I know that classes in Python are typically cased using camelCase.
Is it also the normal convention to have the file that contains the class also be camelCase'd especially if the file only contains the class?
For example, should class className also be stored in className.py instead of class_name.py?
The following answer is largely sourced from this answer.
If you're going to follow PEP 8, you should stick to all-lowercase names, with optional underscores.
To quote PEP 8's naming conventions for packages & modules:
Modules should have short, all-lowercase names. Underscores can be used in the module name if it improves readability.
And for classes:
Class names should normally use the CapWords convention.
See this answer for the difference between a module, class and package:
A Python module is simply a Python source file, which can expose classes, functions and global variables.
The official convention is to use all lower case for file names (as others have already stated). The reason, however, has not been mentioned...
Since Python works cross platform (and it is common to use it in that manner), but file systems vary in the use of casing, it is better to just eliminate alternate cases. In Linux, for instance, it is possible to have MyClass.py and myclass.py in the same directory. That is not so in Windows!
On a related note, if you have MyClass.py and myclass.py in a git repo, or even just change the casing on the same file, git can act funky when you push/pull across from Linux and Windows.
And, while barely on topic, but in the same vein, SQL has these same issues where different standards and configurations may or may not allow UpperCases on table names.
I, personally, find it more pleasant to read TitleCasing / camelCasing even on filenames, but when you do anything that can work cross platform it's safest not to.
My question is, is it also the normal convention to have the file that contains the class also be camelCase'd especially if the file only contains the class
Short answer: No.
Longer answer: should be all lower case and underscores as needed.
From PEP8 "Package and Module Names":
Modules should have short, all-lowercase names. Underscores can be used in the module name if it improves readability. Python packages should also have short, all-lowercase names, although the use of underscores is discouraged.
If you're unclear what a module is:
A module is a file containing Python definitions and statements. The file name is the module name with the suffix .py appended.