Frequency of rank 3 in a family of quadratic twists of a fixed elliptic curve

For how many fundamental discriminants $d$ with $\vert d\vert\le X$ does the quadratically twisted elliptic curve $E_d$ have rank 3? This question seems to have resisted modeling by random matrix theory. Conjectures have ranged all the way from $x^{1/4}$ all the way up to $x^{1-\epsilon}$. The data sets of Watkins and of Delaunay and the examples of Rubin and Silverberg may give some hints.

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