Transaxle gear oil
Oil grade API GL–4 or GL–5
Viscosity SAE 75W–90
Capacity 2.6 liters (2.7 US qts, 2.3 Imp. qts)

and if a 4 wheel drive Corolla:
Transaxle oil (M/T, differential and transfer):
Recommended oil Transaxle oil E50
(08885–80206) or equivalent
Oil grade API GL–5
Viscosity Above –181C (O°F) SAE
75W–90, 80W–90 or 90
Below –180C (O*F) SAE
75W–90 80W–90 or 80W
Capacity 5.0 liters
(5.3 US qts, 4.4 Imp. qts)

Anyway, you'll need to look in your owners manual or call a toyota dealer. These day's they switch what they use in manual trannys too much. Once you find out what it is then just use a good name brand, and if you want to drive the car forever then use a synthetic version(just an opinion).