Irreducible plane curves with the Albanese dimension 2

Let $B$ be a plane curve given by an equation $F(X_{0}, X_{1}, X_{2}) = 0$, and let $B_{a}$ be the affine plane curve given by $f(x, y) = F(1,x, y) = 0$. Let $S_{n}$ denote a cyclic covering of ${\mathbf{P}}^{2}$ determined by $z^{n} = f(x, y)$. The number $\max _{ n \in {\mathbf{N}}} \left ( \text{\rm dim} \, Im(S_{n} \to Alb (S_{n})) \right )$ is called the Albanese dimension of $B_{a}$. In this article, we shall give examples of $B_{a}$ with the Albanese dimension 2.