12V battery specs.?

IIRC this is the one most commonly used for the Gen III Prius:
Optima DS46B24R Yellow Top Battery for Toyota Prius with SmartKey System - Free Shipping: BatteryMart.com

 

The battery is an AGM VRLA rated I believe at 40 AH capacity. CCA's do not come into the equation because the
12 volt battery does not start the engine "the engine does not have a traditional starter motor" and should not be used directly for jump starting other vehicles.
The battery does not seem to withstand deep discharges well and this often leads to an early demise. This is possibly because the maximum charge rate for the battery is only 4 amps "stated on the battery label. The Prius charging system is capable of charge rates well in excess of 10 time this figure.
I use a mobility battery in place of the OEM this is rated with a 50% higher capacity and is built to withstand deep discharges on a day by day basis without damage.

John (Britprius)

 

You want to replace it with an AGM Battery with external venting. (AGM limits the amount of battery acid thrown about in an accident, external venting limits the build up of flammable or caustic gases, both important as the battery is in the passenger compartment with humans)

It is a group 51 sized battery with JIS posts (smaller than the usual SAE posts) with the posts 'reversed', whch keeps the positive post away from the body. This is designated S46B24R.

Here are two such batteries:

Optima DS46B24R Optima battery direct fit replacement for Prius 2004 + , Prius V & Plug-in Prius with Instructions

Exide AGM Car Battery (Group S46B24R)

 

Yeah, so don't let some 'Good Ol'Boy' shop hang one of those old school load testers on it.
Those testers load the battery higher than that little battery has ever experienced or was designed to handle.