The elephant is a minor alter ego of Calvin's. It was featured in an 8-page original strip featured at the beginning of The Authoritative Calvin and Hobbes. In it, Calvin has trouble memorizing his vocabulary words for school, so he uses his transmogrifier to change into an elephant. Now endowed with elephants' supposed good memory, he finishes his homework instantly. Calvin then goes outside to play in the mud with Hobbes.
Susie appears at this point, and Calvin cracks a joke about elephants being the Republican mascot; however, Susie does not get it as she cannot see the elephant.
At dinnertime, Calvin (now muddy all over) is noticed by his mother and forced to take a bath; he interprets his mother's disgust as shock towards his elephant form. After bathing, he transmogrifies back into a boy but, to his surprise, is unable to remember the vocabulary after changing back.