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We compute the Hodge polynomials for the moduli space of representations ofan elliptic curve with two marked points into SL(2,C). When we fix theconjugacy classes of the representations around the marked points to bediagonal and of modulus one, the character variety is diffeomorphic to themoduli space of strongly parabolic Higgs bundles, whose Betti numbers areknown. In that case we can recover some of the Hodge numbers of the charactervariety. We extend this result to the moduli space of doubly periodicinstantons.

Hodge polynomials of the SL(2,C)-character variety of an elliptic curve with two marked points