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2012 On Group Structures Realized by Elliptic Curves over a Fixed Finite Field
Reza Rezaeian Farashahi, Igor E. Shparlinski
Experiment. Math. 21(1): 1-10 (2012).

Abstract

We obtain explicit formulas for the number of nonisomorphic elliptic curves with a given group structure (considered as an abstract abelian group) and the number of distinct group structures of all elliptic curves over a finite field. We use these formulas to derive some asymptotic estimates and tight upper and lower bounds for various counting functions related to classification of elliptic curves according to their group structure. Finally, we present results of some numerical tests that exhibit several interesting phenomena in the distribution of group structures.

Citation

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Reza Rezaeian Farashahi. Igor E. Shparlinski. "On Group Structures Realized by Elliptic Curves over a Fixed Finite Field." Experiment. Math. 21 (1) 1 - 10, 2012.

Information

Published: 2012
First available in Project Euclid: 31 May 2012

zbMATH: 1257.11061
MathSciNet: MR2904903

Subjects:
Primary: 11G05 , 11G20 , 14H52

Keywords: Elliptic curve , finite field , group structure

Rights: Copyright © 2012 A K Peters, Ltd.

Vol.21 • No. 1 • 2012
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