Elliptic curves with nonsplit mod $11$ representations

We calculate explicitly the $j$-invariants of the elliptic curves corresponding to rational points on the modular curve $X_{ns}^+(11)$ by giving an expression defined over $\mathbb{Q}$ of the $j$-function in terms of the function field generators $X$ and $Y$of the elliptic curve $X_{ns}^+(11)$. As a result we exhibit infinitely many elliptic curves over $\mathbb{Q}$ with nonsplit mod $11$representations.