Quadratic points on non-split Cartan modular curves

In this paper, we study quadratic points on the non-split Cartan modular curves Xns(p), for p=7,11, and 13. Recently, Siksek proved that all quadratic points on Xns(7) arise as pullbacks of rational points on X+ns(7). Using similar techniques for p=11, and employing a version of Chabauty for symmetric powers of curves for p=13, we show that the same holds for Xns(11) and Xns(13). As a consequence, we prove that certain classes of elliptic curves over quadratic fields are modular