There particular weed dominates my garden annually. It seemed to come about after one particular season when I picked up a load of cow manure. I keep it under control throughout the growing season but once the garden has breathed it's last, this weed takes over. It is the last to die back and the first to emerge. I till it under every spring. It flowers extremely early. It is in full bloom right now. It doesn't seem to hurt the fertility of my soil. In fact, i think it may be a benificial ground cover only because my soil is always rich and I plant the same plants in the same place each year and they always thrive. Of course I amend the soil each season. Can you identify from the photos?
