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We show that trace functions on modules of topological N=2 super vertexalgebras give rise to conformal blocks on elliptic supercurves. We show thatthey satisfy a system of linear partial differential equations with respect tothe modular parameters of the supercurves. Under some finiteness condition onthe vertex algebra these differential equations can be interpreted as aconnection on the vector bundle of conformal blocks. We show that thisconnection is equivariant with respect to a natural action of the Jacobimodular group on the modular parameters and the trace functions. In theappendix we prove the convergence of the trace functions.

Characters of topological N=2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves