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 |
---|---|---|---|---|
6.0.9747.1 | $x^{6} - x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ | $-\,3^{3}\cdot 19^{2}$ | $S_3\times C_3$ (as 6T5) | trivial |
6.0.10051.1 | $x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,19\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.10571.1 | $x^{6} - x^{5} - x^{4} + 2 x^{3} - x + 1$ | $-\,11\cdot 31^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.10816.1 | $x^{6} - x^{4} - 2 x^{3} + 2 x + 1$ | $-\,2^{6}\cdot 13^{2}$ | $S_3\times C_3$ (as 6T5) | trivial |
6.0.11691.1 | $x^{6} - x^{5} - x^{2} + x + 1$ | $-\,3^{3}\cdot 433$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.12167.1 | $x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$ | $-\,23^{3}$ | $S_3$ (as 6T2) | trivial |
6.0.14283.1 | $x^{6} - x^{5} + x^{4} - 2 x^{3} + x^{2} + 1$ | $-\,3^{3}\cdot 23^{2}$ | $D_{6}$ (as 6T3) | trivial |
6.0.14731.1 | $x^{6} - x^{5} + x^{3} - x^{2} + 1$ | $-\,14731$ | $S_6$ (as 6T16) | trivial |
6.0.16551.1 | $x^{6} - x^{5} - x^{4} + 3 x^{3} - 2 x + 1$ | $-\,3^{3}\cdot 613$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.16807.1 | $x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ | $-\,7^{5}$ | $C_6$ (as 6T1) | trivial |
6.0.18515.1 | $x^{6} + 2 x^{4} - x^{3} + 2 x^{2} + 1$ | $-\,5\cdot 7\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.19683.1 | $x^{6} - x^{3} + 1$ | $-\,3^{9}$ | $C_6$ (as 6T1) | trivial |
6.0.20627.1 | $x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - x + 1$ | $-\,20627$ | $S_6$ (as 6T16) | trivial |
6.0.21168.1 | $x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - 2 x^{2} + x + 1$ | $-\,2^{4}\cdot 3^{3}\cdot 7^{2}$ | $S_3\times C_3$ (as 6T5) | trivial |
6.0.21296.1 | $x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ | $-\,2^{4}\cdot 11^{3}$ | $S_3$ (as 6T2) | trivial |
6.0.22291.1 | $x^{6} + x^{4} - x^{3} - x + 1$ | $-\,22291$ | $S_6$ (as 6T16) | trivial |
6.0.22592.1 | $x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 1$ | $-\,2^{6}\cdot 353$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.22707.1 | $x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$ | $-\,3^{3}\cdot 29^{2}$ | $D_{6}$ (as 6T3) | trivial |
6.0.22747.1 | $x^{6} - x^{5} - 2 x^{3} + x^{2} + x + 1$ | $-\,23^{2}\cdot 43$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.23031.1 | $x^{6} + x^{4} - x^{3} + x^{2} - 2 x + 1$ | $-\,3^{3}\cdot 853$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.24003.1 | $x^{6} - x^{5} + 3 x^{3} - x^{2} - 2 x + 1$ | $-\,3^{3}\cdot 7\cdot 127$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.25747.1 | $x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - x + 1$ | $-\,25747$ | $S_6$ (as 6T16) | trivial |
6.0.25947.1 | $x^{6} - x^{4} - 2 x^{3} + x^{2} + x + 1$ | $-\,3^{3}\cdot 31^{2}$ | $D_{6}$ (as 6T3) | trivial |
6.0.27556.1 | $x^{6} - x^{5} + 2 x^{3} - x + 1$ | $-\,2^{2}\cdot 83^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.27848.1 | $x^{6} - x^{5} + 2 x^{4} + 2 x^{2} - x + 1$ | $-\,2^{3}\cdot 59^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.27971.1 | $x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,83\cdot 337$ | $S_6$ (as 6T16) | trivial |
6.0.29095.1 | $x^{6} - x^{5} + 3 x^{4} - x^{3} + 3 x^{2} - x + 1$ | $-\,5\cdot 11\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.29791.1 | $x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} + 7 x^{2} - 3 x + 1$ | $-\,31^{3}$ | $S_3$ (as 6T2) | trivial |
6.0.30808.1 | $x^{6} - x^{4} - x^{3} + x^{2} + x + 1$ | $-\,2^{3}\cdot 3851$ | $S_6$ (as 6T16) | trivial |
6.0.30976.1 | $x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 2$ | $-\,2^{8}\cdot 11^{2}$ | $D_{6}$ (as 6T3) | trivial |
6.0.31211.1 | $x^{6} - x^{4} - x^{3} + 2 x^{2} + 3 x + 1$ | $-\,23^{2}\cdot 59$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.31223.1 | $x^{6} - x^{5} + x^{4} - x^{3} + 2 x^{2} - x + 1$ | $-\,31223$ | $S_6$ (as 6T16) | trivial |
6.0.31347.1 | $x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x + 1$ | $-\,3^{6}\cdot 43$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.32171.1 | $x^{6} - x^{5} + 2 x^{4} - x^{3} + x^{2} + 1$ | $-\,53\cdot 607$ | $S_6$ (as 6T16) | trivial |
6.0.32911.1 | $x^{6} - x^{3} - x^{2} + x + 1$ | $-\,32911$ | $S_6$ (as 6T16) | trivial |
6.0.33791.1 | $x^{6} - x^{5} + x^{4} + x^{3} + x + 1$ | $-\,33791$ | $S_6$ (as 6T16) | trivial |
6.0.33856.1 | $x^{6} - x^{4} + 1$ | $-\,2^{6}\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.33856.2 | $x^{6} + x^{4} + 2 x^{2} + 1$ | $-\,2^{6}\cdot 23^{2}$ | $D_{6}$ (as 6T3) | trivial |
6.0.34371.1 | $x^{6} - x^{5} - 2 x^{3} + 2 x + 1$ | $-\,3^{3}\cdot 19\cdot 67$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.34992.1 | $x^{6} - 3 x^{5} + 5 x^{3} - 3 x + 1$ | $-\,2^{4}\cdot 3^{7}$ | $S_3$ (as 6T2) | trivial |
6.0.35099.1 | $x^{6} + x^{4} + x^{2} - x + 1$ | $-\,35099$ | $S_6$ (as 6T16) | trivial |
6.0.36107.1 | $x^{6} - 2 x^{5} + x^{4} - x^{2} + x + 1$ | $-\,36107$ | $S_6$ (as 6T16) | trivial |
6.0.36235.1 | $x^{6} - x^{5} + x^{2} - x + 1$ | $-\,5\cdot 7247$ | $S_6$ (as 6T16) | trivial |
6.0.36963.1 | $x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ | $-\,3^{3}\cdot 37^{2}$ | $S_3\times C_3$ (as 6T5) | trivial |
6.0.37423.1 | $x^{6} - x^{5} + x^{4} + 1$ | $-\,37423$ | $S_6$ (as 6T16) | trivial |
6.0.37463.1 | $x^{6} - x^{4} - x^{3} + 2 x^{2} + 2 x + 1$ | $-\,37463$ | $S_6$ (as 6T16) | trivial |
6.0.37479.1 | $x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - x + 1$ | $-\,3\cdot 13\cdot 31^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.40203.1 | $x^{6} - x^{5} - 3 x^{4} + 4 x^{3} + 3 x^{2} - 4 x + 1$ | $-\,3^{3}\cdot 1489$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.0.40543.1 | $x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,40543$ | $S_6$ (as 6T16) | trivial |
6.0.41472.1 | $x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 1$ | $-\,2^{9}\cdot 3^{4}$ | $S_3\times C_3$ (as 6T5) | trivial |