Statistics for Iwasawa invariants of elliptic curves, III

Given a prime p≥ 5, a conjecture of Greenberg predicts that the μ-invariant of the p-primary Selmer group should vanish for most elliptic curves with good ordinary reduction at p. In support of this conjecture, I show that the $5$-primary Iwasawa μ- and λ-invariants simultaneously vanish for an explicit positive density of elliptic curves E/Q. The elliptic curves in question have good ordinary reduction at $5$, and are ordered by their height. The results are proven by leveraging work of Bhargava and Shankar on the distribution of $5$-Selmer groups of elliptic curves defined over Q.