CARUSO, Xavier; EID, Elie; LERCIER, Reynald

doi:10.1112/jlms.12487

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CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

EID, Elie
Institut de Recherche Mathématique de Rennes [IRMAR]

LERCIER, Reynald
Institut de Recherche Mathématique de Rennes [IRMAR]

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Article de revue

Este ítem está publicado en

Journal of the London Mathematical Society. 2021-11, vol. 104, n° 4, p. 1901-1929

London Mathematical Society ; Wiley

Resumen en inglés

We propose an algorithm that calculates isogenies between elliptic curves defined over an extension $K$ of $\mathbb{Q}_2$. It consists in efficiently solving with a logarithmic loss of $2$-adic precision the first order differential equation satisfied by the isogeny. We give some applications, especially computing over finite fields of characteristic 2 isogenies of elliptic curves and irreducible polynomials, both in quasi-linear time in the degree.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192344

DOI

http://dx.doi.org/10.1112/jlms.12487

Proyecto ANR

Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251