  The genus $4$ modular curve $X_{ns}(11)$ attached to a non-split Cartan group
of level $11$ admits a model defined over $\mathbb{Q}$. We compute generators
for its function field in terms of Siegel modular functions. We also show that
its Jacobian is isomorphic over $\mathbb{Q}$ to the new part of the Jacobian of
the classical modular curve $X_0(121)$.
