Curves in the complement of a smooth plane cubic whose normalizations   are $\Bbb A^1$
  For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves intersecting $B$ at only one point. 
Nobuyoshi Takahashi