%0 Journal Article
	%A Ahmet Tekcan
	%D 2007
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 1, 2007
	%T The Elliptic Curves y2 = x3 - t2x over Fp
	%U https://publications.waset.org/pdf/5174
	%V 1
	%X 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.

	%P 84 - 90