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ELLIPTIC CURVES ARISING FROM THE TRIANGULAR NUMBERS
Abhishek Juyal1, Shiv Datt Kumar2, Dustin Moody3
1Department of Mathematics Motilal Nehru National Institute of Technology, Allahabad, 211004, India.
Integers : Electronic Journal of Combinatorial Number Theory
|July 6, 2019
Abstract
None:
We study the Legendre family of elliptic curves Et : y 2 = x(x - 1)(x - Δ t ), parametrized by triangular numbers Δ t = t(t + 1)/2. We prove that the rank of Et over the function field is 1, while the rank is 0 over . We also produce some infinite subfamilies whose Mordell-Weil rank is positive, and find high rank curves from within these families.
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