Further refine search
Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.2954312706550833698643.2 | x18 - 9x15 + 36x12 - 53x9 + 27x6 + 1 | \( -\,3^{45} \) | $C_9\times S_3$ (as 18T16) | Trivial |
| 18.0.258151783382020583032356864.1 | x18 + 27x14 + 207x10 - 4x9 + 126x7 + 414x6 + 108x5 - 420x3 + 81x2 - 36x + 53 | \( -\,2^{18}\cdot 3^{44} \) | $C_9\times S_3$ (as 18T16) | Trivial |
| 18.18.7878167217468889863048000000000.1 | x18 - 36x16 + 540x14 - 4368x12 + 20592x10 - 72x9 - 57024x8 + 1296x7 + 88704x6 - 7776x5 - 69120x4 + 17280x3 + 20736x2 - 10368x + 1216 | \( 2^{12}\cdot 3^{44}\cdot 5^{9} \) | $C_9\times S_3$ (as 18T16) | Trivial (GRH) |
| 18.18.42774537890835454566245668796878848.1 | x18 - 72x16 + 2160x14 - 34944x12 + 329472x10 - 1728x9 - 1824768x8 + 62208x7 + 5677056x6 - 746496x5 - 8847360x4 + 3317760x3 + 5308416x2 - 3981312x + 733184 | \( 2^{12}\cdot 3^{44}\cdot 13^{9} \) | $C_9\times S_3$ (as 18T16) | $[3]$ (GRH) |