In most ways, the reproductive physiology of female elephants is very similar to that of other mammals.  Estrogen and progesterone levels rise and fall in a hormonal cycle in much the same way as it does in females of other species. 

Estrogen (E) and progesterone (P) levels rising and falling in an Asian Elephant over a 40 week period

However, there is something about the reproductive cycle of female elephants that is quite puzzling to reproductive biologists.  In between their peaks of progesterone, elephant females experience peaks of Lutenizing Hormone (LH)—just as females of other species do—and, like females of other species, she is sexually receptive at this time.  However, when a female comes into heat as a consequence of the first LH surge, she evidently can not become pregnant—even if she mates with a male.  As far as scientists can tell, a female elephant needs to come into heat a second time three weeks later, and it is only within this second period of receptivity that she can actually become pregnant.  In other words, each female has two LH hormonal peaks within each progesterone cycle, and only the second peak is a fertile one. 

Lutenizing Hormone (LH) levels rising and falling twice per progesterone cycle in an Asian Elephant, over a 40 week period

We know of no other species of animal in which this occurs, and we can only speculate about how this is beneficial to the elephants.  All we can say at this point is that the reproductive rules that apply to nearly all other mammal species do not function in exactly the same way in elephants.