arXiv:1702.02325math.NT
$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture
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Abstract
We prove that the $2^\infty$-class groups of the imaginary quadratic fields have the distribution predicted by the Cohen-Lenstra heuristic. Given an elliptic curve E/Q with full rational 2-torsion and no rational cyclic subgroup of order four, we analogously prove that the $2^\infty$-Selmer groups of the quadratic twists of E have distribution as predicted by Delaunay's heuristic. In particular, among the twists E^d with |d| < N, the number of curves with rank at least two is $o(N)$.
It's not accurate. Looking at the arxiv link (https://arxiv.org/abs/1702.02325), the idea is you fix some elliptic curve E, and you look at its "twists" E^d, where the parameter d is a nonzero integer. If you only look at twists where |d| < N, you can ask "What proportion of…
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