The Iwasawa Invariants of the Plus/Minus Selmer Groups

Abstract

We study the Iwasawa $\mu$- and $\lambda$-invariants of the non-primitive plus/minus Selmer groups of elliptic curves for supersingular primes. We prove that they are constant for a family of elliptic curves with the same residual representation if the $\mu$-invariant of any of them is 0. As an application we find a family of elliptic curves whose plus/minus Selmer groups have arbitrarily large $\lambda$-invariants.