We determine the quadratic Chabauty set for integral points on elliptic curves of rank 2 defined over imaginary quadratic fields. This builds on the work of Bianchi ( \({\mathbb {Q} }(\sqrt{-3})\) -Integral points on a Mordell curve, International Congress on Mathematical Software, Springer, 2020) and Balakrishnan et al. (Israel J. Math. 243(1):185–232, 2021). We give the first instance of the implementation of anticyclotomic heights for curves which are not base changes, along with an implementation of a certain sieve for elliptic curves introduced by Balakrishnan et al. (Math. Comput. 86(305):1403–1434, 2017) and used by Bianchi ( \({\mathbb {Q} }(\sqrt{-3})\) -Integral points on a Mordell curve, International Congress on Mathematical Software, Springer, 2020) to determine integral points of rank 2. We give the first example of the determination of the integral points of an elliptic curve of rank 2 defined over an imaginary quadratic field, which is not a base change via quadratic Chabauty.
