When studying 2D gabor functions why is a gaussian called elliptical?

Question

Consider $$G(x,y)=\frac{1}{2\pi\sigma\beta}e^{-\pi\left[\frac{(x-x_0)^2}{\sigma^2}+\frac{(y-y_0)^2}{\beta^2}\right]}e^{i[\xi_0x+\nu_0y]}.$$ This is the product of a complex plane wave and what this paper calls an elliptical Gaussian. I see the complex plane wave but why is $$e^{-\pi\left[\frac{(x-x_0)^2}{\sigma^2}+\frac{(y-y_0)^2}{\beta^2}\right]}$$ called "elliptical" and not just a Gaussian? Are all Gaussians elliptical?