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The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithmto evaluate all genus Gromov-Witten invariants of quintic Calabi-Yauthreefolds. This paper is to apply the algorithm in genus one case. We use thelocalization formula, the proposed algorithm in [CLLL1, CLLL2], and Zinger'spackaging technique to compute the genus one Gromov-Witten invariants ofquintic Calabi-Yau threefolds. New hypergeometric series identities are alsodiscovered in the process.

Genus one GW invariants of quintic threefolds via MSP localization