I agree with Paul on the 10 gallon per inch rule. Most people don't realise that turtles can be pretty active animals and like to have room to move around and explore. If you want a turtle to keep in an aquarium I too would recommend one of the species of musk or mud turtles. They tend to stay on the small side.
10 gallons/inch is a decent rule of thumb (as good as anything anyway)...I usually go with 5xadult length of the turtle long by 2xlength wide, by that metric you could keep a 10" turt in a 75G (48x18). Of course you have to adjust if there are multiple turts.
So anyway you could probably keep one of the smaller (North American) mud/musk turtle species in a 20G (long). I'm not sure if there's a basking-type turtle that would fit the bill, the smallest commonly available basking turt is probably Reeve's turtle, and I think a Reeves would be cramped in a 20.
stink pots are fun to observe the breed easy (mr jars has a pair about 3inch shell length in a 20L growout and they breed)...a single will be ok for a while in a 20L...
if you have a 40 or 60 gallon that's only 12inches deep what's the difference from that and a 20L... a breeder tank is the minimum needed for a turtle... 36x18x? that's the minimum footprint you should look for......