i found this. click the first line, alternator, controls ect. you'll find the coil #333

/www.partstree.com/parts/briggs-and-stratton/engines-vertical-engine-with-recoil-starter/125k02-0243-e1-briggs-stratton-engine-rewind-starter/

Or Google-

Briggs 802574

Download the parts list for your specific engine from Briggs to get the current part number.

Briggs manuals

these ignition coils seldom experience failure. Here are some thoughts to further examine

1. remove the top shroud to gain access. Remove the coil and wire brush any corrosion on the laminated stack where the mounting screws attach. Also clean the aluminum posts where the coil is mounted. Reinstall with the proper gap.

2. Remove the grounding wire from the bottom of the coil. The other end is normally is attached to a connection on the flywheel brake. This step will eliminate any chance of a shorted wire that is grounding your ignition.

3. Test the flywheel magnet to ensure there is strong magnetic attraction. The service manual contains a procedure for this.

4. install the shroud and test for spark. Do not use the glow testers. Use a Briggs gap tester. Otherwise, duct tape the spark plug lead so there is a .166 inch gap between the cylinder head and the end of the spark plug lead. The Briggs tester and the gap test are more demanding than the glow testers and will ensure there is adequate energy to ignite.

5. Test in a darken area such as your garage. There should be a steady stream of sparks. The spark can be blue or amber or invisible.

6. If spark is observed, reinstall the shut off wire to the brake mechanism and retest. If there is no spark, examine the shut off switch.

Briggs Magnetron coils are pretty robust, but they do fail occasionally. Also, Briggs used to make their own coils in the USA while most aftermarket were from all over the place. Briggs now sources offshore so quality has declined. I've got a dead Briggs OEM made in Argentina on the bench.

Your engine calls for a 802574 or 590454. Supposed to be interchangeable but they are different. I'd recommend going with the one which matches visually. B&S OEM should be $40 - $50; aftermarket will range from $20 - $35. OEM doesn't command as large a premium to the decline in quality.

5590454

802574