1. The problem statement, all variables and given/known data Construct the Cayley table for the group of points on the elliptic curve [tex]y^2=x^3+x+4[/tex] over the field F7 of integers modulo seven. 3. The attempt at a solution So I'm familiar with the constructing a Cayley table, but I've not encountered the group of points on the elliptic curve before. 1. Am I right that over the field of integers modulo seven, there are only 4 group elements: the point at infinity, (0,2), (2,0) and (5,1)? (I took x=0,1,2,... found only these integer values of y.) 2. If I understand this correctly, the composition law is to construct a line intersecting any of these two points, and find a third point of intersection between this line and the curve. The problem is, if I take any of the 2 points above, I don't seem to obtain other group elements and maintain closure. Did I misunderstand something in step 1?