Generators for congruent number curves of ranks at least two and three (Q2927748)

Let \(N\) be a positive integer and \(E_N\) be an elliptic curve defined by \(y^2=x^3-N^2x\). This curve is called a congruent number elliptic curve since \(N\) is a congruent number if and only if it has a positive rank. In this paper, the author studies the Mordell-Weil groups \(E_N(\mathbb{Q})\) and gives generators for the rank two and three parts of \(E_N(\mathbb{Q})\) for infinitely many integers \(N\).