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Results (displaying all 3 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.258151783382020583032356864.2 | x18 + 18x16 - 18x15 + 135x14 - 270x13 + 699x12 - 1620x11 + 3123x10 - 5760x9 + 10044x8 - 15390x7 + 21528x6 - 28674x5 + 34641x4 - 33822x3 + 32643x2 - 28566x + 12301 | \( -\,2^{18}\cdot 3^{44} \) | $C_3\times D_9$ (as 18T19) | Trivial (GRH) |
| 18.18.14019349946482311002129152886409.1 | x18 - 42x16 - 4x15 + 621x14 + 69x13 - 4331x12 + 16005x10 - 3117x9 - 31995x8 + 13491x7 + 31560x6 - 20790x5 - 10521x4 + 10989x3 - 1728x2 - 216x + 9 | \( 3^{27}\cdot 107^{9} \) | $C_3\times D_9$ (as 18T19) | Trivial (GRH) |
| 18.18.53056553186191280403749586075084940824853751509.1 | x18 - 3x17 - 635x16 + 637x15 + 147470x14 + 31278x13 - 15388414x12 - 4948990x11 + 811072595x10 - 33481138x9 - 21732949914x8 + 10719756413x7 + 274397510025x6 - 231330970625x5 - 1350644250998x4 + 1050009163838x3 + 2453632857591x2 - 1197940138849x - 1164062910163 | \( 7^{12}\cdot 19^{12}\cdot 229^{9} \) | $C_3\times D_9$ (as 18T19) | $[3, 3]$ (GRH) |