In case the diagram of my LW/MW passive loop could not be depicted from the description in a previous post, here is a graphical representation.
The transformer core is unknown, salvaged from some electronic equipment that needed an RF-choke to prevent RF radiation.
As a rule of thumb I would assume all those cores are good candidates for LW/MW use. I used 24 turns on the loop side and 4 turns on the 50 ohm side.