Quadratic Chabauty and rational points I: p-adic heights
  We give the first explicit examples beyond the Chabauty-Coleman method where Kim's nonabelian Chabauty program determines the set of rational points of a curve defined over $\mathbb{Q}$ or a quadratic number field. We accomplish this by studying the role of $p$-adic heights in explicit nonabelian Chabauty. 
Jennifer S. Balakrishnan and Netan Dogra
math.NT math.AG