  We provide an estimate for the number of nontrivial integer points on the
Pellian surface $t^2 - du^2 = 1$ in a bounded region. We give a lower bound on
the size of fundamental solutions for almost all $d$ in a certain class, based
on a recent conjecture of Browning and Wilsch about integer points on log K3
surfaces. We also obtain an upper bound on the average of class number in this
class, assuming the same conjecture.
