Statistics for Iwasawa invariants of elliptic curves, III

Given a prime p 5, a conjecture of Greenberg predicts that the -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 - and -invariants simultaneously vanish for an explicit positive density of elliptic curves E/ₐ. 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.