Lethbridge Number Theory and Combinatorics Seminar: James Parks

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. Let $M_E(N)$ be the function that counts the number of primes $p$ of good reduction such that $\#E_p(\mathbb{F}_p) = N$ where $N$ is a fixed integer and $E_p(\mathbb{F}_p)$ denotes the group of points on the elliptic curve modulo $p$. We consider this function on average and discuss recent results related to the constant in the asymptotic result in the average.