Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$

Chantal David, Lucile Devin, Alessandro Fazzari +1

We study the average analytic rank in the family of $L$-functions $L(s,E_d)$ associated with the elliptic curves $E_d:y^2=x^3-dx$, as $d$ varies over fourth-power-free odd integ…