Title: On a local invariant of elliptic curves with a p-isogeny,
Abstract: An elliptic curve $E$ defined over a $p$-adic field $K$ with a $p$-isogeny
$\phi:E\rightarrow E^\prime$ comes equipped with an invariant $\alpha_{\phi/K}$
that measures the valuation of the leading term of the formal group
homomorphism $\Phi:\hat E \rightarrow \hat E^\prime$. We prove that if
$K/\mathbb{Q}_p$ is unramified and $E$ has additive, potentially supersingular
reduction, then $\alpha_{\phi/K}$ is determined by the number of distinct
geometric components on the special fibers of the minimal proper regular models
of $E$ and $E^\prime$.