Zywina's agreeable-closure classification for rational non-CM $j$-invariants

Let $j \in \Q$ be a non-CM rational $j$-invariant. Write $\cG_j$ for the associated adelic Galois-image subgroup, let $(\cG_j)_{\operatorname{agr}}$ be its agreeable closure, and let $X_{(\cG_j)_{\operatorname{agr}}}$ be the corresponding modular curve. Zywina's agreeable-closure classification. If the modular curve $X_{(\cG_j)_{\operatorname{agr}}}$ has infinitely many rational points, then the intersection $\cG_j \cap \operatorname{SL}(\widehat{\mathbb Z})$ is one of the conjugacy classes given in the paper's table of infinite special-linear intersections. On the other hand, if $X_{(\cG_j)_{\operatorname{agr}}}$ has finitely many rational points, then $j$ and $\cG_j$ are given in the paper's table of exceptional $j$-invariants. This is a conjectural classification of the possible agreeable closures, and hence of the intersections with $\operatorname{SL}(\widehat{\mathbb Z})$, for non-CM elliptic curves over $\mathbb Q$; the stated alternatives organize the cases according to whether the associated modular curve has infinitely or finitely many rational points.