  Let $S$ be an elliptic surface over a smooth curve $C$ with a section $O$. We
denote its generic fiber by $E_S$. For a divisor $D$ on $S$, we canonically
associate a $C(C)$-rational point $P_D$. In this note, we give a description of
$P_D$ of $E_S$, when the rank of the group of $C(C)$-rational points is one. We
apply our description to refine our result on a Zariski pair for a cubic-line
arrangement.
