What is the standard shape of the crowned spur gear?
I've checked the ISO 6331-1, and there is no point for shape.
Is there any other standard about the shape of crowning?
There is no "standard" for modifying the face profile (crown, lead) of spur gear teeth, or any other type of gear teeth. You should apply whatever amount of crown or lead adjustment your design requires. This is defined by charts/tables in the engineering documentation created for the gear. The optimum amount of crown/lead is a compromise between reduced contact/bending stress levels and increased size of the gears.