{"id":"https://openalex.org/W7220448556","doi":"https://doi.org/10.48550/arxiv.2610.03121","title":"Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census","display_name":"Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220448556","doi":"https://doi.org/10.48550/arxiv.2610.03121"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03121","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03121","pdf_url":"https://arxiv.org/pdf/2610.03121","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/2610.03121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014699368","display_name":"Sompong Chuysurichay","orcid":"https://orcid.org/0000-0002-8394-9806","observed_orcids":["https://orcid.org/0000-0002-8394-9806"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chuysurichay, Sompong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012893636","display_name":"Sawian Jaidee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jaidee, Sawian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019366641","display_name":"Chatchawan Panraksa","orcid":"https://orcid.org/0000-0003-0692-5453","observed_orcids":["https://orcid.org/0000-0003-0692-5453"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panraksa, Chatchawan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065229683","display_name":"Teerapol Sukhonwimolmal","orcid":"https://orcid.org/0000-0001-5101-7951","observed_orcids":["https://orcid.org/0000-0001-5101-7951"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sukhonwimolmal, Teerapol","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9945999979972839,"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":0.9945999979972839,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0017999999690800905,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.001500000013038516,"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/finite-fields","display_name":"finite fields","score":0.6700000166893005},{"id":"https://openalex.org/keywords/elliptic-curves-over-finite-fields","display_name":"elliptic curves over finite fields","score":0.8130000233650208},{"id":"https://openalex.org/keywords/diophantine-triples","display_name":"Diophantine triples","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C52130261","wikidata":"https://www.wikidata.org/wiki/Q39825","display_name":"Census","level":3,"score":0.7297000288963318},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7190999984741211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5622000098228455},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27410000562667847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26100000739097595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2596000134944916},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2320999950170517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21580000221729279}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03121","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03121","pdf_url":"https://arxiv.org/pdf/2610.03121","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.2610.03121","doi":"https://doi.org/10.48550/arxiv.2610.03121","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03121","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:2610.03121","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03121","pdf_url":"https://arxiv.org/pdf/2610.03121","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220448556.pdf","grobid_xml":"https://content.openalex.org/works/W7220448556.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1979485530","https://openalex.org/W2019816098","https://openalex.org/W2039327237","https://openalex.org/W2046569422","https://openalex.org/W2048703701","https://openalex.org/W2075252632","https://openalex.org/W2086378201","https://openalex.org/W2092715653","https://openalex.org/W2094556471","https://openalex.org/W2111310412","https://openalex.org/W2176523713","https://openalex.org/W2508581812","https://openalex.org/W2963982562","https://openalex.org/W4292027090"],"related_works":["https://openalex.org/W2098377074","https://openalex.org/W4247879069","https://openalex.org/W1986671489","https://openalex.org/W2319891616","https://openalex.org/W4416319175","https://openalex.org/W1494827185","https://openalex.org/W2162814723","https://openalex.org/W2019693612","https://openalex.org/W2060357618","https://openalex.org/W2764493397"],"abstract_inverted_index":{"We":[0],"record":[1],"a":[2,25],"finite-field":[3],"census":[4],"of":[5],"the":[6],"split-cubic":[7],"elliptic":[8],"curves":[9],"$E_{a,b,c}^{(n)}:y^2=(ax+n)(bx+n)(cx+n)$":[10],"attached":[11],"to":[12],"positive":[13],"integral":[14],"$D(n)$-triples.":[15],"For":[16],"$n\\in\\{-3,3,5,8,12,20\\}$":[17],"there":[18],"are":[19],"$164$":[20],"such":[21],"triples":[22],"with":[23],"$1\\le":[24]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}
