On Greenberg's conjecture for rational elliptic curves at Eisenstein primes

Let $E/\mathbb{Q}$ be an elliptic curve, and let $p$ be an odd prime of ordinary reduction for $E$, and assume that $E$ admits a rational $p$-isogeny. In this paper we prove Greenberg's conjecture on the vanishing of algebraic Iwasawa $μ$-invariants of the Selmer groups attached to $E$ over the cycl