Photoshop Curve is a Photoshop format that describes one or more mathematical functions most likely used as transfer functions, i.e. ways to adjust the brightness, contrast, etc. of an image.
It is distinct from Photoshop Transfer Function (ATF) format, though the formats appear to be used for roughly the same purposes.
A Curve file begins with bytes
00 01 or
00 04, and is usually under 100 bytes in size.