{"id":"https://openalex.org/W2037752680","doi":"https://doi.org/10.1090/s0025-5718-99-01055-8","title":"Computing the rank of elliptic curves over real quadratic number fields of class number 1","display_name":"Computing the rank of elliptic curves over real quadratic number fields of class number 1","publication_year":1999,"publication_date":"1999-02-15","ids":{"openalex":"https://openalex.org/W2037752680","doi":"https://doi.org/10.1090/s0025-5718-99-01055-8","mag":"2037752680"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01055-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01055-8","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01055-8/S0025-5718-99-01055-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01055-8/S0025-5718-99-01055-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084924590","display_name":"J. E. Cremona","orcid":"https://orcid.org/0000-0002-7212-0162"},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. Cremona","raw_affiliation_strings":["Department of Mathematics, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE, U.K","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001989791","display_name":"P. Serf","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"P. Serf","raw_affiliation_strings":["Fachbereich 9 Mathematik, Universit\u00e4t des Saarlandes, Postfach 151150, D-66041 Saarbr\u00fccken, Germany","Fachbereich 9 Mathematik, Universit\u00e4t des Saarlandes, Postfach 151150 D-66041 Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich 9 Mathematik, Universit\u00e4t des Saarlandes, Postfach 151150, D-66041 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"Fachbereich 9 Mathematik, Universit\u00e4t des Saarlandes, Postfach 151150 D-66041 Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2472,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92198122,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"68","issue":"227","first_page":"1187","last_page":"1200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6309467554092407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6025221347808838},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5650071501731873},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5281262993812561},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5194277763366699},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5000402927398682},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47290122509002686},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4594178795814514},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3362233638763428},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3266446888446808},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25803902745246887},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18628740310668945},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1591968834400177},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.152427077293396}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6309467554092407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6025221347808838},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5650071501731873},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5281262993812561},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5194277763366699},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5000402927398682},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47290122509002686},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4594178795814514},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3362233638763428},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3266446888446808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25803902745246887},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18628740310668945},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1591968834400177},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.152427077293396}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-99-01055-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01055-8","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01055-8/S0025-5718-99-01055-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01055-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01055-8","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01055-8/S0025-5718-99-01055-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037752680.pdf","grobid_xml":"https://content.openalex.org/works/W2037752680.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1529471319","https://openalex.org/W1568270702","https://openalex.org/W1604636366","https://openalex.org/W2006264362","https://openalex.org/W2010380496","https://openalex.org/W2118942434","https://openalex.org/W4241352183","https://openalex.org/W4247003770","https://openalex.org/W4254792708","https://openalex.org/W4292482156"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W1888039291","https://openalex.org/W1944395271","https://openalex.org/W2336546597","https://openalex.org/W1983888982","https://openalex.org/W4226038908","https://openalex.org/W3215550945"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"describe":[4],"an":[5,12],"algorithm":[6,26],"for":[7,36],"computing":[8],"the":[9,28],"rank":[10],"of":[11,21],"elliptic":[13],"curve":[14],"defined":[15],"over":[16,38],"a":[17],"real":[18],"quadratic":[19],"field":[20],"class":[22],"number":[23],"one.":[24],"This":[25],"extends":[27],"one":[29],"originally":[30],"described":[31],"by":[32],"Birch":[33],"and":[34],"Swinnerton-Dyer":[35],"curves":[37],"Q":[39],"\\mathbb":[40],"{Q}":[41],".":[42],"Several":[43],"examples":[44],"are":[45],"included.":[46]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
