p = 1000171, w = 553925, parameters (11) all in F_p
vertex structure (33 cubics, 11 directions x 3 cubics of 3 pencils at every vertex): True
distinct off-vertex intersection points of pencil-0 and pencil-1 cubics over F_p: 297 (expected 297); non-generic vertical lines: 0
pencils of the cubics through each such point -> count: {(0, 1, 2, 3): 297}
time 2.1s
t = 0: #conditions = 1221 (ell = 1221), dim S_t = 1, rank mod p = 1, h^1 mod p = 1220   [0s]
total time 2.1s
p = 1000171 ; quadruple points: 297
reading P (reduced proper points):
  J: t=22 #cond=309 dimS=276 rank=270  h^1=39  dim(kernel)=6   [2s]
  J: t=23 #cond=309 dimS=300 rank=285  h^1=24  dim(kernel)=15   [2s]
  J: t=24 #cond=309 dimS=325 rank=297  h^1=12  dim(kernel)=28   [2s]
  J: t=25 #cond=309 dimS=351 rank=303  h^1=6  dim(kernel)=48   [3s]
  J: t=26 #cond=309 dimS=378 rank=306  h^1=3  dim(kernel)=72   [3s]
  J^(3)=I(3V+3S): t=36 #cond=1854 dimS=703 rank=703  h^1=1151  dim(kernel)=0   [6s]
  J^(3)=I(3V+3S): t=40 #cond=1854 dimS=861 rank=861  h^1=993  dim(kernel)=0   [10s]
  J^(3)=I(3V+3S): t=44 #cond=1854 dimS=1035 rank=1035  h^1=819  dim(kernel)=0   [15s]
  J^(3)=I(3V+3S): t=48 #cond=1854 dimS=1225 rank=1225  h^1=629  dim(kernel)=0   [22s]
  J^(3)=I(3V+3S): t=50 #cond=1854 dimS=1326 rank=1326  h^1=528  dim(kernel)=0   [30s]
  J^(3)=I(3V+3S): t=52 #cond=1854 dimS=1431 rank=1431  h^1=423  dim(kernel)=0   [39s]
reading W (literal weights -> I' = I(3V+S)):
  I': t=24 #cond=369 dimS=325 rank=317  h^1=52  dim(kernel)=8   [39s]
  I': t=25 #cond=369 dimS=351 rank=333  h^1=36  dim(kernel)=18   [39s]
  I': t=26 #cond=369 dimS=378 rank=348  h^1=21  dim(kernel)=30   [39s]
  I': t=27 #cond=369 dimS=406 rank=360  h^1=9  dim(kernel)=46   [39s]
  I': t=28 #cond=369 dimS=435 rank=366  h^1=3  dim(kernel)=69   [40s]
  I': t=29 #cond=369 dimS=465 rank=369  h^1=0  dim(kernel)=96   [40s]
  I'^(3)=I(9V+3S): t=54 #cond=2322 dimS=1540 rank=1540  h^1=782  dim(kernel)=0   [53s]
  I'^(3)=I(9V+3S): t=56 #cond=2322 dimS=1653 rank=1653  h^1=669  dim(kernel)=0   [67s]
  I'^(3)=I(9V+3S): t=58 #cond=2322 dimS=1770 rank=1770  h^1=552  dim(kernel)=0   [82s]
  I'^(3)=I(9V+3S): t=60 #cond=2322 dimS=1891 rank=1891  h^1=431  dim(kernel)=0   [99s]
total 99s
