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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.32829069322819602987363.1 | x18 + 6x16 - 6x15 + 27x14 - 21x13 + 53x12 - 9x11 + 57x10 + x9 + 18x8 + 18x7 + 4x6 + 27x5 + 18x4 + 10x3 + 9x2 + 3x + 1 | \( -\,3^{21}\cdot 11^{12} \) | $S_3\wr C_2$ (as 18T36) | Trivial |
| 18.0.184020479637478805864448.1 | x18 - 3x17 - 3x16 + 10x15 + 21x14 - 45x13 - 17x12 + 18x11 + 126x10 - 184x9 + 162x8 - 318x7 + 523x6 - 471x5 + 309x4 - 138x3 + 45x2 - 9x + 1 | \( -\,2^{44}\cdot 3^{21} \) | $S_3\wr C_2$ (as 18T36) | Trivial |
| 18.2.490721279033276815638528.1 | x18 - 6x16 + 24x14 - 60x12 - 18x10 + 24x8 - 72x6 - 180x4 + 33x2 - 2 | \( 2^{47}\cdot 3^{20} \) | $S_3\wr C_2$ (as 18T36) | Trivial |
| 18.2.2155257587919164038447104.1 | x18 - 6x17 + 9x16 + 18x15 - 54x14 - 24x13 + 135x12 + 78x11 - 303x10 - 104x9 + 321x8 + 180x7 + 9x6 - 762x5 + 354x4 + 660x3 - 720x2 + 216x - 43 | \( 2^{18}\cdot 3^{20}\cdot 11^{9} \) | $S_3\wr C_2$ (as 18T36) | Trivial |
| 18.18.244362898413546378439384960598016.1 | x18 - 6x17 - 33x16 + 222x15 + 441x14 - 3228x13 - 3519x12 + 23940x11 + 20004x10 - 95540x9 - 76188x8 + 196728x7 + 156600x6 - 190776x5 - 145320x4 + 67824x3 + 44124x2 - 2688x - 1756 | \( 2^{24}\cdot 3^{20}\cdot 11^{15} \) | $S_3\wr C_2$ (as 18T36) | Trivial (GRH) |
| 18.18.287700265443621620596836604575744.1 | x18 - 6x17 - 39x16 + 186x15 + 516x14 - 2286x13 - 2829x12 + 14238x11 + 4938x10 - 47130x9 + 10971x8 + 77838x7 - 51087x6 - 48144x5 + 54420x4 - 5076x3 - 9012x2 + 2568x - 100 | \( 2^{33}\cdot 3^{24}\cdot 17^{9} \) | $S_3\wr C_2$ (as 18T36) | $[2]$ (GRH) |