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...
| Autores: | , , |
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| 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 |
| 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. |
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