class no. # of curves class leader # Aut(E) # points
1 27 y2 + 1xy + 1y = x3 2 2
2 27 y2 + 1xy + 1y = x3 + 1x 2 5
3 27 y2 + 1xy + 1y = x3 + 1x2 + 1 2 4
4 27 y2 + 1xy + 1y = x3 + 1x2 + 1x + 1 2 1
5 9 y2 + 1xy + 1y = x3 + 2x2 6 6
6 9 y2 + 1xy + 1y = x3 + 2x2 + 1 6 0
7 9 y2 + 1xy + 1y = x3 + 2x2 + 2 6 3
8 27 y2 + 1xy + 1y = x3 + 2x2 + 2x 2 3