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Rational Points on Elliptic Curves $y^{2}=x^{3}+a^{3}$ in ${\bf F}_p$ where $p\equiv 1\pmod6$ is Prime
In this work, we consider the rational points on elliptic curves over finite fields F_{p}. We give results concerning the number of points on the elliptic curve y^2{\equiv}x^3+a^3(mod p)where p is a prime congruent to 1 modulo 6. Also some results are given on the sum of abscissae of these …