The elliptic Gromov-Witten invariants of CP^3
  We present two explicit recursions which determine the elliptic Gromov-Witten invariants of CP^3 in terms of the rational ones, and give a table up to degree 5. Unlike the rational Gromov-Witten invariants, the coefficients are negative and fractional.   In a further paper, we will prove that   N^1_ab + (2n-1)N^0_ab/12   is the number of elliptic space curves through a generic lines and b generic points. 
Ezra Getzler (Northwestern University)