  Let $X$ be one of the $28$ Atkin-Lehner quotients of a curve $X_0(N)$ such
that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We
show that the Shafarevich-Tate group of $J/\mathbb{Q}$ is trivial. This
verifies the strong BSD conjecture for $J$.
