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Spanning the isogeny class of a power of an elliptic curve / Markus Kirschmer in Mathematics of computation, vol 91 n° 333 ([01/01/2022])  

Public [article]  inMathematics of computation > vol 91 n° 333 [01/01/2022] . - pp 401 - 449 Titre : Spanning the isogeny class of a power of an elliptic curve Type de document : Article/Communication Auteurs : Markus Kirschmer, Auteur ; Fabien Narbonne, Auteur ; Christophe Ritzenthaler, Auteur ; Damien Robert , Auteur Année de publication : 2022 Article en page(s) : pp 401 - 449 Note générale : bibliographie Langues : Anglais (eng) Résumé : (auteur) Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of Eg. The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E3 and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. Numéro de notice : A2022-627 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1090/mcom/3672 Date de publication en ligne : 16/09/2021 En ligne : https://doi.org/10.1090/mcom/3672 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=101457 [article]