We state and prove a long-elusive relation between genus-one Gromov-Witten of a complete intersection and twisted Gromov Witten invariants of the ambient projective space. As shown in a previous paper, certain naturally arising cones of holomorphic
vector bundle sections over the main component M 0 1,k(Pn, d) of the moduli space of stable genus-one holomorphic maps into Pn
have a well-defined euler class. In this paper, we extend this result to moduli spaces of perturbed, in a restricted way, J-holomorphic
maps. This extension is used to show that these cones are the correct genus-one analogues of the vector bundles relating genuszero
Gromov-Witten invariants of a complete intersection to those of the ambient projective space. A relationship for higher-genus invariants is conjectured as well.