@article{(Open Science Index):https://publications.waset.org/pdf/5174, title = {The Elliptic Curves y2 = x3 - t2x over Fp}, author = {Ahmet Tekcan}, country = {}, institution = {}, abstract = {Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- 0. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {1}, number = {1}, year = {2007}, pages = {84 - 90}, ee = {https://publications.waset.org/pdf/5174}, url = {https://publications.waset.org/vol/1}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 1, 2007}, }