Selmer groups of certain abelian varieties with complex multiplication

Abstract

Let $A$ denote a quadratic twist of the Gross curve over $H$ with complex multiplication by $K=\mathbb {Q}(\sqrt {-q})$, where $q$ is a prime with $q \equiv 7\, \mathrm {mod}\, 8$, and $H$ is the Hilbert class field of $K$. We assume that $A$ has good red