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10 matroids

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.9.423975108✓∅-1rational
3.9.7739759✓all2rational
3.9.80397512✓all2rational
3.9.103397436✓all1rational
3.9.109397336✓all4empty
3.9.1103972432✓all2point over Q(a)/(a^2 - a + 1)
3.9.15139746✓all1point over Q(a)/(a^2 + 1)
3.9.152397412✓all but 21empty
3.9.29339724✓all2point over Q(a)/(a^2 - a - 1)
3.9.353396912✓all2empty