The frame says 48Y, which is usually a square flange. But this is a through bolt style where the motor is mounted to the seal plate with long screws from the back.
The screws go from the back of the motor, through the motor and into the seal plate.
So, you need a 1 hp thru-bolt style motor. But, not just any motor will work. Many thru-bolt motors come with a welded foot called a rigid base. You need one without the rigid base. You also need to make sure that the motor is outdoor compatible and you need to verify the voltage will match.
The motor is a Century motor part number 193004 made on May 03 2013 Friday.
The Century catalog lists the part number but it does not show the matching catalog number.
I would suggest that you contact Century with the part number 193004 and ask for the corresponding catalog number and a dealer that would stock the motor.
The catalog number might make a Google search easier.
https://www.centuryelectricmotor.com/PoolLanding.aspx
https://www.centuryelectricmotor.com/Applications/CrossReference.aspx
Here is the Century cross reference tool, but I couldn't get it to work. It just kept loading.
A local motor repair shop might have a suitable motor or be able to fix this one.
You can get the whole pump for about $320. So, I definitely wouldn't buy a motor for anywhere near that much.
Maybe contact Nidec (U.S Motors) to see if they have a compatible motor.
Pool Spa Motors
http://acim.nidec.com/motors/usmotors/-/media/usmotors/documents/catalogs/fl600/pool-55dia-thrubolt.ashx
This motor might work. It's part number AGL10FL1NB and it's 230 volts only if that's what you need.
Nidec Motor Corporation (formerly Emerson Motors) Thru Bolt Motor, 1hp, 1spd, Heat Transfer (agl10fl1nb, C55CXGBM3784, C55TRM3784) - INYOPools.com
This motor might work AGL10FL1H2.
Be careful to verify voltage and that the motor does not have the rigid base. The pictures are sometimes stock and not accurate. The voltage also seems to be different from the manufacturer list and seller description. There are also some left hand threaded motors. So, be careful to verify all specifications.
What voltage is the motor wired for?