Ordered by max(|A|,|B|), elliptic curves have average rank at most 1.5, proved via a new semi-invariant counting argument for binary quartic forms.
Binary quartic forms having bounded invariants, and the bound- edness of the average rank of elliptic curves.Annals of Mathematics, 181(1):191–242, 2015
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Boundedness of average rank of elliptic curves ordered by the coefficients
Ordered by max(|A|,|B|), elliptic curves have average rank at most 1.5, proved via a new semi-invariant counting argument for binary quartic forms.