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

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2015
Author
Miret, Josep M. (Josep Maria)
Pujolàs Boix, Jordi
Valera Martín, Javier
Suggested citation
Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Valera Martín, Javier; . (2015) . On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq. Archiv der Mathematik, 2015, vol.105, núm. 3, p. 261-269. https://doi.org/10.1007/s00013-015-0798-6.
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Abstract
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.
URI
http://hdl.handle.net/10459.1/48929
DOI
https://doi.org/10.1007/s00013-015-0798-6
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Archiv der Mathematik, 2015, vol.105, núm. 3, p. 261-269
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