It is about 1 inch wide at most, which I think fits the definition of a rapier. An article on Wikipedia says that a long pointy blade 2.5 cm (i.e., an inch) or less qualifies. Of course, Wikipedia is not an infallible authority.
Perhaps it is more properly called a cut-and-thrust sword, but it is too thin and light to be a broadsword, IMO. Aren't they more in the range of 3 - 3.5 cm?
Another interesting thing about my blade is that there are the faint traces of an etched motto on both sides of the blade, but it has been almost polished out over time and is now illegible (at least to me).