Parametrization of virtually $K$-rational Drinfeld modules of rank two

For an extension $K/\mathbb{F}_q(T)$ of the rational function field over a finite field, we introduce notion virtually $K$-rational Drinfeld modules as analogue $\mathbb{Q}$-curves. Our goal in this article is to prove that all rank two with no complex multiplication are parametrized up isogeny by points quotient curve modular $Y_0(\mathfrak{n})$ some square-free level $\mathfrak{n}$. This Elkies' well-known result on