That's an AE86 Corolla with a 1.6/16v 4AGE. And yeah they did come with that engine, but there are other versions of the 4AGE, 20v and 16v, aswell as supercharged (4AGZE). They have different names like blacktop/silvertop but I don't know which ones are which, all I know is that there are quite a few variants of it. Looks pretty much standard to me but it needs a bit of TLC!