  We discuss Jacobi forms that are invariant under the action of the Weyl group
of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of
generators of the algebra of E_n weak Jacobi forms. We first construct n+1
independent E_n Jacobi forms in terms of Jacobi theta functions and modular
forms. By using them we obtain Seiberg-Witten curves of type E_6 and E_7 for
the E-string theory. The coefficients of each curve are E_n weak Jacobi forms
of particular weights and indices specified by the root system, realizing the
generators whose existence was shown some time ago by Wirthm\"uller.

High Energy Physics - Theory;Algebraic Geometry;Number Theory