Elliptic Curves Arising from Triangular Numbers

Published: February 01, 2019

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
Pub Type: Journals

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Keywords

elliptic curves, triangular numbers
Created February 01, 2019, Updated February 22, 2019