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Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava and Shankar studying the average sizes of
-Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over
, ordered by height. We describe databases of elliptic curves over
, ordered by height, in which we compute ranks and
-Selmer group sizes, the distributions of which may also be compared to these theoretical results. A striking new phenomenon that we observe in our database is that the average rank eventually decreases as height increases.
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