Strictly speaking, the conjugations of 得る are: - negative: えない - masu form: えます - te form: えて - terminal form (i.e. at the end of sentences, or when attaching to べき): える／うる - attributive form (i.e. akin to such things as すきな for すき; used when attaching to nouns): うる - conditional form: うれば
It is the only 二段 (nidan) verb from old Japanese that hasn't fully become an 一段 (ichidan) verb in modern Japanese. (える／うる in old Japanese was う, so it has changed a little already.)
In summary, although うる is a more archaic way of saying える, the only time you can choose between える／うる is when it comes at the end of the sentence, or when attaching to べき (in which case, however, うる is also preferable due to the also archaic nature of べき). This means one should say for example うるために, うるように, うること, うるところ and so on. Additionally, ありうる is never ありえる.
However, in practice, the "wrong" forms are still somewhat often used.
うる is archaic or 文語体 whereas える is modern. However,うる is still used, e.g., 考えうる、成しうる, etc.
Try not to get confused with える (same kanji /generally/ different meaning).
A verb-suffix 得る will generally have this meaning and /usually/ be pronounced うる but I hear that it's increasingly common for that usage to /also/ be pronounced える
In summary : This is a pig of a word(s) ;-)
Note that Edict examples presently include える and うる in the same list.
#6482 should say "medal in THE Olympics" and should have a period at the end.