{"id":"https://openalex.org/W4312205633","doi":"https://doi.org/10.1145/3573105.3575682","title":"Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves","display_name":"Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves","publication_year":2023,"publication_date":"2023-01-11","ids":{"openalex":"https://openalex.org/W4312205633","doi":"https://doi.org/10.1145/3573105.3575682"},"language":"en","primary_location":{"id":"doi:10.1145/3573105.3575682","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3573105.3575682","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3573105.3575682","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3573105.3575682","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042441311","display_name":"Anne Baanen","orcid":"https://orcid.org/0000-0001-8497-3683"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Anne Baanen","raw_affiliation_strings":["Vrije Universiteit Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam, Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011843451","display_name":"Alex J. Best","orcid":"https://orcid.org/0000-0002-5741-674X"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Alex J. Best","raw_affiliation_strings":["Vrije Universiteit Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam, Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037277043","display_name":"Nirvana Coppola","orcid":"https://orcid.org/0000-0002-8313-5984"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nirvana Coppola","raw_affiliation_strings":["Vrije Universiteit Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam, Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007693622","display_name":"Sander R. Dahmen","orcid":"https://orcid.org/0000-0002-0014-0789"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sander R. Dahmen","raw_affiliation_strings":["Vrije Universiteit Amsterdam, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam, Netherlands","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1495,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.910438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"47","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9955999851226807,"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":0.9955999851226807,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9812999963760376,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9800000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.7158732414245605},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.6765620708465576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.653626024723053},{"id":"https://openalex.org/keywords/ideal-class-group","display_name":"Ideal class group","score":0.6439935564994812},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6041843295097351},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5652486085891724},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.562653660774231},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5273457765579224},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5234370231628418},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5099138021469116},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.48661884665489197},{"id":"https://openalex.org/keywords/algebraic-number-theory","display_name":"Algebraic number theory","score":0.47354811429977417},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.45248347520828247},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.4431207776069641},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43066030740737915},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.407162606716156},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3849383592605591},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33057546615600586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23287972807884216},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17463737726211548},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16751185059547424}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.7158732414245605},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.6765620708465576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.653626024723053},{"id":"https://openalex.org/C8367249","wikidata":"https://www.wikidata.org/wiki/Q912083","display_name":"Ideal class group","level":3,"score":0.6439935564994812},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6041843295097351},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5652486085891724},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.562653660774231},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5273457765579224},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5234370231628418},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5099138021469116},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.48661884665489197},{"id":"https://openalex.org/C52690540","wikidata":"https://www.wikidata.org/wiki/Q613048","display_name":"Algebraic number theory","level":3,"score":0.47354811429977417},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.45248347520828247},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.4431207776069641},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43066030740737915},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.407162606716156},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3849383592605591},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33057546615600586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23287972807884216},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17463737726211548},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16751185059547424},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3573105.3575682","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3573105.3575682","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3573105.3575682","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},{"id":"pmh:oai:research.vu.nl:openaire/cbfcb207-66a1-426b-8c00-7a1bdd3826e8","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/cbfcb207-66a1-426b-8c00-7a1bdd3826e8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Baanen, A, Best, A J, Coppola, N & Dahmen, S R 2023, Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves. in R Krebbers, D Traytel, B Pientka & S Zdancewic (eds), CPP 2023 : Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs. Association for Computing Machinery, Inc, pp. 47-62, 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2023 - Co-located with POPL 2023, Boston, United States, 16/01/23. https://doi.org/10.1145/3573105.3575682","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/cbfcb207-66a1-426b-8c00-7a1bdd3826e8","is_oa":true,"landing_page_url":"https://hdl.handle.net/1871.1/cbfcb207-66a1-426b-8c00-7a1bdd3826e8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Baanen, A, Best, A J, Coppola, N & Dahmen, S R 2023, Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves. in R Krebbers, D Traytel, B Pientka & S Zdancewic (eds), CPP 2023 : Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs. Association for Computing Machinery, Inc, pp. 47-62, 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2023 - Co-located with POPL 2023, Boston, United States, 16/01/23. https://doi.org/10.1145/3573105.3575682","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:www.research.unipd.it:11577/3551906","is_oa":false,"landing_page_url":"https://hdl.handle.net/11577/3551906","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1145/3573105.3575682","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3573105.3575682","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3573105.3575682","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1397346294","display_name":null,"funder_award_id":"639.032.613","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3936710689","display_name":null,"funder_award_id":"016.Vidi.189.037","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312205633.pdf","grobid_xml":"https://content.openalex.org/works/W4312205633.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W769299933","https://openalex.org/W1464569014","https://openalex.org/W1501162952","https://openalex.org/W1557871226","https://openalex.org/W1567380020","https://openalex.org/W1587426425","https://openalex.org/W1621047391","https://openalex.org/W2067280441","https://openalex.org/W2083807032","https://openalex.org/W2773734888","https://openalex.org/W2786181488","https://openalex.org/W2953924437","https://openalex.org/W2981188613","https://openalex.org/W3020731832","https://openalex.org/W3102327505","https://openalex.org/W3122538476","https://openalex.org/W3128482940","https://openalex.org/W3147695068","https://openalex.org/W3178506813","https://openalex.org/W4229883074","https://openalex.org/W4238728065","https://openalex.org/W4251478687","https://openalex.org/W4293774222","https://openalex.org/W6910446013"],"related_works":["https://openalex.org/W2489377303","https://openalex.org/W2052454793","https://openalex.org/W116313202","https://openalex.org/W2043491846","https://openalex.org/W1499372654","https://openalex.org/W2060509762","https://openalex.org/W2089171228","https://openalex.org/W3144037495","https://openalex.org/W4297733311","https://openalex.org/W12356481"],"abstract_inverted_index":{"Diophantine":[0],"equations":[1,72],"are":[2,21,94],"a":[3,29],"popular":[4],"and":[5,34,40,57,107,109,132],"active":[6],"area":[7],"of":[8,22,70,76,112],"research":[9],"in":[10,37,65,122,129],"number":[11,33,91],"theory.":[12],"In":[13,78],"this":[14,50],"paper":[15],"we":[16,63,83,117],"consider":[17],"Mordell":[18,71],"equations,":[19],"which":[20],"the":[23,53,68,113],"form":[24],"y2=x3+d,":[25],"where":[26],"d":[27],"is":[28,52],"(given)":[30],"nonzero":[31],"integer":[32],"all":[35],"solutions":[36],"integers":[38],"x":[39],"y":[41],"have":[42],"to":[43,80,85,124],"be":[44],"determined.":[45],"One":[46],"non-elementary":[47],"approach":[48],"for":[49,73],"problem":[51],"resolution":[54,69],"via":[55],"descent":[56],"class":[58,114],"groups.":[59],"Along":[60],"these":[61],"lines":[62],"formalized":[64],"Lean":[66],"3":[67],"several":[74,87],"instances":[75],"d<0.":[77],"order":[79,123],"achieve":[81],"this,":[82],"needed":[84],"formalize":[86],"other":[88],"theories":[89],"from":[90],"theory":[92],"that":[93],"interesting":[95],"on":[96],"their":[97],"own":[98],"as":[99,102],"well,":[100],"such":[101],"ideal":[103],"norms,":[104],"quadratic":[105,130],"fields":[106],"rings,":[108],"explicit":[110],"computations":[111,128],"number.":[115],"Moreover,":[116],"introduced":[118],"new":[119],"computational":[120],"tactics":[121],"carry":[125],"out":[126],"efficiently":[127],"rings":[131],"beyond.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
