In 1972, Serre proved the celebrated Open Image Theorem, asserting that for a product of two non-CM, not geometrically isogenous elliptic curves E1,E2 over the rationals, the residue modulo l Galois rep- resentation associated with E1 × E2 is surjective in an appropriate finite group for each sufficiently large prime l. An effective version of this theo- rem seeks to bound the least non-surjective such l. In the talk, I will focus on a family of pairs of semistable elliptic curves, ordered by conductor, and provide upper bounds of the least non-surjective prime within a density one set in this family. This is joint work in progress with Zhining Wei (Brown University).