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- W2255367803 abstract "Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes of $n$-Selmer groups, have given new upper bounds on the 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, the distributions of which may also be compared to these theoretical results. A striking new phenomenon observed in these databases is that the average rank eventually decreases as height increases." @default.
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- W2255367803 date "2016-01-01" @default.
- W2255367803 modified "2023-09-26" @default.
- W2255367803 title "Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks" @default.
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- W2255367803 doi "https://doi.org/10.1112/s1461157016000152" @default.
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