I am currently revising for an exam and need some help with a question. Below is an example from my notes which I am trying to understand. I can fill out the table just fine, but I can't figure out how to find the points from it. If someone could run through getting each point I would be grateful.
Example 1: Let p = 5 and y2 = x3-3x^2+3x. Draw up a table of values of x^3-3x^2+3x. x x^2 x^3 -3x^2 3x x^3-3x^2+3x 0 0 0 0 0 0 1 1 1 2 3 1 2 4 3 3 1 2 3 4 2 3 4 4 4 1 4 2 2 3 Now mod p, 0^2=0, 1^2=1, 2^2=4, 3^2=4 and 4^2=1.
(please note that the equal signs in the above line are congruence signs in notes, I don't know how to put them in here)
Thus we can list the points of our elliptic curve mod p. (0, 0) (1, 1) (1, 4) (3, 2) (3, 3)