Nominative and genitive are cases for nouns, it has nothing to do with verbs. At first you may think that declensions are just bizarre, but in fact they are nicely arranged into a system. Otherwise, noone would be able to learn the language!
So there are types of declensions, and if you know genitive - you know the type of declension - you know all other cases. This works not only for Russian students - when I studied Latin we had to memorize nominative and genitive at once too.