Because of math, the JPEG format does support lossless rotation, as long as the dimensions of the image are multiples of 16 pixels (or 8 depending on the file).

Because of math, the JPEG format does support lossless rotation, as long as the dimensions of the image are multiples of 16 pixels (or 8 depending on the file). But this requires working directly with the JPEG image data, so a package like ImageMagick that reads a formatted file into a pixel buffer, then transforms it and writes it from that buffer to a new formatted file can't support the feature.