楕円曲線
Over an algebraically closed field "K" an elliptic curve is determined by its "j"-invariant, so there are only a finite number of supersingular elliptic curves. If each such curve is weighted by 1/|Aut("E")| then the total weight of the supersingular curves is ("p"–1)/24. Elliptic curves have automorphism groups of order 2 unless their "j"-invariant is 0 or 1728, so the supersingular elliptic curves are classified as follows.