As with all trumpets (with the exception of the bass trumpet) the natural harmonic series (scale of partials) is only used from the 2nd partial, since the 1st partial cannot be intoned clearly.
In the low register E4 is reached from the 2nd natural by closing all three valves. By depressing the 4th valve even D4 can be reached. This means that two additional half tones are gained (in the A tuning even C#4 can theoretically be played).
As a rule the scale goes up to G6 (8th partial with the 3rd valve depressed). Trumpet virtuosos can reach even higher notes, but the piercing quality of notes at this pitch is very rarely called for in orchestral literature.