Congruent number elliptic curves with rank at least two

TL;DR

This paper constructs an infinite family of congruent number elliptic curves with rank at least two, linking their properties to specific integral solutions of a quadratic form.

Contribution

It introduces a new infinite family of congruent number elliptic curves with high rank, based on solutions to a particular quadratic equation.

Findings

Established an infinite family of congruent number elliptic curves with rank ≥ 2.

Connected elliptic curve properties to solutions of m^2=n^2+nl+l^2.

Provided a method to generate such curves using integral solutions.

Abstract

We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of $m^2=n^2+nl+l^2$.