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A classification of ECM-friendly families using modular curves

hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierInstitut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
dc.contributor.authorBARBULESCU, Razvan
hal.structure.identifierOUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs [OURAGAN]
hal.structure.identifierInstitut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
dc.contributor.authorSHINDE, Sudarshan
dc.date.accessioned2024-04-04T03:02:06Z
dc.date.available2024-04-04T03:02:06Z
dc.date.created2020-07-10
dc.date.issued2022
dc.identifier.issn0025-5718
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192950
dc.description.abstractEnIn this work, we establish a link between the classification of ECM-friendly curves and Mazur's program B, which consists in parameterizing all the families of elliptic curves with exceptional Galois image. Building upon two recent works which treated the case of congruence subgroups of prime-power level which occur for infinitely many $j$-invariants, we prove that there are exactly 1525 families of rational elliptic curves with distinct Galois images which are cartesian products of subgroups of prime-power level. This makes a complete list of rational families of ECM-friendly elliptic curves, out of which less than 25 were known in the literature. We furthermore refine a heuristic of Montgomery to compare these families and conclude that the best 4 families which can be put in $a=-1$ twisted Edwards' form are new.
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.title.enA classification of ECM-friendly families using modular curves
dc.typeArticle de revue
dc.identifier.doi10.1090/mcom/3697
dc.subject.halInformatique [cs]/Cryptographie et sécurité [cs.CR]
bordeaux.journalMathematics of Computation
bordeaux.page1405-1436
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue91
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01822144
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01822144v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematics%20of%20Computation&rft.date=2022&rft.issue=91&rft.spage=1405-1436&rft.epage=1405-1436&rft.eissn=0025-5718&rft.issn=0025-5718&rft.au=BARBULESCU,%20Razvan&SHINDE,%20Sudarshan&rft.genre=article


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