Hasse-principle frequency conjecture for genus-one hyperelliptic twists

Let $C/\mathbb Q$ be a genus-one hyperelliptic curve, let $E$ be its Jacobian, let $\Sigma$ be the specified finite set of places, and let $\mathcal F_b$ be the corresponding twist family. Assume every $C_d$ has points everywhere locally and the $2^\infty$-Selmer rank of $E_d/\mathbb Q$ is odd. Let $n_b=\dim\mathcal S_b$. Hasse-principle frequency conjecture. The density of twists having a rational point is

$$\lim_{X\to\infty}\frac{\#\{d\in\mathcal F_b:|d|<X,\,C_d(\mathbb Q)\neq\varnothing\}}{\#\{d\in\mathcal F_b:|d|<X\}}= \begin{cases} 1/2,&n_b=1,\\ 1/8,&n_b=2,\\ 5/64,&n_b=3,\\ 29/1024,&n_b=4. \end{cases}$$

This gives a conjectural exact density for the Hasse principle in the twist family, refining the preceding positive lower bound; it is not resolved in the source.