{"id":"https://openalex.org/W2056440656","doi":"https://doi.org/10.1080/10586458.2001.10504463","title":"Mordell\u2013Weil Lattices in Characteristic 2, III: A Mordell\u2013Weil Lattice of Rank 128","display_name":"Mordell\u2013Weil Lattices in Characteristic 2, III: A Mordell\u2013Weil Lattice of Rank 128","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2056440656","doi":"https://doi.org/10.1080/10586458.2001.10504463","mag":"2056440656"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2001.10504463","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504463","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504463","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504463","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104946848","display_name":"Noam D. Elkies","orcid":null},"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"]},{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Noam D. Elkies","raw_affiliation_strings":["Department of Mathematics, Harvard University, Cambridge, MA, 02138, United States E-mail: elkies@math.harvard.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvard University, Cambridge, MA, 02138, United States E-mail: elkies@math.harvard.edu","institution_ids":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5104946848"],"corresponding_institution_ids":["https://openalex.org/I136199984","https://openalex.org/I2801851002"],"apc_list":null,"apc_paid":null,"fwci":0.5816,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.7982838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"10","issue":"3","first_page":"467","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9955000281333923,"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":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8697779178619385},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.7424718141555786},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6203116774559021},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.4982600212097168},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4409734904766083},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4226631224155426},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.41815292835235596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36987459659576416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33004409074783325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07870930433273315}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8697779178619385},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7424718141555786},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6203116774559021},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.4982600212097168},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4409734904766083},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4226631224155426},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.41815292835235596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36987459659576416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33004409074783325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07870930433273315},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2001.10504463","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504463","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504463","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1080/10586458.2001.10504463","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504463","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504463","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5600000023841858}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056440656.pdf","grobid_xml":"https://content.openalex.org/works/W2056440656.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1995990042","https://openalex.org/W2048253404","https://openalex.org/W2050212755","https://openalex.org/W2067181780","https://openalex.org/W2073111855","https://openalex.org/W2166747492","https://openalex.org/W2327956313","https://openalex.org/W3187268046"],"related_works":["https://openalex.org/W1994422831","https://openalex.org/W3105629360","https://openalex.org/W2964335068","https://openalex.org/W2964131781","https://openalex.org/W4293482052","https://openalex.org/W4312108549","https://openalex.org/W4302791201","https://openalex.org/W4299694176","https://openalex.org/W3099755295","https://openalex.org/W2765283459"],"abstract_inverted_index":{"We":[0,75],"analyze":[1],"the":[2,12,29,46,50,65,78,82,90],"128-dimensional":[3],"Mordell\u2013Weil":[4],"lattice":[5,95],"of":[6,23,40,81],"a":[7,20,62,69,87,94],"certain":[8],"elliptic":[9,30],"curve":[10,31],"over":[11],"rational":[13,38],"function":[14],"field":[15,22],"k(t),":[16],"where":[17],"k":[18],"is":[19,60,85],"finite":[21],"212":[24],"elements.":[25],"By":[26],"proving":[27],"that":[28,45],"has":[32],"trivial":[33],"Tate\u2013\u0160afarevi\u010d":[34],"up":[35],"and":[36],"nonzero":[37],"points":[39],"height":[41],"22,":[42],"we":[43],"show":[44],"lattice's":[47],"density":[48,59],"achieves":[49],"lower":[51],"bound":[52],"derived":[53],"in":[54,72,96],"our":[55],"earlier":[56],"work.":[57],"This":[58],"by":[61,86],"considerable":[63,88],"factor":[64,89],"largest":[66,91],"known":[67,92],"for":[68,93],"sphere":[70],"packing":[71],"dimension":[73],"128.":[74],"also":[76],"determine":[77],"kissing":[79],"number":[80],"lattice,":[83],"which":[84],"this":[97],"dimension.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}