It looks like standard rings for your mower are either part number 13010-ze6-003 or 004, but both appear to supercede to 13010-ze6-013 And a gasket kit is available for your engine.
As far as the engine numbers there should be a 3 or 4 digit number and a 5 digit number stamped into the engine block right next to the engine serial number. but I used your mower model number and serial number to find your engine parts.