Local invariants of isogenous elliptic curves

Abstract

We investigate how various invariants of elliptic curves, such as the discriminant, Kodaira type, Tamagawa number and real and complex periods, change under an isogeny of prime degree p. For elliptic curves over l-adic fields, the classification is almost complete (the exception is wild potentially supersingular reduction when l=p), and is summarised in a table.