Most systematic tables of data associated to ranks of elliptic curves orderthe curves by conductor. Recent developments, led by work of Bhargava-Shankarstudying the average sizes of $n$-Selmer groups, have given new upper bounds onthe average algebraic rank in families of elliptic curves over $\mathbb{Q}$ordered by height. We describe databases of elliptic curves over $\mathbb{Q}$ordered by height in which we compute ranks and $2$-Selmer group sizes, thedistributions of which may also be compared to these theoretical results. Astriking new phenomenon observed in these databases is that the average rankeventually decreases as height increases.
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