February 1, 2019
Author(s)
Abhishek Juyal, Shiv D. Kumar, Dustin Moody
We study the Legendre family of elliptic curves E_t : y^2 = x(x − 1)(x − ∆t), parametrized by triangular numbers ∆t = t(t + 1)/2. We prove that the rank of E_t over the function field Q(t) is 1, while the rank is 0 over Q(t). We also produce some infinite