The probability that the number of points on an elliptic curve over a finite field is prime

摘要

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 thar a randomly chosen elliptic curve over a finite field has kq points where k is a small number and q is a prime. [References: 9]