Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

Abstract

We explore the relation between the Iwasawa invariants $\mu ^{+}$ and $\mu ^{-}$ associated respectively with the plus and the minus Selmer groups of two elliptic curves $E_{1}$ and $E_{2}$ over $\mathbb {Q}$ having isomorphic Galois representations $E_{1}[p^{r}]\cong E_{2}[p^{r}]$ at a prime $p$ of supersingular reduction. We prove that $\mu ^{\pm }(E_{1})=\mu ^{\pm }(E_{2})$ if either is less than $r$, and $\mu ^{\pm }(E_{1}), \mu ^{\pm }(E_{2})\geq r$ if either is greater than or equal to $r$.