Caen \u2013 France, Campus II \u2013 Boulevard Mar\u00e9chal Juin, BP 5186, 14032 Caen cedex, France, Denis.Simon@math.unicaen.fr","institution_ids":["https://openalex.org/I98702875"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210110254","https://openalex.org/I98702875"],"apc_list":null,"apc_paid":null,"fwci":6.2584,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.96203691,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":null,"first_page":"7","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9988999962806702,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9710000157356262,"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/mathematics","display_name":"Mathematics","score":0.8439128398895264},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.7096909284591675},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.6362992525100708},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6044980883598328},{"id":"https://openalex.org/keywords/edwards-curve","display_name":"Edwards curve","score":0.5358966588973999},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.534953236579895},{"id":"https://openalex.org/keywords/hessian-form-of-an-elliptic-curve","display_name":"Hessian form of an elliptic curve","score":0.4925130307674408},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.469951868057251},{"id":"https://openalex.org/keywords/counting-points-on-elliptic-curves","display_name":"Counting points on elliptic curves","score":0.42334115505218506},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35123130679130554},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3280392289161682},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31373077630996704},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2092709243297577},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.18067756295204163}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8439128398895264},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7096909284591675},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.6362992525100708},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6044980883598328},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.5358966588973999},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.534953236579895},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.4925130307674408},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.469951868057251},{"id":"https://openalex.org/C68782407","wikidata":"https://www.wikidata.org/wiki/Q5177153","display_name":"Counting points on elliptic curves","level":5,"score":0.42334115505218506},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35123130679130554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3280392289161682},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31373077630996704},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2092709243297577},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.18067756295204163}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157000000668","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000668","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8FAFF26D93D01A154C51CF897E4BE6CD/S1461157000000668a.pdf/div-class-title-computing-the-rank-of-elliptic-curves-over-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1112/s1461157000000668","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000668","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8FAFF26D93D01A154C51CF897E4BE6CD/S1461157000000668a.pdf/div-class-title-computing-the-rank-of-elliptic-curves-over-number-fields-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1986401942.pdf","grobid_xml":"https://content.openalex.org/works/W1986401942.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W131639599","https://openalex.org/W1496801598","https://openalex.org/W1511533198","https://openalex.org/W1523310006","https://openalex.org/W1529471319","https://openalex.org/W1577641406","https://openalex.org/W1598030683","https://openalex.org/W1608498041","https://openalex.org/W1976120821","https://openalex.org/W1982264769","https://openalex.org/W2037752680","https://openalex.org/W2038180223","https://openalex.org/W2040541934","https://openalex.org/W2053499741","https://openalex.org/W2054773951","https://openalex.org/W2066187694","https://openalex.org/W2118942434","https://openalex.org/W2168648858","https://openalex.org/W2478134785","https://openalex.org/W2489377303","https://openalex.org/W2774686533","https://openalex.org/W2962988729","https://openalex.org/W3007836994","https://openalex.org/W3215931976","https://openalex.org/W4235125007","https://openalex.org/W4241352183","https://openalex.org/W4293193836","https://openalex.org/W6747379421"],"related_works":["https://openalex.org/W2548082687","https://openalex.org/W3138493780","https://openalex.org/W3172172454","https://openalex.org/W2374597101","https://openalex.org/W4245179206","https://openalex.org/W74147110","https://openalex.org/W2559355736","https://openalex.org/W3211097549","https://openalex.org/W28923676","https://openalex.org/W2071707911"],"abstract_inverted_index":{"Abstract":[0],"This":[1,24],"paper":[2],"describes":[3],"an":[4,13],"algorithm":[5],"of":[6,12,33],"2-descent":[7],"for":[8],"computing":[9],"the":[10],"rank":[11],"elliptic":[14],"curve":[15],"without":[16],"2-torsion,":[17],"defined":[18],"over":[19],"a":[20],"general":[21],"number":[22],"field.":[23],"allows":[25],"one,":[26],"in":[27],"practice,":[28],"to":[29,37],"deal":[30],"with":[31],"fields":[32],"degree":[34],"from":[35],"1":[36],"5.":[38]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}