  The magnetic dipole, the electric quadrupole and the Coulomb quadrupole
amplitudes for the transition \gamma N\to \Delta are calculated in quenched
lattice QCD at \beta=6.0 with Wilson fermions. Using a new method combining an
optimal combination of interpolating fields for the $\Delta$ and an
overconstrained analysis, we obtain statistically accurate results for the
dipole form factor and for the ratios of the electric and Coulomb quadrupole
amplitudes to the magnetic dipole amplitude, R_{EM} and R_{SM}, up to momentum
transfer squared 1.5 GeV^2. We show for the first time using lattice QCD that
both R_{EM} and R_{SM} are non-zero and negative, in qualitative agreement with
experiment and indicating the presence of deformation in the N- Delta system.
