The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime
Steven D. Galbraith⋆, James McKee · Journal of the London Mathematical Society · 2000
The paper gives a formula for the probability that a randomly chosen elliptic curve over a finite field has a prime number of points. Two heuristic arguments in support of the formula are given as well as experimental evidence. The paper also gives a formula for the probability that a randomly chosen elliptic curve over a finite field has kq points where k is a small number and q is a prime.