  An algorithm to determine all the Gromov-Witten invariants of any smooth
projective curve was obtained by Okounkov and Pandharipande in 2006. They
identified stationary invariants with certain Hurwitz numbers and then
presented Virasoro type constraints that allow to determine all the other
Gromov-Witten invariants in terms of the stationary ones. In the case of an
elliptic curve, we show that these Virasoro type constraints can be explicitly
solved leading to a very explicit formula for the full Gromov-Witten potential
in terms of the stationary invariants.
