Let \(E\) be an elliptic curve defined by the equation: \(Y^2+11Y=X^3+11X^2+33X\) and \(X_{\text{ns}}(11)\) the modular curve associated to the normalizer of a non-split Cartan subgroup of level \(11\). By applying the method of linear forms in elliptic logarithms, the authors show the following result: The points \((x,y)\) on \(E\) such that \(x/(xy-11)\in \mathbb Z\) are \((0,0),(0,-11),(-2,-5),\) \((-2,-6),(-6,-2),(-11/4,-33/8)\) and the point at infinity. Further using an isomorphism of \(E\) to \(X_{\text{ns}}(11)\) they show that these seven points correspond precisely to integral points on \(X_{\text{ns}}(11)\), i.e., rational points for which the parametrized elliptic curve has its \(j\)-invariant in \(\mathbb Z\). Especially the result about integral points on \(X_{\text{ns}}(11)\) gives an independent proof of the Baker-Heeger-Stark theorem on imaginary quadratic fields of class number one.