I have some experience with Elatine triandra. Basically, it was a macronutrient loving plant, so don't let the nitrate or phosphate drop down to zero. Preferably, boost the phosphate to around 1-2 ppm and the nitrate to 10-15 ppm or more. The result will be intensive, fast growth.
Seems to prefer high light and CO2. You have to train it, though, to grow it flat as a foreground plant just like glosso. Plant the stems/runners horizontally along the substrate in parallels.
It's not too different from glossostigma in terms of nutrient demands and maintenance.
Great plant. Another thing that is interesting is that little bulbs grow on the leaf nodes. Eventually those fall off and get buried in other areas around the tank and turn into a full plant. I'm just getting through some algae wars, and the Elatine made it through. If it is left alone it can take some abuse, but once you start moving it around it will melt like a crypt does.
I think its growing habits may have a lot to do with its environment. I've seen photos of it growing in mostly a single layer. But I've also seen it as stems, growing somewhat diagonally. It's the latter that tends to grow the little seed-like nubs at the nodes.
Unfortunately, this stuff starts rotting as soon as it's cut or uprooted, especially the submersed growth. It's really difficult to plant it when the stem is so mushy. But what I've found is that sometimes, if you bury the whole thing, leaves and all, you'll get some new leaves poking out a few days/weeks later. I got really mad when like two pieces kept getting uprooted by some MTS's and I'd find them floating around on the surface every morning. So I finally jammed the darn things all the way into the substrate just so I didn't have to look at them any more, and I really didn't care if they disappeared completely - food for MTS's, I thought. But lo and behold, pretty much where I buried these pieces, I discovered new leaves sprouting. And I don't remember any nubs on these pieces, either.
Oh, and they look more like pearlgrass in their emersed form. Glosso is two leaves per node. Elatine has more leaves per node, I think. So you should be able to tell the difference between glosso and elatine without much problem.
Elatine will grow under medium or strong lighting (possibly even low) - it might affect the growth speed and what it ends up looking like, but I think the key to this plant is macronutrients, as already mentioned. Put some in an over-stocked tank and an under-stocked one, and it's more likely to die away in the under-stocked one. Elatine also doesn't take well to trimming, according to some who have experience keeping this plant.