{"id":"https://openalex.org/W2048279404","doi":"https://doi.org/10.1090/s0025-5718-02-01458-8","title":"Modular curves of genus 2","display_name":"Modular curves of genus 2","publication_year":2002,"publication_date":"2002-06-04","ids":{"openalex":"https://openalex.org/W2048279404","doi":"https://doi.org/10.1090/s0025-5718-02-01458-8","mag":"2048279404"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-02-01458-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01458-8","pdf_url":"https://www.ams.org/mcom/2003-72-241/S0025-5718-02-01458-8/S0025-5718-02-01458-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2003-72-241/S0025-5718-02-01458-8/S0025-5718-02-01458-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Enrique Gonz\u00e1lez-Jim\u00e9nez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Enrique Gonz\u00e1lez-Jim\u00e9nez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Josep Gonz\u00e1lez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josep Gonz\u00e1lez","raw_affiliation_strings":["Escola Universit\u00c3\u00a0ria Polit\u00c3\u00a8cnica de Vilanova i la Geltr\u00c3\u00ba, Av. Victor Balaguer s/n, E-08800 Vilanova i la Geltr\u00c3\u00ba, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escola Universit\u00c3\u00a0ria Polit\u00c3\u00a8cnica de Vilanova i la Geltr\u00c3\u00ba, Av. Victor Balaguer s/n, E-08800 Vilanova i la Geltr\u00c3\u00ba, Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4811,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.61853696,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"72","issue":"241","first_page":"397","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.8801000118255615,"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":0.8801000118255615,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.03370000049471855,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.019500000402331352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.8130000233650208},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.6819000244140625},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.667900025844574},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6151000261306763},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5289000272750854},{"id":"https://openalex.org/keywords/abelian-variety","display_name":"Abelian variety","score":0.4708999991416931}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9524999856948853},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.8130000233650208},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.6819000244140625},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.667900025844574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.630299985408783},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6151000261306763},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5289000272750854},{"id":"https://openalex.org/C46709022","wikidata":"https://www.wikidata.org/wiki/Q318751","display_name":"Abelian variety","level":3,"score":0.4708999991416931},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C72587816","wikidata":"https://www.wikidata.org/wiki/Q7497063","display_name":"Shimura variety","level":3,"score":0.4357999861240387},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-02-01458-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01458-8","pdf_url":"https://www.ams.org/mcom/2003-72-241/S0025-5718-02-01458-8/S0025-5718-02-01458-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0105232","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0105232","pdf_url":"https://arxiv.org/pdf/math/0105232","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-02-01458-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01458-8","pdf_url":"https://www.ams.org/mcom/2003-72-241/S0025-5718-02-01458-8/S0025-5718-02-01458-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2048279404.pdf","grobid_xml":"https://content.openalex.org/works/W2048279404.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W6604009900","https://openalex.org/W6604359591","https://openalex.org/W6606541913","https://openalex.org/W6609625124","https://openalex.org/W6609985758","https://openalex.org/W6631530779"],"related_works":["https://openalex.org/W2095206009","https://openalex.org/W2963835107","https://openalex.org/W3104808134","https://openalex.org/W1964823515","https://openalex.org/W2105603074","https://openalex.org/W2061938945","https://openalex.org/W4232143973","https://openalex.org/W2964084657","https://openalex.org/W1991544716","https://openalex.org/W1506406535"],"abstract_inverted_index":{"We":[0,247],"prove":[1],"that":[2,56],"there":[3,57],"are":[4],"exactly":[5],"<inline-formula":[6,21,36,62,108,131,145,169,193],"content-type=\"math/mathml\">":[7,22,37,63,109,132,146,170,194],"<mml:math":[8,23,38,64,110,133,147,171,195],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,24,39,65,111,134,148,172,196],"alttext=\"149\">":[10],"<mml:semantics>":[11,27,43,78,115,137,152,177,212],"<mml:mn>149</mml:mn>":[12],"<mml:annotation":[13,29,49,99,121,139,158,182,239],"encoding=\"application/x-tex\">149</mml:annotation>":[14],"</mml:semantics>":[15,31,52,103,124,141,161,184,243],"</mml:math>":[16,32,53,104,125,142,162,185,244],"</inline-formula>":[17,33,54,105,126,143,163,186,245],"genus":[18],"two":[19],"curves":[20],"alttext=\"upper":[25,135,173],"C\">":[26,77,136],"<mml:mi>C</mml:mi>":[28,97,138],"encoding=\"application/x-tex\">C</mml:annotation>":[30,140],"defined":[34,106],"over":[35,107],"alttext=\"double-struck":[40,112,149],"upper":[41,68,72,76,113,150,199,204,208],"Q\">":[42,114,151],"<mml:mrow":[44,116,153],"class=\"MJX-TeXAtom-ORD\">":[45,117,154],"<mml:mi":[46,118,155,225],"mathvariant=\"double-struck\">Q</mml:mi>":[47,119,156],"</mml:mrow>":[48,98,120,157,238],"encoding=\"application/x-tex\">\\mathbb":[50,122,159],"{Q}</mml:annotation>":[51,123,160],"such":[55],"exists":[58],"a":[59,191],"nonconstant":[60],"morphism":[61],"alttext=\"pi":[66],"colon":[67],"X":[69],"1":[70,206],"left-parenthesis":[71,202,207],"N":[73,209],"right-parenthesis":[74,210],"right-arrow":[75],"<mml:mrow>":[79,213],"<mml:mi>":[80],"\u03c0":[81],"</mml:mi>":[82,228],"<mml:mo>:</mml:mo>":[83],"<mml:msub>":[84,178,218,224],"<mml:mi>X</mml:mi>":[85],"<mml:mn>1</mml:mn>":[86,229],"</mml:msub>":[87,181,221,230],"<mml:mo":[88,91,93,222,231,234,236],"stretchy=\"false\">(</mml:mo>":[89,223,232],"<mml:mi>N</mml:mi>":[90,233],"stretchy=\"false\">)</mml:mo>":[92,235,237],"stretchy=\"false\">":[94],"\u2192":[95],"</mml:mo>":[96,217],"encoding=\"application/x-tex\">\\pi":[100],":X_1(N)\\rightarrow":[101],"C</mml:annotation>":[102],"and":[127,252],"the":[128,166,249],"jacobian":[129],"of":[130],"is":[144],"-isogenous":[164],"to":[165,190],"abelian":[167],"variety":[168],"A":[174],"Subscript":[175],"f\">":[176],"<mml:mi>A</mml:mi>":[179],"<mml:mi>f</mml:mi>":[180,214],"encoding=\"application/x-tex\">A_f</mml:annotation>":[183],"attached":[187],"by":[188],"Shimura":[189],"newform":[192],"alttext=\"f":[197],"element-of":[198],"S":[200],"2":[201],"normal":[203],"Gamma":[205],"right-parenthesis\">":[211],"<mml:mo>":[215],"\u2208":[216],"<mml:mi>S</mml:mi>":[219],"<mml:mn>2</mml:mn>":[220],"mathvariant=\"normal\">":[226],"\u0393":[227],"encoding=\"application/x-tex\">f\\in":[240],"S_2(\\Gamma":[241],"_1(N))</mml:annotation>":[242],".":[246],"determine":[248],"corresponding":[250],"newforms":[251],"present":[253],"equations":[254],"for":[255],"all":[256],"these":[257],"curves.":[258]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}