  Let $K=\Bbb Q(\sqrt{-q})$, where $q$ is a prime congruent to $3$ modulo $4$.
Let $A=A(q)$ denote the Gross curve. Let $E=A^{(-\beta)}$ denote its quadratic
twist, with $\beta=\sqrt{-q}$. The curve $E$ is defined over the Hilbert class
field $H$ of $K$. We use Magma to calculate the values $L(E/H,1)$ for all such
$q$'s up to some reasonable ranges (different for $q\equiv 7 \, \text{mod} \,
8$ and $q\equiv 3 \, \text{mod} \, 8$). All these values are non-zero, and
using the Birch and Swinnerton-Dyer conjecture, we can calculate hypothetical
orders of $\sza(E/H)$ in these cases. Our calculations extend those given by J.
Choi and J. Coates [{\it Iwasawa theory of quadratic twists of $X_0(49)$}, Acta
Mathematica Sinica(English Series) {\bf 34} (2017), 19-28] for the case $q=7$.
