PASS  A H0 = -H0 B
PASS  B H0 = -H0 C
PASS  C H0 =  H1 A
PASS  A H1 =  H1 C
PASS  B H1 =  H1 B
PASS  C H1 =  H0 A
PASS  trd(A) = 0
PASS  nrd(A) = rho
PASS  A^2 = -rho
PASS  trd(B) = 0
PASS  nrd(B) = rho
PASS  B^2 = -rho
PASS  trd(C) = 0
PASS  nrd(C) = rho
PASS  C^2 = -rho
PASS  nrd(H0) = 36(rho+1)
PASS  nrd(H1) = 36(rho+1)
PASS  trd(H0) = -6 alpha
PASS  trd(H1) = -12
PASS  A,B not proportional
PASS  A,C not proportional
PASS  B,C not proportional
PASS  H0,H1 not proportional
PASS  I^2 = -1
PASS  J^2 = -3
PASS  IJ = -JI
PASS  matrix: A H0 = -H0 B
PASS  matrix: B H0 = -H0 C
PASS  matrix: C H0 =  H1 A
PASS  matrix: A H1 =  H1 C
PASS  matrix: B H1 =  H1 B
PASS  matrix: C H1 =  H0 A
PASS  matrix det/trace agree with nrd/trd
PASS  tr(H0)^2 det(H1) != tr(H1)^2 det(H0)  [i.e. alpha^2 != 4]
      tr(H0)^2 = (72 + -108 a + 0 z + 0 az) ; tr(H1)^2 = (144 + 0 a + 0 z + 0 az) ; nrd(H0) = nrd(H1) = (72 + -36 a + 0 z + 0 az)
PASS  alpha even root, alpha^2+3alpha-2 = 0 mod 2^PREC
PASS  z even root, z^2+z+2 = 0 mod 2^PREC
PASS  alpha = 10 mod 16
PASS  z = 2 mod 8
PASS  A,B,C have 2-integral entries and are = scalar (=1) mod 2  [K-V (4.8)]
PASS  v2(det A) = v2(rho) = 0 (A,B,C in GL_2(Z_2))
PASS  U0 = H0/4 = [[2,0],[6,7]] mod 8  [K-V (6.6)]
PASS  U1 = H1/4 = [[2,6],[4,3]] mod 8  [K-V (6.6)]
PASS  v2(det U0) = v2(det U1) = 1
PASS  A~ (t-coord) has odd diagonal and lower-left = 0 mod 4
PASS  B~ (t-coord) has odd diagonal and lower-left = 0 mod 4
PASS  C~ (t-coord) has odd diagonal and lower-left = 0 mod 4
PASS  h0: a = 2 mod 4, b/2 = 0 mod 2, 2c = 0 mod 4, d odd
PASS  h1: a = 2 mod 4, b/2 = 1 mod 2, 2c = 0 mod 4, d odd
t-coordinate matrices mod 2^16 (entries exact mod 2^128 in the json):
  A~ = [[27099, 16212], [10652, 38437]]
  B~ = [[5325, 19218], [688, 60211]]
  C~ = [[33111, 30105], [54200, 32425]]
  h0~ = [[62418, 50488], [11580, 26975]]
  h1~ = [[40754, 28827], [33800, 24779]]
ALL CHECKS PASSED
