%0 Journal Article %A Nazli Yildiz İkikardes and Gokhan Soydan and Musa Demirci and Ismail Naci Cangul %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 Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime %U https://publications.waset.org/pdf/11483 %V 1 %X In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime. %P 123 - 125