Try this.
Go to the BIOS and if the bios permits it disallow
'wake on Lan' or 'wake on magic packet'
If the BIOS doesn't have this and many don't, then go to Network adapter properties-> Advanced and scroll down there looking for Wake on LAN. I just looked at mine and the default seems to be disabled but yours might not be.
Maybe your ISP is waking you up accidentally.
Also is it being woken up by Windows update I wonder? That 'half way through the night' is suspicious as 3am is the default time for Windows update to do a shutdown and restart.