The Spectrum of $\mathbb{Q}$-Isotropic Binary Quadratic Forms

We give a complete list of the points in the spectrum $$\mathcal{Z}=\{\underset{(x,y)\in \mathrm{\Lambda },xy\mathrm{\ne }0}{\inf }\mid xy\mid ,\mathrm{\Lambda }\text{ is a unimodular rational lattice of }{\mathbb{R}}^2\}$$ above $\frac{1}{3}\mathrm{.}$ We further show that the set of limit points of $\mathcal{Z}$ with values larger than $\frac{1}{3},$ is equal to the set \{\frac{2m}{\sqrt{9m^2-4}+3m},\text{ wheremis a Markoff number}\}.