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Elliptic Curves Arising from Triangular Numbers

Published

Author(s)

Abhishek Juyal, Shiv D. Kumar, Dustin Moody

Abstract

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 subfamilies whose Mordell-Weil rank is positive, and find high rank curves from within these families.
Citation
INTEGERS, The electronic journal of combinatorial number theory
Volume
19

Keywords

elliptic curves, triangular numbers
Created February 1, 2019, Updated February 22, 2019