I made a soup last night using leftover ham with what I had in the kitchen.

one qt. carton Pacific organic chicken broth + 1/2 carton water (4g)
three cups of fresh mixed southern greens from package (3 effective grams on label)
1/2 cup chopped green onions (2.2 g)
14 oz can of chopped tomatoes (9 eff g)
two cans of black soy beans (6 eff g)
ground Pepper

I had a small ham bone so I simmered it in the broth for a while and then added everthing but the ham. Simmered some more and then added the ham for the last ten min. about an hour total. It made a big pot of soup, six large servings for us at about 8 carbs each. I am diabetic and the black soybeans don't bother my blood sugar. My husband said it was the best soup he ever had. I used either the label or Atkins for the carb counts.
Is there a "shorthand" for effective carbs?

I believe the shorthand for 'effective carb' is ECC which stands for 'effective carbohydrate count'. By the way, I made a ham soup similar to yours today (before I read this) and used dry black soy beans, soaked them, etc. Quite delicious with a big dollop of sour cream on top.