[en] We present a high-statistics calculation of nucleon electromagnetic form factors in N_f=2+1 lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use 32³x64 lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to Q²≅1.05 GeV². Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius r₁^v, Pauli radius r₂^v and anomalous magnetic moment κ_v. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon small scale expansion and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed.