Score is given in two parts: a base and an extra. The extra varies with HP, relative scores of you and your opponent in PvP, and variable electrum gains in Arena.
AI1 - Base score is 2.
AI2 - Base score is 5.
AI3 - Base score is 10.
Arena - Base score is 15.
Half-Bloods - Base score is 20.
False Gods - Base score is 60.
There is no base for PvP1 or 2.
For a non-PvP EM, you gain extra score equal to 5 * level (where level is 1 for AI1, 2 for AI2, 3 for AI3, 4 for Arena, 5 for Half-Bloods and 6 for False Gods).
Hmm ... I think I should actually write a Wiki article on the mechanics of electrum and score gaining. It's a bit complex and I'm one of the few who actually knows how it works. So. Hang in there, baby.