p = 1002073; eps -> 426127
P^1[6] modulo p: 11 roots in F_p
cubics: 44
vertices: 33 cubics through each, 11 tangent lines, 3 cubics from 3 pencils on each: True
pairs (pencil 0, pencil 1): 6 common vertices, 3 - (shared tangents) further points, all F_p-rational: True; distinct further points: 297 (expected 297)
each of these points on exactly 4 cubics, one per pencil, with 4 distinct tangent lines: True ; number on each cubic: [27]
t   dim R_t  rank  h^1(I_Z(t)) modulo p
 45   1081   1078   143
 46   1128   1119   102
 47   1176   1158    63
 48   1225   1186    35
 49   1275   1203    18
 50   1326   1218     3
 51   1378   1221     0
running time 25.2 s

Remark 1.2(b): vertices at which every element of I_t has multiplicity >= k+1 = 12
  t = 45: dim I_t = 3; vertices where every element has multiplicity >= 12: 0
  t = 46: dim I_t = 9; vertices where every element has multiplicity >= 12: 0
  t = 47: dim I_t = 18; vertices where every element has multiplicity >= 12: 0
  t = 48: dim I_t = 39; vertices where every element has multiplicity >= 12: 0
  t = 49: dim I_t = 72; vertices where every element has multiplicity >= 12: 0
  t = 50: dim I_t = 108; vertices where every element has multiplicity >= 12: 0
  t = 51: dim I_t = 157; vertices where every element has multiplicity >= 12: 0
