m=2 p=1000171 k=11: 44 cubics
all cubics smooth mod p: True
each cubic through exactly its 9 base vertices; at each vertex 33 cubics with 11 tangent lines, 3 cubics from 3 pencils per line, none a configuration line: True
all 9 intersection points of every pair found over F_p: True (2s)
  pair type cross vertex mults (1, 1, 1, 1, 1, 1) off-vertex mults (1, 1, 1) : 432 pairs
  pair type cross vertex mults (1, 1, 1, 1, 1, 2) off-vertex mults (1, 1) : 216 pairs
  pair type cross vertex mults (1, 1, 1, 1, 2, 2) off-vertex mults (1,) : 54 pairs
  pair type cross vertex mults (1, 1, 1, 2, 2, 2) off-vertex mults () : 24 pairs
  pair type same vertex mults (1, 1, 1, 1, 1, 1, 1, 1, 1) off-vertex mults () : 220 pairs
off-vertex intersection points: 297  (number of cubics through it, pencils): {(4, (0, 1, 2, 3)): 297}
quadruple points per cubic (value: number of cubics): {27: 44}
expected number of quadruple points 9k(m^2-1) = 297
Z: t=50 monomials 1326 conditions 1221 rank 1218 h1 3 dim I_t 108  (6s)
Z: t=51 monomials 1378 conditions 1221 rank 1221 h1 0 dim I_t 157  (10s)
Z: t=63 monomials 2080 conditions 1221 rank 1221 h1 0 dim I_t 859  (15s)
