You won't start finding elven longswords in random loot at just lvl 4, so if you want one your just going to have to wait until you're about lvl 15. It's true Azani Blackheart, who can be encountered during that pesky fighter's guild quest has an elven claymore (that also deals pretty good fire damage).
Also Umaril the Unfeathered in the K of the 9 quest has an elven sword too.
There's a ceremonial Elven Longsword in Chorrol's Fighter's Guild so if your security is good you can get that, though bear in mind it'll only do 1 damage cos' it's ceremonial.
Hope that helped, just your friendly neighborhood Oblivion nerd here.