Reduction and isogenies of elliptic curves

Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p \gt 0$. Let $E/K$ be an elliptic curve with a $K$-rational isogeny of prime degree $\ell $. We study the possible Kodaira types of reduction that $E/K$ can have. We also prove some related results for elliptic curves over $\mathbb Q$.