David–Fearnley–Kisilevsky weak conjecture on cubic and quintic twists

Let $E$ be the elliptic curve under consideration, let $\mathcal{C}_p(X)$ denote the even primitive Dirichlet characters of order $p$ and conductor at most $X$, and define $n_p(X)=\#\{\chi\in\mathcal{C}_p(X):L(E,\chi,1)=0\}$. David–Fearnley–Kisilevsky weak conjecture.

$$\lim_{X\to\infty}\frac{\log n_3(X)}{\log X}=\frac12,$$

and $n_5(X)$ is unbounded but satisfies $n_5(X)\ll X^\epsilon$ as $X$ tends to infinity for every $\epsilon>0$. This is explicitly described in the source as a weaker conjecture than the sharper random-matrix predictions for $n_3(X)$ and $n_5(X)$; it concerns the growth exponents rather than exact logarithmic factors.