1Department of Mathematics, Uludaĝ University, 16059, Bursa, Turkey.
2Department of Mathematics, Balıkesir University, 10100, Balıkesir, Turkey. E-mail: nyildiz@balikesir.edu.tr
*E-mail: mdemirci@uludag.edu.tr
**E-mail: gsoydan@uludag.edu.tr
***E-mail: cangul@uludag.edu.tr
AMS Subject Classification: 11G20, 14H25, 14K15, 14G99.
In this work, we study the rational points on elliptic curves of the form over finite fields Fp. These kind of elliptic curves are widely known as Frey curves. We show that there are two different possible cases where p ≡ 1 or 3 (mod 4). In the former case there is no general result which can be obtained about the rational points while in the latter case, we find exactly p + 1 points on these curves. We give results on the abscissae and ordinates of these points according to whether they are quadratic residues or not.
Elliptic curves over finite fields, rational points
