Ahmet Tekcan
The Elliptic Curves y2 x3 t2x over Fp
84 - 90
2007
1
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/5174
https://publications.waset.org/vol/1
World Academy of Science, Engineering and Technology
Let p be a prime number, Fp be a finite field and t ∈ Fp 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 xandycoordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et y2 x3 t2x and its 2isogenous 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∈Fpanp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.
Open Science Index 1, 2007