Doing a tensile test at very slow loading rate and measuring the elastic modulus from very initial linear part of stress-strain curve may give you the elastic modulus, which calls Long Term elastic modulus. However, for elastomers it is difficult to get a linear elastic part of stress-strain curve.

If using a linear elastic pavement analysis model, you will need a single, representative modulus for the asphalt.  As you note, modulus varies substantially depending on temperature and load rate.  It is common to construct a master curve and then select the modulus based on the expected service temperature and traffic speed combination.  However, visco-elastic models can be built into finite element tools so that the modulus will vary with the stress state and temperature.  A Prony series is often used for this purpose.  So the answer depends significantly on the intent of your work and the nature of the modelling tool, as well as the asphalt  sample and test results you have available.