There won''t be an $E/\mathbb Q$ with CM by an order $R$ in $\mathbb Q(\sqrt{-D})$ unless $R$ has class number 1, and there are only finitely many such orders. There is a complete list of the corresponding elliptic curves (probably already since the 19th century, modulo the problem that they didn't know the non-existence of a 10th field of class number 1). The isogenies won't be defined over $\mathbb Q$, but certainly one can write them down, fairly easily for the smaller values of $D$. I'm not sure I've seen the $\frac12(1+\sqrt{-163})$ isogeny written down explicitly.