Let $K$ be a quadratic field which is not an imaginary of class number one. We describe algorithm to compute the primes $p$ for there exists elliptic curve over admitting $K$-rational $p$-isogeny. This builds on work David, Larson-Vaintrob, and Momose. Combining this with Bruin-Najman, \"{O}zman-Siksek, most recently Box, we determine above set three fields $\mathbb{Q}(\sqrt{-10})$, $\mathbb{Q}...