We prove the elliptic transformation law of Jacobi forms for the generating series of
Pandharipande–Thomas invariants of an elliptic Calabi–Yau threefold over a reduced class
in the base. This proves part of a conjecture by Huang, Katz, and Klemm. For the proof we
construct an involution of the derived category and use wall-crossing methods. We express
the generating series of PT invariants in terms of low genus Gromov–Witten invariants and
universal Jacobi forms. As applications we prove new formulas and recover several known …