Std Tranny In A 2004 Corolla

Short answer yes. The engines are the same and the bolt pattern on the bell housing would be the same. The gears are slightly different between the two generations - the 8th gen were catered for lower RPM power, with the 9th gen were more for mid-range power. Would still work, but at cruise, the 8th gen transaxle will run the engine off its power band. Probably OK, but you'll likely find yourself feeling like the car is low on power.