Elliptic Curve

Hello,

The equation for an elliptic curve E is y^2 = x^3+ax+b mod n.
E is also equal to a set of points (x,y) such that x is <= n-1 and y can be found by plugging x into the equation mod n and solving that discrete log problem for y. Those points, what are they? Are they all of the points that make up the graph, meaning the domain consists of all integers <= n-1 and the range is the values gotten when plugging x in?