  We construct curves of each genus $g\geq 2$ for which Coleman's effective
Chabauty bound is sharp and Coleman's theorem can be applied to determine
rational points if the rank condition is satisfied. We give numerous examples
of genus two and rank one curves for which Coleman's bound is sharp. Based on
one of those curves, we construct an example of a curve of genus five whose
rational points are determined using the descent method together with Coleman's
theorem.
