  The MAGIC stereoscopic system collected 69 hours of Crab Nebula data between
October 2009 and April 2011. Analysis of this data sample using the latest
improvements in the MAGIC stereoscopic software provided an unprecedented
precision of spectral and night-by-night light curve determination at gamma
rays. We derived a differential spectrum with a single instrument from 50 GeV
up to almost 30 TeV with 5 bins per energy decade. At low energies, MAGIC
results, combined with Fermi-LAT data, show a flat and broad Inverse Compton
peak. The overall fit to the data between 1 GeV and 30 TeV is not well
described by a log-parabola function. We find that a modified log-parabola
function with an exponent of 2.5 instead of 2 provides a good description of
the data ($\chi^2=35/26$). Using systematic uncertainties of red the MAGIC and
Fermi-LAT measurements we determine the position of the Inverse Compton peak to
be at (53 $\pm$ 3stat + 31syst -13syst) GeV, which is the most precise
estimation up to date and is dominated by the systematic effects. There is no
hint of the integral flux variability on daily scales at energies above 300 GeV
when systematic uncertainties are included in the flux measurement. We consider
three state- of-the-art theoretical models to describe the overall spectral
energy distribution of the Crab Nebula. The constant B-field model cannot
satisfactorily reproduce the VHE spectral measurements presented in this work,
having particular difficulty reproducing the broadness of the observed IC peak.
Most probably this implies that the assumption of the homogeneity of the
magnetic field inside the nebula is incorrect. On the other hand, the
time-dependent 1D spectral model provides a good fit of the new VHE results
when considering a 80 {\mu}G magnetic field. However, it fails to match the
data when including the morphology of the nebula at lower wavelengths.
