Yeah, there is a rare kind of system that I like to call the "ringed" system. In those, the majority of planets are ringed, even those which are rarely ringed - and often a number of the moons are ringed as well. Yours obviously goes into this category too, since the first two planets are also ringed.
These are pretty good places to find ringed ELWs - but the problem is that I don't think there's actually a way of being able to tell from the galaxy map what systems might have better chances of being "ringed" systems.
"You get a ring, and you get a ring, and everyone gets a ring! RINGS!!!"