wow! 1360kg is serious!
Last time I had my tank on the weight it showed 1518kg but with a full tank of gas, full carpet and the rear roll cage like the GTS has it.
Don't you worry about the battery?
The M3 has a intelligent battery management and the smallest value you can program is a 55Ah Battery (what I'm running)
Everybody I talked to adviced me not to go smaller as the system will go crazy and in the worst case your alternator will charge at 100% all the time which will cost additional HP.
If you know more - let us know!