Betül Gezer and Hacer Özden and Ahmet Tekcan and Osman Bizim
The Number of Rational Points on Elliptic Curves y2 x3 b2 Over Finite Fields
97 - 103
2007
1
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/3721
https://publications.waset.org/vol/1
World Academy of Science, Engineering and Technology
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 &isin; Fp. Recall that theorder of Ep,bover Fpis p 1 if p &equiv; 5(mod 6). We generalize thisresult to any field Fnp for an integer n&ge; 2. Further we obtain someresults concerning the sum &Sigma;xEp,b(Fp) and &Sigma;yEp,b(Fp), thesum of x and y coordinates of all points (x, y) on Ep,b, and alsothe the sum &Sigma;(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.
Open Science Index 1, 2007