Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
9.1.29510281.1 | $x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{5} + 7 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$ | $101\cdot 292181$ | $S_9$ (as 9T34) | trivial |
9.1.30073129.1 | $x^{9} - 2 x^{8} + 2 x^{7} - x^{5} + x^{3} + x^{2} - 2 x + 1$ | $353\cdot 85193$ | $S_9$ (as 9T34) | trivial |
9.1.30450401.1 | $x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + x^{3} - 1$ | $31\cdot 982271$ | $S_9$ (as 9T34) | trivial |
9.1.30453593.1 | $x^{9} - x^{7} - x^{6} + x^{4} - x^{3} + x + 1$ | $137\cdot 222289$ | $S_9$ (as 9T34) | trivial |
9.1.30544313.1 | $x^{9} - x^{8} + x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{2} + 2 x - 1$ | $47\cdot 649879$ | $S_9$ (as 9T34) | trivial |
9.1.30626693.1 | $x^{9} - x^{6} - 2 x^{5} - x^{4} + 2 x^{2} + x + 1$ | $30626693$ | $S_9$ (as 9T34) | trivial |
9.1.30861161.1 | $x^{9} - 3 x^{8} + 5 x^{7} - 5 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} + 3 x - 1$ | $30861161$ | $S_9$ (as 9T34) | trivial |
9.1.31042889.1 | $x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + 2 x^{5} - 2 x^{4} + 3 x^{3} - 3 x^{2} + 3 x - 1$ | $37\cdot 47\cdot 17851$ | $S_9$ (as 9T34) | trivial |
9.1.31508353.1 | $x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - x + 1$ | $359\cdot 87767$ | $S_9$ (as 9T34) | trivial |
9.1.31638601.1 | $x^{9} - x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 2 x^{4} + 1$ | $31638601$ | $S_9$ (as 9T34) | trivial |
9.1.31759433.1 | $x^{9} - 3 x^{5} + 2 x - 1$ | $179\cdot 177427$ | $S_9$ (as 9T34) | trivial |
9.1.32029433.1 | $x^{9} - 2 x^{8} + 3 x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$ | $32029433$ | $S_9$ (as 9T34) | trivial |
9.1.32031161.1 | $x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} - 5 x^{2} + 3 x - 1$ | $61\cdot 525101$ | $S_9$ (as 9T34) | trivial |
9.1.32058553.1 | $x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} + 2 x - 1$ | $32058553$ | $S_9$ (as 9T34) | trivial |
9.1.32206049.1 | $x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - 6 x^{4} + 5 x^{3} - 4 x^{2} + 3 x - 1$ | $23^{3}\cdot 2647$ | $S_3\wr S_3$ (as 9T31) | trivial |
9.1.32344469.1 | $x^{9} - x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + 1$ | $53\cdot 89\cdot 6857$ | $S_9$ (as 9T34) | trivial |
9.1.32652713.1 | $x^{9} - 2 x^{8} + 4 x^{6} - 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x + 1$ | $32652713$ | $S_9$ (as 9T34) | trivial |
9.1.32768213.1 | $x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{2} + x - 1$ | $3413\cdot 9601$ | $S_9$ (as 9T34) | trivial |
9.1.32855993.1 | $x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} - x^{2} - 1$ | $113\cdot 290761$ | $S_9$ (as 9T34) | trivial |
9.1.32894473.1 | $x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 3 x^{4} + x^{3} + x^{2} - 2 x + 1$ | $17\cdot 1934969$ | $S_9$ (as 9T34) | trivial |
9.1.32923873.1 | $x^{9} - x^{8} + 3 x^{7} - 4 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} + 2 x - 1$ | $809\cdot 40697$ | $S_9$ (as 9T34) | trivial |
9.1.32987233.1 | $x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} + x^{4} - 2 x^{3} + 2 x^{2} + 1$ | $32987233$ | $S_9$ (as 9T34) | trivial |
9.1.33121433.1 | $x^{9} + x^{7} - x^{6} - 2 x^{5} - x^{3} + x^{2} + x - 1$ | $1321\cdot 25073$ | $S_9$ (as 9T34) | trivial |
9.1.33445561.1 | $x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{4} + 5 x^{3} - 2 x^{2} - x + 1$ | $449\cdot 74489$ | $S_9$ (as 9T34) | trivial |
9.1.33571261.1 | $x^{9} - x^{8} + x^{6} + x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + x - 1$ | $43\cdot 857\cdot 911$ | $S_9$ (as 9T34) | trivial |
9.1.33626161.1 | $x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 12 x^{5} - 12 x^{4} + 11 x^{3} - 8 x^{2} + 4 x - 1$ | $23\cdot 67\cdot 21821$ | $S_9$ (as 9T34) | trivial |
9.1.33860761.1 | $x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{5} + 2 x^{4} - x + 1$ | $11^{2}\cdot 23^{4}$ | $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30) | trivial |
9.1.33984793.1 | $x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{2} - x - 1$ | $33984793$ | $S_9$ (as 9T34) | trivial |
9.1.34090153.1 | $x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$ | $71\cdot 480143$ | $S_9$ (as 9T34) | trivial |
9.1.34349041.1 | $x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + x^{2} - 1$ | $34349041$ | $S_9$ (as 9T34) | trivial |
9.1.34405373.1 | $x^{9} - x^{8} + x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + x^{2} - 2 x - 1$ | $34405373$ | $S_9$ (as 9T34) | trivial |
9.1.34573709.1 | $x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} - x + 1$ | $34573709$ | $S_9$ (as 9T34) | trivial |
9.1.34590113.1 | $x^{9} - x^{8} + x^{7} + x^{6} - x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1$ | $509\cdot 67957$ | $S_9$ (as 9T34) | trivial |
9.1.34628113.1 | $x^{9} - x^{6} - x^{5} + x^{4} + x^{3} + x^{2} - 1$ | $13\cdot 2663701$ | $S_9$ (as 9T34) | trivial |
9.1.35028793.1 | $x^{9} - 2 x^{8} + 4 x^{7} - 7 x^{6} + 10 x^{5} - 11 x^{4} + 11 x^{3} - 8 x^{2} + 4 x - 1$ | $23^{3}\cdot 2879$ | $S_3\wr S_3$ (as 9T31) | trivial |
9.1.35050633.1 | $x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x^{2} + x - 1$ | $43\cdot 311\cdot 2621$ | $S_9$ (as 9T34) | trivial |
9.1.35051893.1 | $x^{9} - x^{8} + 3 x^{7} - 3 x^{6} + 5 x^{5} - 5 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $109\cdot 321577$ | $S_9$ (as 9T34) | trivial |
9.1.35234033.1 | $x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{3} - 2 x^{2} + 2 x - 1$ | $59\cdot 347\cdot 1721$ | $S_9$ (as 9T34) | trivial |
9.1.35357129.1 | $x^{9} + x^{7} - 3 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - x^{2} + 2 x - 1$ | $41\cdot 862369$ | $S_9$ (as 9T34) | trivial |
9.1.35607973.1 | $x^{9} - 2 x^{7} + 4 x^{5} - 4 x^{3} - x^{2} + 2 x + 1$ | $5501\cdot 6473$ | $S_9$ (as 9T34) | trivial |
9.1.35666053.1 | $x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 1$ | $787\cdot 45319$ | $S_9$ (as 9T34) | trivial |
9.1.35678113.1 | $x^{9} - x^{8} + 3 x^{6} - 3 x^{5} + 3 x^{3} - 2 x^{2} - x + 1$ | $199\cdot 179287$ | $S_9$ (as 9T34) | trivial |
9.1.35686793.1 | $x^{9} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} - 3 x - 1$ | $35686793$ | $S_9$ (as 9T34) | trivial |
9.1.35935321.1 | $x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{4} - x^{2} - 1$ | $29\cdot 337\cdot 3677$ | $S_9$ (as 9T34) | trivial |
9.1.36055441.1 | $x^{9} - x^{8} - x^{7} + x^{6} + x^{5} + x^{4} - x^{3} - 2 x^{2} + x + 1$ | $41\cdot 879401$ | $S_9$ (as 9T34) | trivial |
9.1.36155633.1 | $x^{9} - x^{8} + x^{7} - x^{6} - x^{3} + x^{2} + 1$ | $36155633$ | $S_9$ (as 9T34) | trivial |
9.1.36722413.1 | $x^{9} - x^{8} + x^{6} - x^{4} + x^{3} + x^{2} - 2 x + 1$ | $7^{2}\cdot 13\cdot 57649$ | $S_9$ (as 9T34) | trivial |
9.1.36743849.1 | $x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 13 x^{5} - 14 x^{4} + 12 x^{3} - 8 x^{2} + 4 x - 1$ | $37\cdot 71^{2}\cdot 197$ | $S_9$ (as 9T34) | trivial |
9.1.37009129.1 | $x^{9} - 2 x^{8} + x^{7} - x^{6} + x^{5} + x^{4} + x^{2} - 2 x + 1$ | $839\cdot 44111$ | $S_9$ (as 9T34) | trivial |
9.1.37065113.1 | $x^{9} - x^{8} - x^{6} + x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + x + 1$ | $5849\cdot 6337$ | $S_9$ (as 9T34) | trivial |