{"id":"https://openalex.org/W7220458949","doi":"https://doi.org/10.48550/arxiv.2610.03100","title":"Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves","display_name":"Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220458949","doi":"https://doi.org/10.48550/arxiv.2610.03100"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03100","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03100","pdf_url":"https://arxiv.org/pdf/2610.03100","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/2610.03100","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005988524","display_name":"Noriyuki Otsubo","orcid":"https://orcid.org/0000-0002-7880-0505","observed_orcids":["https://orcid.org/0000-0002-7880-0505"]},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Otsubo, Noriyuki","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS AND INFORMATICS , CHIBA UNIVERSITY , INAGE , CHIBA , 263-8522 JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS AND INFORMATICS , CHIBA UNIVERSITY , INAGE , CHIBA , 263-8522 JAPAN","institution_ids":["https://openalex.org/I159385669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005988524"],"corresponding_institution_ids":["https://openalex.org/I159385669"],"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":0.9926999807357788,"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":0.9926999807357788,"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":0.0019000000320374966,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0015999999595806003,"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/isogenies","display_name":"isogenies","score":0.7390000224113464},{"id":"https://openalex.org/keywords/ordinary-elliptic-curves","display_name":"ordinary elliptic curves","score":0.9440000057220459},{"id":"https://openalex.org/keywords/characteristic-3","display_name":"characteristic 3","score":0.8209999799728394},{"id":"https://openalex.org/keywords/hypergeometric-functions","display_name":"hypergeometric functions","score":0.8600000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8125},{"id":"https://openalex.org/C92727272","wikidata":"https://www.wikidata.org/wiki/Q3001190","display_name":"Edwards curve","level":5,"score":0.5680999755859375},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5480999946594238},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.5397999882698059},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.444599986076355},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.42010000348091125},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.37929999828338623},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36329999566078186},{"id":"https://openalex.org/C104993295","wikidata":"https://www.wikidata.org/wiki/Q17023345","display_name":"Hessian form of an elliptic curve","level":5,"score":0.35749998688697815},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.30720001459121704},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03100","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03100","pdf_url":"https://arxiv.org/pdf/2610.03100","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.2610.03100","doi":"https://doi.org/10.48550/arxiv.2610.03100","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03100","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03100","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03100","pdf_url":"https://arxiv.org/pdf/2610.03100","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":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220458949.pdf","grobid_xml":"https://content.openalex.org/works/W7220458949.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4406023336","https://openalex.org/W7213319844"],"related_works":["https://openalex.org/W1977700936","https://openalex.org/W2167229579","https://openalex.org/W2319891616","https://openalex.org/W7155514777","https://openalex.org/W1567236289","https://openalex.org/W1590120681","https://openalex.org/W7123250052","https://openalex.org/W2029148888","https://openalex.org/W7099275612","https://openalex.org/W7057320103"],"abstract_inverted_index":{"We":[0,50],"construct":[1],"degree-three":[2],"isogenies":[3],"of":[4,12,22,36,55],"Hesse":[5,57],"elliptic":[6,39],"curves":[7,58],"over":[8],"an":[9,28,37],"arbitrary":[10],"field":[11],"characteristic":[13,42],"different":[14],"from":[15],"three,":[16],"which":[17],"correspond":[18],"to":[19],"a":[20],"step":[21],"the":[23,32,45,53,56],"cubic":[24,47],"arithmetic-geometric":[25,48],"mean.":[26,49],"As":[27],"application,":[29],"we":[30],"describe":[31],"Serre-Tate":[33],"canonical":[34],"lift":[35],"ordinary":[38],"curve":[40],"in":[41],"three":[43],"by":[44],"3-adic":[46],"also":[51],"discuss":[52],"relations":[54],"with":[59],"complex":[60],"and":[61],"finite":[62],"hypergeometric":[63],"functions.":[64]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-06T00:00:00"}