The optimal s-stage second order implicit SSP Runge-Kutta method has SSP coefficient 2s and Shu-Osher form $$\begin{align} \lambda &= \begin{bmatrix} 0 & & & \\ 1 & 0 & & \\ & 1 & \ddots & \\ & & \ddots & 0 \\ & & & 1 \\ \end{bmatrix}, \quad \mu = \begin{bmatrix} \frac{1}{2s} & & & \\ \frac{1}{2s} & \frac{1}{2s} & & \\ & \frac{1}{2s} & \ddots & \\ & & \ddots & \frac{1}{2s} \\ & & & \frac{1}{2s} \\ \end{bmatrix}. \end{align} $$