  We evaluate the strange nucleon electromagnetic form factors using an
ensemble of gauge configurations generated with two degenerate maximally
twisted mass clover-improved fermions with mass tuned to approximately
reproduce the physical pion mass. In addition, we present results for the
disconnected light quark contributions to the nucleon electromagnetic form
factors. Improved stochastic methods are employed leading to high-precision
results. The momentum dependence of the disconnected contributions is fitted
using the model-independent z-expansion. We extract the magnetic moment and the
electric and magnetic radii of the proton and neutron by including both
connected and disconnected contributions. We find that the disconnected light
quark contributions to both electric and magnetic form factors are non-zero and
at the few percent level as compared to the connected. The strange form factors
are also at the percent level but more noisy yielding statistical errors that
are typically within one standard deviation from a zero value.
