These are parametrized by $H^1(Gal(\mathbb{Q}), Aut X)$, where X is *some* $\mathbb{Q}$-model of the curve.

It was established in Confusion about how the first cohomology classifies torsors that fiber bundles over $B$ with fiber $F$, structure group $G$ and transition maps with property $P$ are classified by $T$-torsors, where $T$ is the sheaf on $B$ of functions to $G$ with property $P$. $T$-torsors, in turn, are classified by $H^1(B, T)$.

Is there a way to interpret the aforementioned classification of $\mathbb{Q}$-models of a curve in these terms?