Juyal, A.
, Kumar, S.
and Moody, D.
(2019),
Elliptic Curves Arising from Triangular Numbers, INTEGERS, The electronic journal of combinatorial number theory, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=927507
(Accessed October 9, 2024)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Elliptic Curves Arising from Triangular Numbers
Published
Author(s)
Abhishek Juyal, Shiv D. Kumar,
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
Download Paper
Keywords
elliptic curves, triangular numbers
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.
Created January 31, 2019, Updated October 12, 2021