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), continued:
  J: t=27 #cond=309 dimS=406 rank=308  h^1=1  dim(kernel)=98   [2s]
  J: t=28 #cond=309 dimS=435 rank=309  h^1=0  dim(kernel)=126   [2s]
  J: t=29 #cond=309 dimS=465 rank=309  h^1=0  dim(kernel)=156   [3s]
  J: t=30 #cond=309 dimS=496 rank=309  h^1=0  dim(kernel)=187   [3s]
  J^(3)=I(3V+3S): t=54 #cond=1854 dimS=1540 rank=1539  h^1=315  dim(kernel)=1   [12s]
  J^(3)=I(3V+3S): t=56 #cond=1854 dimS=1653 rank=1647  h^1=207  dim(kernel)=6   [22s]
  J^(3)=I(3V+3S): t=58 #cond=1854 dimS=1770 rank=1743  h^1=111  dim(kernel)=27   [34s]
  J^(3)=I(3V+3S): t=60 #cond=1854 dimS=1891 rank=1814  h^1=40  dim(kernel)=77   [45s]
reading W, continued:
  I'^(3)=I(9V+3S): t=59 #cond=2322 dimS=1830 rank=1830  h^1=492  dim(kernel)=0   [62s]
  I'^(3)=I(9V+3S): t=60 #cond=2322 dimS=1891 rank=1891  h^1=431  dim(kernel)=0   [78s]
total 78s
