m = 3, k = 26: |P^1[9]| = 26
cubics: 104
each vertex: exactly 3k = 78 cubics through it (none from its own pencil), exactly k = 26 tangent directions, each shared by 3 cubics from 3 different pencils: True
every pair of cubics from different pencils: 6 common vertices, intersection multiplicity 2 exactly at the common vertices with a shared tangent, and 3 - (number of shared tangents) further points: True (shared tangents counted over all pairs: 936, expected 6*12*k/2 = 936)
distinct intersection points off the vertices: 1872 (expected 9k(m^2-1) = 1872)
each of these points lies on exactly 4 cubics, one from each pencil, with 4 distinct tangent lines, and was found from all 6 pairs of pencils: True
number of these points on each cubic: [72] (expected 9(m^2-1) = 72)
running time 1820.1 s
