The batteries are either lead calcium or AGM. The E9x has IBS (Intelligent Battery System) that theoretically needs to be told when you replace the battery, even if it's like-for-like - this takes about 2 minutes with INPA or Tool32. Some people replace without telling the car, but I've seen stories that this kills the new battery as the system doesn't recalibrate the charging voltage - sounds a bit like urban myth to me, but up to you if you want to take the risk!
If you replace with a different capacity or type, this needs recoding (ideally through an update to the vehicle order), which takes probably 5-10 minutes with NCS). Codeable battery options are:
E B046 BATT_46AH //46 Ah-Batterie
E B055 BATT_55AH //55 Ah-Batterie
E B070 BATT_70AH //70 Ah-Batterie
E B080 BATT_80AH //80 Ah-Batterie
E B090 BATT_90AH //90 Ah-Batterie
E A070 BATT_AGM_70AH //70 Ah-AGM Batterie
E A080 BATT_AGM_80AH //80 Ah-AGM Batterie
E A090 BATT_AGM_90AH //90 Ah-AGM Batterie
To tell what type of battery you have now, check the top of the casing. The capacity will be marked on it; lead calcium batteries are white and AGM batteries are black.
FTR, BMW don't make batteries. The standard batteries are made by a variety of manufacturers - I've seen Exide standard and Banner AGM, so these are both safe bets.