Lower Order Biases in Moment Expansions of One Parameter Families of Elliptic Curves

Timothy Cheek, Pico Gilman, Kareem Jaber +3

For a fixed elliptic curve $E$ without complex multiplication, $a_p:=p+1-\#E({\mathbb{F}}_p)$ is $O(\sqrt{p})$ and $a_p/2\sqrt{p}$ converges to a semicircular distribution. Miche…