  Let (A,L) be a principally polarized abelian surface of type (1,3). The
linear system |L| defines a 6:1 covering of A onto P2, branched along a curve B
of degree 18 in P2. The main result of the paper is that for general (A,L) the
curve B irreducible, admits 72 cusps, 36 nodes or tacnodes, each tacnode
counting as two nodes, 72 flexes and 36 bitangents. The main idea of the proof
is to use the fact that for a general (A,L) of type (1,3) the closure of the
Severi variety V in |L| is dual to the curve B in the sense of projective
geometry. We investigate V and B via degeneration to a special abelian surface.
