  Rotation periods of 53 small (diameters $2 < D < 40$ km) Jupiter Trojans
(JTs) were derived using the high-cadence light curves obtained by the FOSSIL
phase I survey, a Subaru/Hyper Suprime-Cam intensive program. These are the
first reported periods measured for JTs with $D < 10$ km. We found a lower
limit of the rotation period near 4 hr, instead of the previously published
result of 5 hr (Ryan et al. 2017; Szabo et al. 2017, 2020) found for larger
JTs. Assuming a rubble-pile structure for JTs, a bulk density of 0.9 gcm$^{-3}$
is required to withstand this spin rate limit, consistent with the value
$0.8-1.0$ gcm$^{-3}$ (Marchis et al. 2006; Mueller et al. 2010; Buie et al.
2015; Berthier et al. 2020) derived from the binary JT system, (617)
Patroclus-Menoetius system.
