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Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.13415474159898041623.1 | x18 - 6x17 + 15x16 - 23x15 + 37x14 - 78x13 + 152x12 - 240x11 + 302x10 - 308x9 + 300x8 - 298x7 + 220x6 - 85x5 + 25x4 - 26x3 + 12x2 + 1 | \( -\,7^{15}\cdot 41^{4} \) | $C_3^3:C_6$ (as 18T85) | Trivial |
| 18.0.16230968037754638343.1 | x18 - x17 - 5x16 + 9x15 + 2x14 - 32x13 + 37x12 + 40x11 - 100x10 + 31x9 + 83x8 - 97x7 + 27x6 + 18x5 - 15x4 + 5x2 - 3x + 1 | \( -\,7^{15}\cdot 43^{4} \) | $C_3^3:C_6$ (as 18T85) | Trivial |
| 18.18.5431100773839594625584038709.1 | x18 - 4x17 - 29x16 + 116x15 + 343x14 - 1372x13 - 2127x12 + 8512x11 + 7445x10 - 29680x9 - 15041x8 + 58009x7 + 18292x6 - 60382x5 - 15218x4 + 30557x3 + 8245x2 - 5735x - 1889 | \( 3^{9}\cdot 7^{15}\cdot 491^{4} \) | $C_3^3:C_6$ (as 18T85) | Trivial (GRH) |
| 18.18.35124402153448444982149980549.1 | x18 - 3x17 - 36x16 + 124x15 + 450x14 - 1869x13 - 2288x12 + 13692x11 + 1698x10 - 51784x9 + 27471x8 + 92763x7 - 99182x6 - 45087x5 + 106008x4 - 41622x3 - 5061x2 + 5313x - 581 | \( 3^{21}\cdot 7^{15}\cdot 29^{4} \) | $C_3^3:C_6$ (as 18T85) | Trivial (GRH) |