2 problems

Let $\mathcal B_{2,\mathcal E}(p)$ denote the normalized second moment of a one-parameter family of elliptic curves, and consider its distribution as the prime $p$ varies. Variance…

For a one-parameter family of elliptic curves $y^2=x^3+A(T)x+B(T)$ with $A(T),B(T)\in\mathbb{Z}[T]$ and non-constant $j$-invariant, write the second moment of the Frobenius traces…