  We prove an explicit formula for the genus-one Fan-Jarvis-Ruan-Witten
invariants associated to the quintic threefold, verifying the genus-one mirror
conjecture of Huang, Klemm, and Quackenbush. The proof involves two steps. The
first step uses localization on auxiliary moduli spaces to compare the usual
Fan-Jarvis-Ruan-Witten invariants with a semisimple theory of twisted
invariants. The second step uses the genus-one formula for semisimple
cohomological field theories to compute the twisted invariants explicitly.
