%0 Journal Article %A Betül Gezer and Hacer Özden and Ahmet Tekcan and Osman Bizim %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 Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields %U https://publications.waset.org/pdf/3721 %V 1 %X Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b. %P 97 - 103