Below, a linear algebraic group stands for a Zariski-closed subgroup of $\operatorname{SL}_d(\mathbb{C})$ for $d\geq 1$.
I say that a linear algebraic group $G$ is realizable over a subfield $F$ of $\mathbb{C}$ if there is $n\geq1$ and Zariski-closed subgroup $H$ of $\operatorname{SL}_n(\mathbb{C})$, where $H$ is defined by a set of polynomials with coefficients in $F$, such that $G$ and $H$ are isomorphic as algebraic groups.
I am only starting to learn about algebraic groups, but would like to know the following while I'm learning:
Is every semisimple linear algebraic group realizable over $\mathbb{Q}$? If not, is it realizable over a number field?