That looks like a Silverfish. Quite common on the third party marketplace. The important parameters are the location of the output pins. Most of the newer units have the output on the bottom. I have one, and it's two pins that go into a receptacle that can hold four.
Polarity is not guaranteed to be a standard. You should look at the positive (+) and negative (-) markings on your battery, and verify that the replacement is the same. An adventurous person can easily change them, but it's best to buy the same.
Replacements vary a little in height, but you will see that the battery is held by a metal bracket which can be adjusted up/down so not a problem.
You'll find them on ebay and amazon under 48V Silverfish. They're like commodity items in that marketplace. Anything from 13aH to 17ah will work. You get a better range with the higher aH.
As to which one to buy, you're on your own. Good luck,