Second moments and the bias conjecture for the family of cubic pencils

Matija Kazalicki, Bartosz Naskręcki

For a 1-parametric family $E_k$ of elliptic curves over $\mathbb{Q}$ and a prime $p$, consider the second moment sum $M_{2,p}(E_k)={\sum }_{k\in {\mathbb{F}}_p}{a}_{k,p}^2$, where $a_{k…