On Conjectures of $μ$-Invariant for Selmer Groups at $p=2$

Let $E$ be an elliptic curve define over $\mathbb{Q}$. Further assume $E$ has good ordinary reduction at $p=2$. In this article, we prove Greenberg's conjecture on the value of the algebraic Iwasawa $μ$-invariant when $E$ has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of