It would help to provide us with your water parameters. The "basic" corys one sees in stores, such as Corydoras aeneus (this may be your "Emerald," or it may be C. splendens which was formerly classified in the genus Brochis), C. paleatus, C.panda and C. sterbai are all commercially raised (as opposed to wild caught) so they are slightly more tolerant of differing parameters (provided they remain stable, I don't mean parameters that fluctuate within the tank, just to be clear).
All other corys--and there are presently more than 150 described species--will be wild caught, and that means more attention must be paid to water parameters. The three "dwarf" type species, C. pygmaeus, C. habrosus and C. hastatus are even more delicate than the larger species and particular of water parameters.
Temperature is an issue with all cories. Very few like it warm, meaning above 76-77F. C. sterbai do well warmer, and are often combined with discus for this reason, and there are a few other species. But the rest prefer cooler water, 76-77F being tops.
C.panda was mentioned, and this is a definite cooler water, 75F is about max long-term. But this species has another requirement, water movement. Most cories do fine in slow-moving water; they inhabit small streams, creeks, some rivers, but remain near the shore in shallow water which will be slower moving. C. panda is one exception, it occurs in the higher mountain streams of Peru, and appreciates more current. Notwithstanding it is being commercially raised now (it is a very prolific spawner, I've have several fry that survived in community tanks) it has not lost its natural preferences. Mine never tire of playing in the stronger current close to the spraybar, whereas the other cories in this tank rarely if ever come close to this end because of the current. It is not "strong" really, just slightly stronger, as the pandas appreciate. So this is something to keep in mind especially with smallish tanks (mine mentioned is a 4-foot). Combining C. panda with (as an example) gourami that inhabit swamps, or hatchetfish and pencilfish that prefer quiet waters, would be a mistake.
Byron.