Musa Demirci and Nazlı Yıldız İkikardeş and Gökhan Soydan and İsmail Naci Cangül
The Number of Rational Points on Elliptic Curves y2 x3 a3 on Finite Fields
130 - 132
2007
1
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/6891
https://publications.waset.org/vol/1
World Academy of Science, Engineering and Technology
In this work, we consider the rational points on elliptic
curves over finite fields Fp. We give results concerning the number
of points Np,a on the elliptic curve y2 ≡ x3 a3(mod p) according
to whether a and x are quadratic residues or nonresidues. We use
two lemmas to prove the main results first of which gives the list of
primes for which 1 is a quadratic residue, and the second is a result
from 1. We get the results in the case where p is a prime congruent
to 5 modulo 6, while when p is a prime congruent to 1 modulo 6,
there seems to be no regularity for Np,a.
Open Science Index 1, 2007