The problem you hit fairly quickly is to define war elephant.

Lets go with the Abyssinian expedition. A 1868 war where for reasons that haven't mattered in over a century the British empire invaded what is now Ethiopia. Along with a lot of mules and Maria Theresa thalers (a serious contender for coin with the weirdest history) they brought elephants to move artillery pieces. Elephants going to war so war elephants right? Well questionable. They weren't being used as front-line combatants so not classical war elephants. On the other hand roles evolve so as elephants at war perhaps they deserve the title.

Source:The Barefoot Emperor:An Ethiopian Tragedy Philip Marsden