1. Given $K$ a number field and $E/K$ an elliptic curve, is there an algorithm which gives all the elliptic curves $F/K$ isogenous to $E$ (up to isomorphism)?

2. Or is there a bound on how many $F/K$ are isogenous to $E/K$?

3. If $E/K$ and $F/K$ are isogenous is the isogeny necessarily defined over $K$?

For a fixed degree, I know we can use modular polynomials to find $F/K$. However is there a bound on the degree? I know that when $K=\mathbb{Q}$, this follows from Mazur's theorem.