Q: Replacement battery on 2006 BMW 530xi

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Can I replace the battery without a visit to the dealer? What is the proper size battery?
(1) Answer
You need either the dealership or a BMW specialty shop.
A technician has to register the battery to the car. It has an intelligent charging system, which "has to see" the battery, otherwise it won't charge correctly and cause various issues in the future. The original battery is an AGM (Absorbed Glass Mat) and it has different characteristics than a regular acid battery. When the battery ages it has to be charged differently, that’s when the intelligent charging system kicks in.
If you don't use an other AGM, vent hose needs to be installed also to prevent corrosion.
Take your car to a BMW specialist or to the dealership and ask them to replace and register the battery to the car. It needs OE or equivalent diagnostic computer to do so.
Battery replacement is not an easy DIY procedure anymore.