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