{"id":"https://openalex.org/W2042628949","doi":"https://doi.org/10.1007/3-540-45455-1_20","title":"Curves Dy 2 = x 3 \u2014 x of Odd Analytic Rank","display_name":"Curves Dy 2 = x 3 \u2014 x of Odd Analytic Rank","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2042628949","doi":"https://doi.org/10.1007/3-540-45455-1_20","mag":"2042628949"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45455-1_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45455-1_20","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057239752","display_name":"Noam D. Elkies","orcid":"https://orcid.org/0000-0001-9296-6299"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Noam D. Elkies","raw_affiliation_strings":["Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057239752"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.5825,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84085511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"244","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9986000061035156,"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/T11166","display_name":"Analytic Number Theory Research","score":0.998199999332428,"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/conjecture","display_name":"Conjecture","score":0.7172552347183228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6022815704345703},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6019971370697021},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5894251465797424},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5382905006408691},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.5211734175682068},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.5051634907722473},{"id":"https://openalex.org/keywords/rational-point","display_name":"Rational point","score":0.48360195755958557},{"id":"https://openalex.org/keywords/modular-curve","display_name":"Modular curve","score":0.46783390641212463},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.4654572308063507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37227606773376465},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1976175606250763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16538989543914795},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.12249448895454407}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7172552347183228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6022815704345703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6019971370697021},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5894251465797424},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5382905006408691},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.5211734175682068},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.5051634907722473},{"id":"https://openalex.org/C156330621","wikidata":"https://www.wikidata.org/wiki/Q3393476","display_name":"Rational point","level":3,"score":0.48360195755958557},{"id":"https://openalex.org/C59766168","wikidata":"https://www.wikidata.org/wiki/Q3001220","display_name":"Modular curve","level":3,"score":0.46783390641212463},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4654572308063507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37227606773376465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1976175606250763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16538989543914795},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.12249448895454407},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-45455-1_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45455-1_20","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.3237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.3237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0208056v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306079","display_name":"David and Lucile Packard Foundation","ror":"https://ror.org/032atxq54"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1486898453","https://openalex.org/W1579710361","https://openalex.org/W1589201628","https://openalex.org/W1976994099","https://openalex.org/W1982832119","https://openalex.org/W2006056381","https://openalex.org/W2027875058","https://openalex.org/W2039187350","https://openalex.org/W2049692870","https://openalex.org/W2104223939","https://openalex.org/W2121902984","https://openalex.org/W2604330053","https://openalex.org/W3013059422","https://openalex.org/W4210871175","https://openalex.org/W4255866901"],"related_works":["https://openalex.org/W1994841333","https://openalex.org/W2244353689","https://openalex.org/W4286912068","https://openalex.org/W2963841585","https://openalex.org/W3102323471","https://openalex.org/W4302317481","https://openalex.org/W4300573607","https://openalex.org/W1919889031","https://openalex.org/W3169715737","https://openalex.org/W2571860849"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
