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

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2015Suggested 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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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.