C~.Z = 36m^2 - 9 : True
degree of the product of the 4k cubics = 36m^2 - 12 : True
N.C~ = -45*m**2 + 3*t + 9 ; equals 3t - 45m^2 + 9 : True
N.Etilde_v = 2
N.E_q = 1 ; N.E_s = 2
N^2 = -216*m**4 + 36*m**2 + t**2 + 6*t - 27
N^2 at t+3 = 6k : 36*m**2*(3*m**2 - 5) ; claim 12(k-4)(k+1) : True
(3.1) reproduces N: True
Z.Etilde_v = 0
incidence count check  sum_C #s(C) = 4|S| : True
incidence count check  sum_C #q(C) = 3 * 12k : True
incidence count check  sum_C #v(C) = 3k * 12 : True
pair bookkeeping 18k^2 = 36k + 6|S| : True
C~^2 + K.C~ = 2g-2 = 0 : True
m=1: k=2, t0=18m^2-9=9, N.C~=-9, a=0, b=-1.0, N^2=-72, 2*reg_bound=20, alpha(I^(3))>=24, criterion FAILS (m=1 needs computation)
m=2: k=11, t0=18m^2-9=63, N.C~=18, a=0, b=3.5, N^2=1008, 2*reg_bound=128, alpha(I^(3))>=132, criterion OK
m=3: k=26, t0=18m^2-9=153, N.C~=63, a=0, b=11.0, N^2=7128, 2*reg_bound=308, alpha(I^(3))>=312, criterion OK
m=4: k=47, t0=18m^2-9=279, N.C~=126, a=0, b=21.5, N^2=24768, 2*reg_bound=560, alpha(I^(3))>=564, criterion OK
m=5: k=74, t0=18m^2-9=441, N.C~=207, a=0, b=35.0, N^2=63000, 2*reg_bound=884, alpha(I^(3))>=888, criterion OK
m=6: k=107, t0=18m^2-9=639, N.C~=306, a=0, b=51.5, N^2=133488, 2*reg_bound=1280, alpha(I^(3))>=1284, criterion OK
m=7: k=146, t0=18m^2-9=873, N.C~=423, a=0, b=71.0, N^2=250488, 2*reg_bound=1748, alpha(I^(3))>=1752, criterion OK
