How do I identify the correct battery for my electric bicycle?
Yes it's possible, but there are a few things to check before getting a new battery:

Some battery systems communicates information to the controller. There are no standards here, so most likely different brands are not compatible. 

To know whether your battery has this, check connector between the battery and controller. If it's more than a simple 2 pin (positive and negative) connection to the battery, it's likely you'll need to get a battery from the same brand and ask them about whether it's compatible.

If there's only a simple connection, then you're in luck, as you can use a generic battery as replacement. But there's still a few things to be aware of:


Find a battery of the same voltage (48V) and type (I'm assuming Li-ion based on the voltage and capacity you provided).
If possible, find out the maximum current draw from the controller. Common values range from 15A to 25A. Your new battery should be able to handle the same amount of current to prevent overheating and damaging the battery.
The new battery should have a battery management system (BMS) with protection from over-current. This will ensure your new battery has a better life span.


Side note: because of the smaller capacity, you'll be using a wider charge and discharge range on the battery. For Li-ion batteries, this results in shorter lifespan of the battery. Just something you might want to be aware of. 

As a rule of thumb, you should get a battery size that will mean you only need to use max 80% of it's full capacity before recharging. This will greatly enhance the lifespan compared to a 100% charge / discharge each time.