I think that all poppies are invasive, Geradine, appart from the blue poppies, Mecanopsis, which be a little more difficult to grow.

I find the oriental poppies well behaved unless you try and move an established clump and then any tap root left behind regrows. but glyphosate like roundup solves that problem. I have several that are now forming nice clumps and they don't seem to seed.