On a local invariant of elliptic curves with a p-isogeny

Matthew Gealy, Zev Klagsbrun

An elliptic curve $E$ defined over a $p$-adic field $K$ with a $p$-isogeny $\varphi :E\to E^{\prime }$ comes equipped with an invariant ${\alpha }_{\varphi /K}$ that measures the valuation of the l…