There are finitely many rational points on a nice projective curve defined over the rationals of genus at least 2, but it is a difficult problem to explicitly determine these points. The quadratic Chabauty method is a p-adic method for determining these rational points under some constraints. In this talk, I will explain how we can leverage information from special values of p-adic L-functions to improve the quadratic Chabauty method for modular curves, leading to a new algorithm to determine rational points on certain modular curves.