Two infinite families of elliptic curves with Mordell-Weil rank at least $3$

Pankaj Patel, Debopam Chakraborty, Jaitra Chattopadhyay

In this paper, we consider two infinite parametric families of elliptic curves defined over $\mathbb{Q}$ given by the equations $E_{a,b}:y^2=x^3-a^{2}x+b^2$ and $E^{\…