  We report a direct lattice QCD calculation of the strange nucleon
electromagnetic form factors $G_E^s$ and $G_M^s$ in the kinematic range $0 \leq
Q^2 \lesssim 1.2\: {\rm GeV}^2$. For the first time, both $G_E^s$ and $G_M^s$
are shown to be nonzero with high significance. This work uses
closer-to-physical lattice parameters than previous calculations, and achieves
an unprecedented statistical precision by implementing a recently proposed
variance reduction technique called hierarchical probing. We perform
model-independent fits of the form factor shapes using the $z$-expansion and
determine the strange electric and magnetic radii and magnetic moment. We
compare our results to parity-violating electron-proton scattering data and to
other theoretical studies.
