I recently evaluated a discriminant of a polynomial $f(u,z)$ related to a dynamical system based on the polynomial $P(z) = z^3 + az + b$. In doing so, I came across the following expression (plus some additional terms) that looks quite striking, but I haven't been able to place it:

$$\frac{3a(b-z^3)}{(\omega-1)\,\lambda} + \frac{z}{\lambda^3}\left(a^2\lambda\left(1-\frac{1}{(\omega-1)^2}\right)-3bz\right)$$

Here, $\omega$ is a real parameter (with $\omega\in(0,1)\cup(1,3)$) associated with the order of a fractional derivative, and $\lambda:= \sqrt[3]{\omega-3}.$

Due to a natural change of variables used to arrive at the above expression (which reduces the additional terms to a simple discriminant of the polynomial below), the expression should possibly be thought of as the “image” of the polynomial

$$\widetilde{P}(z) := z^3 + \frac{a}{(\omega-1)\sqrt[3]{\omega-3}} + \frac{b}{\omega(\omega-3)}$$

under some discriminant-like function.

Does the expression above look familiar, or is it perhaps some determinant related to $\widetilde{P}(z)$?