CM ELLIPTIC CURVES AND BICOLORINGS OF STEINER TRIPLE SYSTEMS
David S. Dummit · Bulletin of the London Mathematical Society · 2002
It is shown that a necessary condition for the existence of a bicolored Steiner triple system of order n is that n can be written in the form A2+3B2 for integers A and B. In the case when n=q is either a prime congruent to 1 mod 3, or the square of a prime congruent to 2 mod 3, it is shown that the numbers of colored vertices in the triple system would be unique, and are given by the number of points on specific twists of the CM elliptic curve y2=x3−1 over the finite field Fq. 2000 Mathematics Subject Classification 05B07, 11G20, 14G15 (primary); 11G15, 14K22 (secondary).