p = 1000039, eps = 146730, parameters U = [853309, 146731, 1000038, 500020, 2, 61239, 210446, 469743, 530297, 789594, 938801]
number of cubics: 44
(1) cubics with J_4 = S_4 (smooth): 44 of 44
(2) vertex v0: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex v1: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex vinf: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex h0: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex h1: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex hinf: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex d0: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex d1: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex dinf: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex g0: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex g1: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) vertex ginf: 33 cubics, 11 tangent directions, sizes [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], one per pencil in each group: True
(2) every cubic passes through exactly the 9 vertices not of its own type
(3) pairs examined: 946; pairs with an anomaly: 0
(3) off-vertex intersection points: 297; on exactly 4 cubics: 297; one cubic per pencil: 297
(3) by direct evaluation, number of cubics through each off-vertex point: [4]
(3) quadruple points per cubic: [27]
    time so far 2.4s
(4) t=46: #monomials=1128, #conditions=1221, rank mod p=1119, h^1 mod p = 102   [5s]
(4) t=47: #monomials=1176, #conditions=1221, rank mod p=1158, h^1 mod p = 63   [7s]
(4) t=48: #monomials=1225, #conditions=1221, rank mod p=1186, h^1 mod p = 35   [9s]
(4) t=49: #monomials=1275, #conditions=1221, rank mod p=1203, h^1 mod p = 18   [11s]
(4) t=50: #monomials=1326, #conditions=1221, rank mod p=1218, h^1 mod p = 3   [14s]
(4) t=51: #monomials=1378, #conditions=1221, rank mod p=1221, h^1 mod p = 0   [16s]
(4) t=52: #monomials=1431, #conditions=1221, rank mod p=1221, h^1 mod p = 0   [18s]
    two consecutive degrees with full rank: stop
