The Mordell-Weil bases for the elliptic curve of the form ${\mathbf{y}}^2={\mathbf{x}}^3-{\mathbf{m}}^2\mathbf{x}+{\mathbf{n}}^2$

Yasutsugu Fujita, Tadahisa Nara

Let $E_{m,n}$ be an elliptic curve over $\mathbb{Q}$ of the form $y^2=x^3-m^{2}x+n^2$, where $m$ and $n$ are positive integers. Brown and Myers showed that the curve $E_{1,n}$ has ra…