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.
The density of discriminants of quintic rings and fields.Ann
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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.