Kunyavskii–Tsfasman conjecture for elliptic curves under base change

Let $X$ be the curve with function field $K$, and let $\{E_i/K_i\}$ be a family of elliptic curves obtained by base change. Write $g_{K_i}$ for the genus of the function field $K_i$, $E_v$ for the reduction at a place $v$ of $X$, and $\mathrm{N}v$ for the norm of $v$. Let $\phi_{v,f}$ denote the asymptotic place-density parameters appearing in the source. Kunyavskii–Tsfasman conjecture. One has

$$\lim_{i\to\infty}\frac{\log |c_{E_i/K_i}|}{g_{K_i}}=-\sum_{v\in X,\,f\geq 1}\phi_{v,f}\log\frac{|E_v(\mathbb{F}_{\mathrm{N}v^f})|}{\mathrm{N}v^f}.$$

This is the base-change form of a Brauer–Siegel-type statement for elliptic curves over function fields. The source presents it as conjectural and relates it to the explicit expression for the limiting $L$-function.