Fine points of the moduli space of cubic rational maps

A rational point of the moduli space $\mathcal{M}_3$ of cubic rational maps is fine if its conjugacy class contains a map defined over $\mathbb{Q}$, and coarse otherwise. In the invariants $ξ_0,\dots,ξ_5$ that embed $\mathcal{M}_3$ in $\mathbb{P}(2,2,3,3,4,6)$, we prove that a point with trivial aut