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Results (displaying all 8 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.2.38000833928000000000.1 | x18 - 2x17 + 2x16 - 3x15 + 2x14 - 4x13 + 2x12 - 10x11 + 2x10 - 3x9 - 2x8 - 10x7 - 2x6 - 4x5 - 2x4 - 3x3 - 2x2 - 2x - 1 | \( 2^{12}\cdot 5^{9}\cdot 41^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.0.66123690216932995947.1 | x18 - 3x17 + 6x16 - 9x15 + 15x14 - 21x13 + 24x12 - 24x11 + 27x10 - 29x9 + 27x8 - 24x7 + 24x6 - 21x5 + 15x4 - 9x3 + 6x2 - 3x + 1 | \( -\,3^{21}\cdot 43^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.2.111799609989175181312.1 | x18 - 4x17 + 8x16 - 8x15 + x14 + 8x13 - 10x12 + 2x11 + 6x10 - 4x9 - 4x8 + 10x7 - 6x6 + 4x5 + x4 + 2x2 + 1 | \( 2^{27}\cdot 97^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.0.129723503874804239427.1 | x18 - x17 + x16 + 4x15 - x14 + x13 + 7x12 + 3x11 + 4x10 - 2x9 + 10x8 + 2x6 - 5x5 + 4x4 + x3 + 2x2 - x + 1 | \( -\,3^{9}\cdot 433^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.6.3909310422393798828125.1 | x18 - 2x15 - 5x14 - 5x13 - 25x12 - 10x11 - 10x10 + 5x9 + 10x8 - 10x7 + 25x6 - 5x5 + 5x4 - 2x3 - 1 | \( 5^{15}\cdot 71^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.6.42302036995916628492288.1 | x18 - 6x17 + 16x16 - 20x15 + 2x14 + 12x13 + x12 + 14x11 - 124x10 + 224x9 - 124x8 + 14x7 + x6 + 12x5 + 2x4 - 20x3 + 16x2 - 6x + 1 | \( 2^{24}\cdot 3^{9}\cdot 71^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial |
| 18.18.6674087489718598592345703125.1 | x18 - 34x16 + 441x14 - 2812x12 + 9602x10 - 17803x8 + 17336x6 - 8330x4 + 1725x2 - 125 | \( 5^{9}\cdot 3881^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial (GRH) |
| 18.18.11945569661051635899513700352.1 | x18 - 32x16 - 14x15 + 350x14 + 254x13 - 1599x12 - 1462x11 + 3065x10 + 3262x9 - 2369x8 - 2968x7 + 677x6 + 1160x5 - 30x4 - 190x3 - 13x2 + 10x + 1 | \( 2^{27}\cdot 2113^{6} \) | $S_3\wr C_2$ (as 18T34) | Trivial (GRH) |