MMN-182
The group structure of Bachet elliptic curves over finite fields $F_p$
Abstract
Bachet elliptic curves are the curves y˛=xł+ał and in this work the group structure E(F_{p}) of these curves over finite fields F_{p} is considered. It is shown that there are two possible structures E(F_{p})≅C_{p+1} or E(F_{p})≅C_{n}×C_{nm}, for m,n∈ℕ, according to p≡5 (mod6) and p≡1 (mod6), respectively. A result of Washington is restated in a more specific way saying that if E(F_{p})≅Z_{n}×Z_{n}, then p≡7 (mod12) and p=n˛∓n+1.
Vol. 10 (2009), No. 2, pp. 129-136