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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.6.306783288013169609929.1 | x18 - x17 - 4x16 - 4x15 + x14 + 11x13 + 13x12 + 4x11 - 11x10 - 19x9 - 11x8 + 4x7 + 13x6 + 11x5 + x4 - 4x3 - 4x2 - x + 1 | \( 7^{12}\cdot 53^{6} \) | $C_3\times S_4$ (as 18T33) | Trivial |
| 18.6.390877006486250192896.1 | x18 + 2x16 - 15x12 - 10x10 + 27x8 - 21x4 + 9x2 - 1 | \( 2^{24}\cdot 13^{12} \) | $C_3\times S_4$ (as 18T33) | Trivial |
| 18.6.1156831381426176000000.1 | x18 - 6x16 + 15x14 - 35x12 + 75x10 - 96x8 + 124x6 - 141x4 + 63x2 - 1 | \( 2^{18}\cdot 3^{24}\cdot 5^{6} \) | $C_3\times S_4$ (as 18T33) | Trivial |
| 18.6.1996132539284958146953321.1 | x18 - 5x16 - 4x15 - 7x14 + 4x13 + 53x12 - 6x11 - 50x10 + 41x9 - 116x8 - 5x7 + 151x6 + 9x5 - 21x4 - 11x3 - 6x2 + 1 | \( 7^{12}\cdot 229^{6} \) | $C_3\times S_4$ (as 18T33) | Trivial (GRH) |
| 18.18.80421398252924334225227776.1 | x18 - 17x16 + 117x14 - 421x12 + 854x10 - 979x8 + 601x6 - 177x4 + 23x2 - 1 | \( 2^{18}\cdot 7^{12}\cdot 53^{6} \) | $C_3\times S_4$ (as 18T33) | Trivial (GRH) |
| 18.18.2948904789736421270045691904.1 | x18 - x17 - 34x16 + 36x15 + 473x14 - 527x13 - 3454x12 + 4023x11 + 14096x10 - 17049x9 - 31528x8 + 39357x7 + 34954x6 - 44887x5 - 14915x4 + 19996x3 + 326x2 - 861x + 43 | \( 2^{12}\cdot 7^{14}\cdot 101^{6} \) | $C_3\times S_4$ (as 18T33) | Trivial (GRH) |