{"id":"https://openalex.org/W4213368801","doi":"https://doi.org/10.1090/mcom/3697","title":"A classification of ECM-friendly families of elliptic curves using modular curves","display_name":"A classification of ECM-friendly families of elliptic curves using modular curves","publication_year":2021,"publication_date":"2021-09-15","ids":{"openalex":"https://openalex.org/W4213368801","doi":"https://doi.org/10.1090/mcom/3697"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3697","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3697","pdf_url":null,"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":["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/A5079156021","display_name":"Razvan Barbulescu","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Razvan Barbulescu","raw_affiliation_strings":["IMJ-PRG (Sorbonne Univ., Univ. Paris Diderot, CNRS), Inria, Paris","IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","LFANT - Lithe and fast algorithmic number theory (200, avenue de la Vieille Tour \r\n33405 Talence cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMJ-PRG (Sorbonne Univ., Univ. Paris Diderot, CNRS), Inria, Paris","institution_ids":["https://openalex.org/I169173203","https://openalex.org/I3017942884","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","institution_ids":["https://openalex.org/I4210166017"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I3017942884"]},{"raw_affiliation_string":"LFANT - Lithe and fast algorithmic number theory (200, avenue de la Vieille Tour \r\n33405 Talence cedex - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000386992","display_name":"Sudarshan Shinde","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4403386633","display_name":"OURAGAN: Outils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses Applications","ror":"https://ror.org/01rrvyp50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4403386633"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sudarshan Shinde","raw_affiliation_strings":["IMJ-PRG (Sorbonne Univ., Univ. Paris Diderot, CNRS), Inria, Paris","OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)","IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMJ-PRG (Sorbonne Univ., Univ. Paris Diderot, CNRS), Inria, Paris","institution_ids":["https://openalex.org/I169173203","https://openalex.org/I3017942884","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"OURAGAN - OUtils de R\u00e9solution Alg\u00e9briques pour la G\u00e9om\u00e9trie et ses ApplicatioNs (France)","institution_ids":["https://openalex.org/I4403386633"]},{"raw_affiliation_string":"IMJ-PRG (UMR_7586) - Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche (Sorbonne Universit\u00e9 - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / \r\nUniversit\u00e9 Paris Diderot - B\u00e2t. Sophie Germain, case 7012\r\n - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079156021"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210166017"],"apc_list":null,"apc_paid":null,"fwci":0.5695,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76420584,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"91","issue":"335","first_page":"1405","last_page":"1436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991000294685364,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9990000128746033,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9789000153541565,"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/elliptic-curve","display_name":"Elliptic curve","score":0.6024675369262695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5011911392211914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47914260625839233},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4430438280105591},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37990060448646545},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.3519955575466156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33363911509513855},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3017326593399048},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1811436116695404}],"concepts":[{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6024675369262695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5011911392211914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47914260625839233},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4430438280105591},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37990060448646545},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.3519955575466156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33363911509513855},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3017326593399048},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1811436116695404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3697","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3697","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W86859466","https://openalex.org/W600997534","https://openalex.org/W1502199504","https://openalex.org/W1516729797","https://openalex.org/W1741621240","https://openalex.org/W1749636891","https://openalex.org/W1971605365","https://openalex.org/W1976120821","https://openalex.org/W1991822009","https://openalex.org/W2001572759","https://openalex.org/W2005317356","https://openalex.org/W2006754831","https://openalex.org/W2015260762","https://openalex.org/W2059326407","https://openalex.org/W2090515343","https://openalex.org/W2092097669","https://openalex.org/W2092705148","https://openalex.org/W2133210885","https://openalex.org/W2134258244","https://openalex.org/W2143650198","https://openalex.org/W2205586407","https://openalex.org/W2257714540","https://openalex.org/W2371015231","https://openalex.org/W2406585997","https://openalex.org/W2509575576","https://openalex.org/W2735145237","https://openalex.org/W2739300320","https://openalex.org/W2892023862","https://openalex.org/W2904427798","https://openalex.org/W2911871489","https://openalex.org/W2962714280","https://openalex.org/W2964124869","https://openalex.org/W3023398280","https://openalex.org/W3104561728","https://openalex.org/W3106466057","https://openalex.org/W4206504405","https://openalex.org/W4241373120","https://openalex.org/W4248011490","https://openalex.org/W4292027090","https://openalex.org/W6630189340"],"related_works":["https://openalex.org/W2003932708","https://openalex.org/W2284877871","https://openalex.org/W2138102289","https://openalex.org/W1967424056","https://openalex.org/W868043274","https://openalex.org/W2513523087","https://openalex.org/W2368346088","https://openalex.org/W1187916458","https://openalex.org/W2373861055","https://openalex.org/W1559716973"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,49,106],"establish":[4],"a":[5,133,161],"link":[6],"between":[7],"the":[8,23,40,80,156,172],"classification":[9],"of":[10,25,39,82,85,114,126,128,136,139,148,163],"ECM-friendly":[11,55,140],"elliptic":[12,26,52,116,141],"curves":[13,27,117,142],"and":[14,63,169],"Mazur\u2019s":[15],"program":[16],"B,":[17],"which":[18,78,88,122,149,176],"consists":[19],"in":[20,155,180],"parameterizing":[21],"all":[22],"families":[24,113,138,168,175],"with":[28,118,143],"exceptional":[29,69],"Galois":[30,66,120,145],"image.":[31],"Motivated":[32],"by":[33],"Barbulescu":[34],"et":[35],"al.":[36],"[ANTS":[37],"X\u2013proceedings":[38],"tenth":[41],"algorithmic":[42],"number":[43],"theory":[44],"symposium,":[45],"Berkeley,":[46],"CA,":[47],"2013],":[48],"say":[50],"an":[51],"curve":[53],"is":[54,68],"if":[56,64],"it":[57],"does":[58],"not":[59],"have":[60],"complex":[61],"multiplication":[62],"its":[65],"image":[67],"for":[70,90],"some":[71],"level.":[72,130],"Building":[73],"upon":[74],"two":[75],"recent":[76],"works":[77],"treated":[79],"case":[81],"congruence":[83],"subgroups":[84,127],"prime-power":[86,129],"level":[87],"occur":[89],"infinitely":[91],"many":[92],"<inline-formula":[93,181],"content-type=\"math/mathml\">":[94,182],"<mml:math":[95,183],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[96,184],"alttext=\"j\">":[97],"<mml:semantics>":[98,189],"<mml:mi>j</mml:mi>":[99],"<mml:annotation":[100,198],"encoding=\"application/x-tex\">j</mml:annotation>":[101],"</mml:semantics>":[102,200],"</mml:math>":[103,201],"</inline-formula>":[104,202],"-invariants,":[105],"prove":[107],"that":[108,171],"there":[109],"are":[110,123,206],"exactly":[111],"1525":[112],"rational":[115,137],"distinct":[119],"images":[121],"cartesian":[124,144],"products":[125],"This":[131],"makes":[132],"complete":[134],"list":[135],"images,":[146],"out":[147],"less":[150],"than":[151],"23":[152],"were":[153],"known":[154],"literature.":[157],"We":[158],"furthermore":[159],"refine":[160],"heuristic":[162],"Montgomery":[164],"to":[165],"compare":[166],"these":[167],"conclude":[170],"best":[173],"4":[174],"can":[177],"be":[178],"put":[179],"alttext=\"a":[185],"equals":[186],"negative":[187],"1\">":[188],"<mml:mrow>":[190],"<mml:mi>a</mml:mi>":[191],"<mml:mo>=</mml:mo>":[192],"<mml:mo>":[193],"\u2212":[194],"</mml:mo>":[195],"<mml:mn>1</mml:mn>":[196],"</mml:mrow>":[197],"encoding=\"application/x-tex\">a=-1</mml:annotation>":[199],"twisted":[203],"Edwards\u2019":[204],"form":[205],"new.":[207]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2022-02-24T00:00:00"}