Kaehler-Einstein Fano threefolds of degree 22

We study the problem of existence of K"ahler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree $22$ that admit a faithful action of the multiplicative group ${\mathbb{C}}^{\ast }$. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are K"ahler–Einstein.