On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq

Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points grows by taking finite extensions of the base field. We also investigate the...

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Detalles Bibliográficos
Autores: Miret, Josep M. (Josep Maria), Pujolàs Boix, Jordi, Valera Martín, Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/48929
Acceso en línea:https://doi.org/10.1007/s00013-015-0798-6
http://hdl.handle.net/10459.1/48929
Access Level:acceso abierto
Palabra clave:Elliptic curve
Finite field
Group order
ℓ-adic valuation
Descripción
Sumario:Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points grows by taking finite extensions of the base field. We also investigate the group structure of the corresponding l-Sylow subgroups.