Let $\delta<-1$ and $\tau<0$. If a $T^{2}$-invariant potential $\phi^{\prime}$ satisfies $(\omega_{\mathbb{C}^{3}}+\sqrt{-1}\partial\bar{\partial}\phi^{\prime})^{3}=\omega_{\mathbb{C}^{3}}^{3}$ with bound $\left\lVert d\phi^{\prime}\right\rVert_{C^{k+1,\alpha}_{\delta+1,\tau}(\mathbb{C}^{3},\Lambda^{1})}<\infty$, then $d\phi^{\prime}=0$.