I recently evaluated a discriminant of a polynomial $f(u,z)$ related to a dynamical system based on the polynomial $P(u) = u^3 + au + b$. 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 the discriminant of the polynomial below), the expression should possibly be thought of as the “image” of the polynomial

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

under some discriminant-like function.

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