  Let $E$ be an elliptic curve defined over rational field $\mathbb{Q}$ and $N$
be a positive integer. Now, $M_E(N)$ denotes the number of primes $p$, such
that the group $E_p(\mathbb{F}_p)$ is of order $N$. We show that $M_E(N)$
follows Poisson distribution when an average is taken over a large class of
curves.
