Q:

Is "elder brother" implicit in "brother"? 

I just watched a film called Diary of a Wimpy Kid: Rodrick Rules. 
I wonder how one knows whether he is an elder brother or a younger brother when he only says that he has a brother and does not specify?  Does brother usually mean elder? 
I saw in the film; when the boy says he has a brother, the girl immediately knows the brother is older than him. 

A:

I've not seen the movie, but the word brother itself doesn't indicate whether the sibling is elder or younger.   If the girl did immediately know the brother was older, she must have been able to infer it from context or have some a priori knowledge. 
Usually when you need to specify the relative age of a sibling, you'll use something like:

my older/younger brother

You'll also frequently see a "size" adjective substituted for a strict age comparative, usually among children (where there's a stronger correlation between size and age than in adults):

my big/little sister

