The group structure of Frey elliptic curves over finite fields FP

Nash Yıldız İkikardeş, Musa Demirci, Gökhan Soydan and İsmail Naci Cangül
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 13, 2007, Number 2, Pages 19—24
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Authors and affiliations

Nash Yıldız İkikardeş
Department of Mathematics, Bahkesir University
10100 Bahkesir, Turkey

Musa Demirci
Department of Mathematics, Uludag University
16059 Bursa, Turkey

Gökhan Soydan
Department of Mathematics, Uludag University
16059 Bursa, Turkey

İsmail Naci Cangül
Department of Mathematics, Uludag University
16059 Bursa, Turkey

Abstract

Frey elliptic curves are the curves y2 = x3n2x and in this work the group structure E(FP) of these curves over finite fields FP is considered.
This group structure and the number of points on these elliptic curves depend on the existence of elements of order 4. Therefore the cases where the group of the curve has such elements are determined. It is also shown that the number of such elements, if any, is either 4 or 12. Classification is made according to n is a quadratic residue or not.

Keywords

  • Elliptic curves over finite fields
  • Rational points

AMS Classification

  • 11G20
  • 14H25
  • 14K15
  • 14G99

References

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Cite this paper

APA

İkikardeş, N. Y., Demirci, M., Soydan, G., & Cangül, İ. N. (2007). The group structure of Frey elliptic curves over finite fields FP. Notes on Number Theory and Discrete Mathematics, 13(2), 19-24.

Chicago

İkikardeş, Nash Yıldız, Musa Demirci, Gökhan Soydan and İsmail Naci Cangül. “The Group Structure of Frey Elliptic Curves over Finite Fields FP.” Notes on Number Theory and Discrete Mathematics 13, no. 2 (2007): 19-24.

MLA

İkikardeş, Nash Yıldız, Musa Demirci, Gökhan Soydan and İsmail Naci Cangül. “The Group Structure of Frey Elliptic Curves over Finite Fields FP.” Notes on Number Theory and Discrete Mathematics 13.2 (2007): 19-24. Print.

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