The optimal s-stage third order implicit SSP Runge-Kutta method has SSP coefficient $s-1+\sqrt{s^2-1}$ and Shu-Osher form $$\begin{align} \mu = \begin{bmatrix} \mu_{11} & & & \\ \mu_{21} & \ddots & & \\ & \ddots & \mu_{11} & \\ & & \mu_{21} & \mu_{11} \\ & & & \mu_{s+1,s} \\ \end{bmatrix}, \quad \lambda = \begin{bmatrix} 0 & & & \\ 1 & \ddots & & \\ & \ddots & 0 & \\ & & 1 & 0 \\ & & & \lambda_{s+1,s} \\ \end{bmatrix}, \end{align} $$ where $$\begin{align} \mu_{11} &= \frac{1}{2}\left(1-\sqrt{\frac{s-1}{s+1}}\right), & \mu_{21} &= \frac{1}{2}\left(\sqrt{\frac{s+1}{s-1}}-1\right), \\ \mu_{s+1,s} &= \frac{s+1}{s(s+1+\sqrt{s^2-1})}, & \lambda_{s+1,s} &= \frac{ (s+1) (s-1+\sqrt{s^2-1}) }{ s(s+1+\sqrt{s^2-1}) }. \end{align} $$