WASET
	@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},
	}