{"id":"https://openalex.org/W7212565343","doi":"https://doi.org/10.48550/arxiv.2609.12846","title":"Classification of torsion of elliptic curves over quintic fields","display_name":"Classification of torsion of elliptic curves over quintic fields","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212565343","doi":"https://doi.org/10.48550/arxiv.2609.12846"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12846","pdf_url":"https://arxiv.org/pdf/2609.12846","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081214859","display_name":"Filip Najman","orcid":"https://orcid.org/0000-0002-0994-0846","observed_orcids":["https://orcid.org/0000-0002-0994-0846"]},"institutions":[{"id":"https://openalex.org/I181343428","display_name":"University of Zagreb","ror":"https://ror.org/00mv6sv71","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428"]}],"countries":["HR"],"is_corresponding":true,"raw_author_name":"Najman, Filip","raw_affiliation_strings":["University of Zagreb , Faculty of Science , Department of Mathematics , Bijeni\u010dka cesta 30 , 10000 Zagreb , Croatia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Zagreb , Faculty of Science , Department of Mathematics , Bijeni\u010dka cesta 30 , 10000 Zagreb , Croatia","institution_ids":["https://openalex.org/I181343428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081214859"],"corresponding_institution_ids":["https://openalex.org/I181343428"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9726999998092651,"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":0.9726999998092651,"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":0.024700000882148743,"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":0.00039999998989515007,"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","display_name":"elliptic curves","score":0.8399999737739563},{"id":"https://openalex.org/keywords/torsion-groups","display_name":"torsion groups","score":0.8939999938011169},{"id":"https://openalex.org/keywords/2-isogeny","display_name":"2-isogeny","score":0.7910000085830688},{"id":"https://openalex.org/keywords/cyclic-torsion","display_name":"cyclic torsion","score":0.3959999978542328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8126999735832214},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.7889999747276306},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.6786999702453613},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.5360999703407288},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.51419997215271},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5127999782562256},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.45210000872612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43059998750686646},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.42160001397132874},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.37279999256134033},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.30630001425743103},{"id":"https://openalex.org/C87905105","wikidata":"https://www.wikidata.org/wiki/Q5284582","display_name":"Division polynomials","level":5,"score":0.2987000048160553},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.2985999882221222},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12846","pdf_url":"https://arxiv.org/pdf/2609.12846","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.12846","doi":"https://doi.org/10.48550/arxiv.2609.12846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12846","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"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":"pmh:oai:arXiv.org:2609.12846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12846","pdf_url":"https://arxiv.org/pdf/2609.12846","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1717035117","display_name":null,"funder_award_id":"PK.1.1.10","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G2319283480","display_name":null,"funder_award_id":"IK IA 1.1.3","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2404623046","display_name":"Number theory and arithemtic geometry","funder_award_id":"IP-2022-10-5008","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G2450643449","display_name":null,"funder_award_id":"PK.1.1.10.0004","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2719336981","display_name":null,"funder_award_id":"PK.1.1.10.0004","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G3408410167","display_name":null,"funder_award_id":"IP-2022-10","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G3611179903","display_name":null,"funder_award_id":"2021-2026","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3678004387","display_name":null,"funder_award_id":"PK.1.1.10.0004","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G3866112975","display_name":null,"funder_award_id":"IP-2022-10-5008","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4938354709","display_name":null,"funder_award_id":"2021-2026","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G675437911","display_name":null,"funder_award_id":"2021 2027","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7799207878","display_name":null,"funder_award_id":"2021\u20132027","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320310928","display_name":"Sveu\u010dili\u0161te u Zagrebu","ror":"https://ror.org/00mv6sv71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322674","display_name":"Hrvatska Zaklada za Znanost","ror":"https://ror.org/03n51vw80"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212565343.pdf","grobid_xml":"https://content.openalex.org/works/W7212565343.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2517959248","https://openalex.org/W4415033153","https://openalex.org/W2807992895","https://openalex.org/W4293437806","https://openalex.org/W7115003719","https://openalex.org/W2155694865","https://openalex.org/W2512949458","https://openalex.org/W7043952005","https://openalex.org/W1977318446","https://openalex.org/W2884293274"],"abstract_inverted_index":{"We":[0],"determine":[1],"all":[2],"the":[3,8,22,48,51,54,65,90,98,126],"groups":[4,23,38],"that":[5,24],"appear":[6],"as":[7],"torsion":[9,106],"group":[10,91,107],"of":[11,47,128],"an":[12],"elliptic":[13,62],"curve":[14,63],"over":[15,73],"a":[16,60,74,103],"quintic":[17,76],"number":[18],"field.":[19,77],"Apart":[20],"from":[21],"already":[25],"occur":[26],"infinitely":[27],"often,":[28],"which":[29,70,102],"were":[30,84],"determined":[31],"by":[32,59,67,86,115],"Derickx":[33,116],"and":[34,42,53,64,82,95,117,119,125],"Sutherland,":[35],"exactly":[36],"three":[37],"occur:":[39],"$\\mathbb{Z}/28\\mathbb{Z}$,":[40],"$\\mathbb{Z}/30\\mathbb{Z}$":[41,83],"$\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/18\\mathbb{Z}$.":[43],"Up":[44],"to":[45],"isomorphism":[46],"pair":[49],"$(K,E)$,":[50],"first":[52],"third":[55],"are":[56,71,120],"each":[57],"realised":[58],"single":[61],"second":[66],"two":[68],"curves,":[69],"$2$-isogenous":[72],"common":[75],"The":[78,109],"curves":[79],"realising":[80],"$\\mathbb{Z}/28\\mathbb{Z}$":[81],"found":[85],"van":[87],"Hoeij,":[88],"while":[89],"$\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/18\\mathbb{Z}$":[92],"is":[93,97],"new,":[94],"$5$":[96],"smallest":[99],"degree":[100],"in":[101],"non-cyclic":[104],"sporadic":[105],"occurs.":[108],"methods":[110],"improve":[111],"on":[112,122],"those":[113],"developed":[114],"Najman,":[118],"based":[121],"Hecke":[123],"sieves":[124],"arithmetic":[127],"cuspidal":[129],"divisor":[130],"classes.":[131]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-15T00:00:00"}
