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Title:
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On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
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Author:
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Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Valera Martín, Javier
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Notes:
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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.
The authors would like to thank the anonymous referee, whose comments highly improved the quality of this publication. The research of the authors was supported in part by the Grants MTM2013-46949-P (Spanish Ministerio de Ciencia e Innovaci´on), 2014SGR-1666 (Generalitat de Catalunya). |
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Subject(s):
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-Elliptic curve
-Finite field
-Group order
-ℓ-adic valuation |
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Rights:
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(c) Springer Basel, 2015
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Document type:
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article
acceptedVersion |
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Published by:
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Springer Verlag
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