  The Virasoro conjecture proposed by Eguchi-Hori-Xiong and S. Katz predicts
that the generating function of Gromov-Witten invariants is annihilated by
infinitely many differential operators which form a half branch of the Virasoro
algebra. In this paper, we study the genus-1 case of the conjecture. In
particular, we will give some necessary and sufficient conditions for the
genus-1 Virasoro conjecture.
