{"id":"https://openalex.org/W2075752836","doi":"https://doi.org/10.1090/s0025-5718-2014-02858-5","title":"Explicit \ud835\udc5b-descent on elliptic curves III. Algorithms","display_name":"Explicit \ud835\udc5b-descent on elliptic curves III. Algorithms","publication_year":2014,"publication_date":"2014-07-29","ids":{"openalex":"https://openalex.org/W2075752836","doi":"https://doi.org/10.1090/s0025-5718-2014-02858-5","mag":"2075752836"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02858-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02858-5","pdf_url":"https://www.ams.org/mcom/2015-84-292/S0025-5718-2014-02858-5/S0025-5718-2014-02858-5.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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2015-84-292/S0025-5718-2014-02858-5/S0025-5718-2014-02858-5.pdf","any_repository_has_fulltext":true},"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/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"J. Cremona","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom","Mathematics Institute, University of Warwick, Coventry, CV4 7AL United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry, CV4 7AL United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020020594","display_name":"Tom Fisher","orcid":"https://orcid.org/0000-0003-2565-8805"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"T. Fisher","raw_affiliation_strings":["University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom","University of Cambridge, DPMMS Centre for Mathematical Sciences, Wilberforce road, Cambridge CB3 0WB, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge, DPMMS Centre for Mathematical Sciences, Wilberforce road, Cambridge CB3 0WB, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043590097","display_name":"Cathy O'Neil","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117172","display_name":"Craig Newmark Graduate School of Journalism at the City University of New York","ror":"https://ror.org/02ae4je14","country_code":"US","type":"education","lineage":["https://openalex.org/I4210117172"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. O\u2019Neil","raw_affiliation_strings":["505 Pulitzer Hall, Columbia University Graduate School of Journalism, 2950 Broadway, New York, New York 10027"],"affiliations":[{"raw_affiliation_string":"505 Pulitzer Hall, Columbia University Graduate School of Journalism, 2950 Broadway, New York, New York 10027","institution_ids":["https://openalex.org/I4210117172","https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":null,"display_name":"D. Simon","orcid":null},"institutions":[{"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":false,"raw_author_name":"D. Simon","raw_affiliation_strings":["Universit\u00c3\u00a9 de Caen, Campus II - Boulevard Mar\u00c3\u00a9chal Juin, BP 5186\u00e2\u0080\u009314032, Caen, France","Universit\u00e9 de Caen, Campus II - Boulevard Mar\u00e9chal Juin, BP 5186\u201314032, Caen, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00c3\u00a9 de Caen, Campus II - Boulevard Mar\u00c3\u00a9chal Juin, BP 5186\u00e2\u0080\u009314032, Caen, France","institution_ids":["https://openalex.org/I98702875"]},{"raw_affiliation_string":"Universit\u00e9 de Caen, Campus II - Boulevard Mar\u00e9chal Juin, BP 5186\u201314032, Caen, France","institution_ids":["https://openalex.org/I98702875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069201482","display_name":"Michael Stoll","orcid":"https://orcid.org/0000-0001-5868-2962"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Stoll","raw_affiliation_strings":["Mathematisches Institut, Universit\u00c3\u00a4t Bayreuth, 95440 Bayreuth, Germany","Mathematisches Institut Universit\u00e4t Bayreuth 95440 Bayreuth, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00c3\u00a4t Bayreuth, 95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]},{"raw_affiliation_string":"Mathematisches Institut Universit\u00e4t Bayreuth 95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084924590"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":1.8311,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.8406762,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"292","first_page":"895","last_page":"922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8199609518051147},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.7058740854263306},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.6794828176498413},{"id":"https://openalex.org/keywords/magma","display_name":"Magma","score":0.6639692187309265},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5155863165855408},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5028602480888367},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4988443851470947},{"id":"https://openalex.org/keywords/supersingular-elliptic-curve","display_name":"Supersingular elliptic curve","score":0.49614962935447693},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.4382484257221222},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41818681359291077},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.41238248348236084},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3789069652557373},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3516141176223755},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.18921509385108948}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8199609518051147},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.7058740854263306},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.6794828176498413},{"id":"https://openalex.org/C183222429","wikidata":"https://www.wikidata.org/wiki/Q42278","display_name":"Magma","level":3,"score":0.6639692187309265},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5155863165855408},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5028602480888367},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4988443851470947},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.49614962935447693},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.4382484257221222},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41818681359291077},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.41238248348236084},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3789069652557373},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3516141176223755},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.18921509385108948},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C120806208","wikidata":"https://www.wikidata.org/wiki/Q8072","display_name":"Volcano","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C165205528","wikidata":"https://www.wikidata.org/wiki/Q83371","display_name":"Seismology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02858-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02858-5","pdf_url":"https://www.ams.org/mcom/2015-84-292/S0025-5718-2014-02858-5/S0025-5718-2014-02858-5.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"},{"id":"pmh:oai:wrap.warwick.ac.uk:128482","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1107.3516","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1107.3516","pdf_url":"https://arxiv.org/pdf/1107.3516","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.9675","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.9675","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe2.uni-bayreuth.de/stoll/papers/Explicit-Descent-III.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02351088v1","is_oa":false,"landing_page_url":"https://normandie-univ.hal.science/hal-02351088","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2015, 84 (292), pp.895-922. &#x27E8;10.1090/S0025-5718-2014-02858-5&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:wrap.warwick.ac.uk:48654","is_oa":false,"landing_page_url":"http://wrap.warwick.ac.uk/48654/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Working or Discussion Paper"},{"id":"doi:10.4230/lipics.icalp.2019.62","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2019.62","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2014-02858-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02858-5","pdf_url":"https://www.ams.org/mcom/2015-84-292/S0025-5718-2014-02858-5/S0025-5718-2014-02858-5.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":[{"id":"https://openalex.org/G694729825","display_name":null,"funder_award_id":"EP/K034383/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2075752836.pdf","grobid_xml":"https://content.openalex.org/works/W2075752836.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W47614929","https://openalex.org/W131639599","https://openalex.org/W187177602","https://openalex.org/W638707814","https://openalex.org/W1496801598","https://openalex.org/W1509364989","https://openalex.org/W1511533198","https://openalex.org/W1513099043","https://openalex.org/W1522188983","https://openalex.org/W1523310006","https://openalex.org/W1553928702","https://openalex.org/W1587972395","https://openalex.org/W1865765009","https://openalex.org/W1976120821","https://openalex.org/W1976677460","https://openalex.org/W1981287047","https://openalex.org/W1982175684","https://openalex.org/W1986401942","https://openalex.org/W1990220158","https://openalex.org/W2000568564","https://openalex.org/W2003929417","https://openalex.org/W2010063482","https://openalex.org/W2010498196","https://openalex.org/W2020601656","https://openalex.org/W2024216855","https://openalex.org/W2058871238","https://openalex.org/W2062350069","https://openalex.org/W2075752836","https://openalex.org/W2078637176","https://openalex.org/W2085914589","https://openalex.org/W2091527967","https://openalex.org/W2105838031","https://openalex.org/W2110288166","https://openalex.org/W2113579323","https://openalex.org/W2122915943","https://openalex.org/W2171649705","https://openalex.org/W2472843284","https://openalex.org/W2500411863","https://openalex.org/W2963065034","https://openalex.org/W2963478770","https://openalex.org/W2963701088","https://openalex.org/W3007836994","https://openalex.org/W4206571527","https://openalex.org/W4238294707","https://openalex.org/W4285719527","https://openalex.org/W4298050776"],"related_works":["https://openalex.org/W2548082687","https://openalex.org/W3172172454","https://openalex.org/W3211097549","https://openalex.org/W4237299327","https://openalex.org/W4300923231","https://openalex.org/W74147110","https://openalex.org/W1591034480","https://openalex.org/W3099821488","https://openalex.org/W2254579146","https://openalex.org/W2963339048"],"abstract_inverted_index":{"This":[0,144],"is":[1,136,145],"the":[2,13,33,97,121],"third":[3],"in":[4,9,55,96,127],"a":[5],"series":[6],"of":[7,28,35,41,133,146],"papers":[8],"which":[10],"we":[11,92],"study":[12],"<inline-formula":[14,43,56,99],"content-type=\"math/mathml\">":[15,44,57,100],"<mml:math":[16,45,58,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,46,59,102],"alttext=\"n\">":[18,47],"<mml:semantics>":[19,48,67,106],"<mml:mi>n</mml:mi>":[20,49,76,108],"<mml:annotation":[21,50,83,112],"encoding=\"application/x-tex\">n</mml:annotation>":[22,51],"</mml:semantics>":[23,52,86,114],"</mml:math>":[24,53,87,115],"</inline-formula>":[25,54,88,116],"-Selmer":[26],"group":[27],"an":[29,137],"elliptic":[30,118],"curve,":[31],"with":[32],"aim":[34],"representing":[36],"its":[37],"elements":[38],"as":[39],"curves":[40,119],"degree":[42],"alttext=\"double-struck":[60],"upper":[61],"P":[62],"Superscript":[63],"n":[64],"minus":[65],"1\">":[66],"<mml:msup>":[68],"<mml:mrow":[69,74],"class=\"MJX-TeXAtom-ORD\">":[70,75],"<mml:mi":[71],"mathvariant=\"double-struck\">P</mml:mi>":[72],"</mml:mrow>":[73,81,111],"<mml:mo>":[77],"\u2212":[78],"</mml:mo>":[79],"<mml:mn>1</mml:mn>":[80],"</mml:msup>":[82],"encoding=\"application/x-tex\">\\mathbb":[84],"{P}^{n-1}</mml:annotation>":[85],".":[89,129],"The":[90],"methods":[91],"describe":[93],"are":[94],"practical":[95],"case":[98],"alttext=\"n":[103],"equals":[104],"3\">":[105],"<mml:mrow>":[107],"<mml:mo>=</mml:mo>":[109],"<mml:mn>3</mml:mn>":[110],"encoding=\"application/x-tex\">n=3</mml:annotation>":[113],"for":[117,139,149,155],"over":[120],"rationals,":[122],"and":[123],"have":[124],"been":[125],"implemented":[126],"<sans-serif>MAGMA</sans-serif>":[128],"One":[130],"important":[131],"ingredient":[132],"our":[134],"work":[135],"algorithm":[138],"trivialising":[140],"central":[141],"simple":[142],"algebras.":[143],"independent":[147],"interest;":[148],"example,":[150],"it":[151],"could":[152],"be":[153],"used":[154],"parametrising":[156],"Brauer-Severi":[157],"surfaces.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}