  Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$, whose Weierstrass
points are defined over extensions of $\mathbb{Q}$ of degree at most three, and
at least one of them is rational. Generalizing a result of R. Soleng (in the
case of elliptic curves), we prove that any line bundle of degree $0$ on $C$
which is not torsion can be specialised into ideal classes of imaginary
quadratic fields whose order can be made arbitrarily large. This gives a
positive answer, for such curves, to a question by Agboola and Pappas.
