Due to the issue Raz mentions, stabilizers at the rear corners are essential. Adding two more at the front corners isn't a bad idea, but it's not essential. It would relieve stress on the tongue transition, a weak point in some designs. I know one person that puts a stabilizer under the door, too, with a board to distribute the load. That spot gets a lot of traffic and the dynamic load of stepping up into the trailer.
By my count that's 8 points of support under a 13' trailer. How far do you want to go?
I use the 5 provided by Scamp
: rear Atwood stabs, wheels, and tongue jack. Feels plenty solid.