A rigorous extraction of the deuteron charge form factors from tensor polarization data in elastic electron-deuteron scattering, at given values of the 4-momentum transfer, is presented. Then the world data for elastic electron-deuteron scattering is used to parameterize, in three different ways, the three electromagnetic form factors of the deuteron in the 4-momentum transfer range 0-7 fm^-1. This procedure is made possible with the advent of recent polarization measurements. The parameterizations allow a phenomenological characterization of the deuteron electromagnetic structure. They can be used to remove ambiguities in the form factors extraction from future polarization data.
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