  We analyse the pp elastic scattering amplitudes using the recent LHC data,
revisiting the model proposed by A. Martin based on analytic continuation and
crossing symmetry. Introducing a new form for the scaling function we show that
the data are consistent with the crossing symmetry of the scattering amplitudes
at $\sqrt{s}= $ 7 and 8 TeV. The complex amplitude automatically obeys the
constraints of dispersion relations and their derivatives. The real part
reproduces the zero predicted by A. Martin, which is crucial to describe with
precision the differential cross section in the forward direction at LHC
energies. Since the free parameters of the model are energy independent, the
analytical form of the amplitude leads to predictions for higher and asymptotic
energies.
