Forget about WDM Bell, who shot his elephants back around 1908, in relatively open country, with small calibers. Bell was famous for using .275, .276, 7x57 etc early on, but even Bell increased the caliber size over his career. He was into .318's and such by the end of his elephant hunting days (which of course is still tiny).
The guys who have shot elephant professionally carry .416's and up. I am reading an excellent book right now by Ian Nyschens, called Months of the Sun. Nyshcens hunted his ele's in think jesse bush and felt woefully undergunned with a .404 Jeffrey, or a .416 Rigby. He was only comfortable with doubles in .450 caliber*. He also was not a fan of magazine rifles; he liked the ability to have the second barrel ready to fire instantly if necessary. But he does tell several stories of hunts where the larger capacity of a magazine rifle was critical in surviving the charges of a herd.
* Nyshcens was not a large man so he disliked the pounding from the .500 class rifles...
I have read numerous books now by the old elephant hunters and the majority preferred .458+ calibers, with 500gr bullets.
Of course I have never shot an elephant but when one charges you, especially bulls, you gotta have a large caliber solid that can travel through several feet of spongy bone to hit the brain.
If you are interested in hunting elephants then you owe it to yourself to check out(buy) the movie, Hunting the African Elephant, by Buzz Charlton. I have the DVD and it is outstanding. Hunting cow elephant is about the most dangerous hunting there is, anywhere in the world.