(untitled) (Journal of the College of Basic Education, 2022)
In the use of elliptic curves in its applications (especially in cryptography), one often needs to construct elliptic curves with a known type (number of points) over a given finite field Fp, where some types are more secure than others. So we introduce a simple way to construct a supersingular elliptic curve by computing the coefficient of xp-1 in f(x)(p-1)/2 wheref(x)= x3+ax+b. And we give an algorithm that compute that coefficient and construct the required curve.