Critical $L$-values for some quadratic twists of Gross curves

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Let $K=\mathbb{Q}(\sqrt{-q})$, 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 $\beta =\sqrt{-q}$. T…