Factors of cocycle twists of Sklyanin algebras · Question 1.1

Let $S$ be a 4-dimensional Sklyanin algebra, not finite over its centre. Odesskii defines a twist by the Klein four-group $K_4$ acts diagonally on $S \otimes_k M_2(k) = M_2(S)$. Let $A = (M_2(S))^{K_4}$. The central elements of $S$, $\Omega_1$ and $\Omega_2$, remain central in $A$. Consider $R_\Omega := A/(\Omega)$, where $\Omega := c_1 \Omega_1 + c_2 \Omega_2$ for some constants $c_1, c_2$. Andrew Davies showed that $R_{\Omega_1}$ is not a domain; is every $R_\Omega$ not a domain?