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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## Details

### 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 *y*^{2} = *x*^{3} − *n*^{2}*x* and in this work the group structure *E*(*F _{P}*) of these curves over finite fields

*F*is considered.

_{P}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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## Related papers

## Cite this paper

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

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

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