Some properties of the distribution of the numbers of points on elliptic curves over a finite prime field

Saiying He, James Mc Laughlin

Let $p\ge 5$ be a prime and for $a,b\in {\mathbb{F}}_p$, let $E_{a,b}$ denote the elliptic curve over ${\mathbb{F}}_p$ with equation $y^2=x^3+ax+b$. As usual define the tra…