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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.123518519069646203531264.1 | x18 - 3x17 + 21x14 - 6x13 - 23x12 - 18x11 + 31x10 - 18x9 - 22x8 - 13x7 + 61x6 + 24x5 + 28x4 + 18x3 + 40x2 + 16x + 32 | \( -\,2^{12}\cdot 59^{11} \) | $C_2^2:D_9$ (as 18T39) | Trivial |
| 18.0.145340952056670741069824.1 | x18 + 2x16 - 4x14 + x12 + 24x10 + 100x8 - 13x6 + 50x4 + 76x2 + 59 | \( -\,2^{24}\cdot 59^{9} \) | $C_2^2:D_9$ (as 18T39) | $[2]$ |
| 18.6.2980200459393400813138329769.1 | x18 - 17x16 - 28x15 + 34x14 + 112x13 + 123x12 + 168x11 + 201x10 + 173x9 + 118x8 - 92x7 - 229x6 - 158x5 - 137x4 - 75x3 - 25x2 - 3x + 1 | \( 1129^{9} \) | $C_2^2:D_9$ (as 18T39) | $[2]$ |
| 18.6.2172566134897789192777842401601.1 | x18 - 6x17 + 5x16 + 68x15 - 308x14 + 426x13 + 318x12 - 1905x11 + 2547x10 - 5955x9 + 25356x8 - 55783x7 + 46314x6 + 41206x5 - 117880x4 + 80053x3 + 5918x2 - 26871x + 7883 | \( 3^{6}\cdot 1129^{9} \) | $C_2^2:D_9$ (as 18T39) | $[4]$ (GRH) |
| 18.18.781241669227223662759334318964736.1 | x18 - 46x16 + 773x14 - 6351x12 + 28570x10 - 72713x8 + 101489x6 - 68726x4 + 16121x2 - 1129 | \( 2^{18}\cdot 1129^{9} \) | $C_2^2:D_9$ (as 18T39) | $[2]$ (GRH) |
| 18.18.140206156168767266840209098851131489.1 | x18 - x17 - 89x16 + 151x15 + 2903x14 - 6917x13 - 41170x12 + 128965x11 + 226382x10 - 1014925x9 - 226188x8 + 3486165x7 - 1433009x6 - 5139518x5 + 3540642x4 + 2797609x3 - 2029989x2 - 568486x + 269671 | \( 19^{6}\cdot 1129^{9} \) | $C_2^2:D_9$ (as 18T39) | $[2]$ (GRH) |