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2012 On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields
William D. Banks, Francesco Pappalardi, Igor E. Shparlinski
Experiment. Math. 21(1): 11-25 (2012).

Abstract

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection that correspond to curves over prime fields or to curves with a prescribed torsion. Some of our results are rigorous and are based on recent advances in analytic number theory; some are conditional under certain widely believed conjectures; and others are purely heuristic in nature.

Citation

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William D. Banks. Francesco Pappalardi. Igor E. Shparlinski. "On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields." Experiment. Math. 21 (1) 11 - 25, 2012.

Information

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

zbMATH: 1257.11060
MathSciNet: MR2904904

Subjects:
Primary: 11D45
Secondary: 11P05 , 14G05

Keywords: Elliptic curve , finite field , group structure

Rights: Copyright © 2012 A K Peters, Ltd.

Vol.21 • No. 1 • 2012
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