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Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.6.16012035393449278995173376.1 | x18 + 3x16 - 27x14 - 113x12 + 15x10 + 465x8 + 366x6 - 102x4 - 39x2 - 1 | \( 2^{12}\cdot 3^{24}\cdot 7^{12} \) | $A_4 \times C_3$ (as 18T8) | $[2]$ |
| 18.6.54498357372899208270500089.1 | x18 - 3x17 + 6x16 - 36x15 + 101x14 - 229x13 + 498x12 - 765x11 + 930x10 - 345x9 - 1994x8 + 7647x7 - 18390x6 + 33475x5 - 47255x4 + 49166x3 - 37440x2 + 18499x - 3991 | \( 7^{12}\cdot 13^{14} \) | $A_4 \times C_3$ (as 18T8) | Trivial (GRH) |
| 18.18.65585296971568246764230148096.1 | x18 - 30x16 + 369x14 - 2407x12 + 8964x10 - 19056x8 + 21848x6 - 11904x4 + 2208x2 - 64 | \( 2^{24}\cdot 3^{24}\cdot 7^{12} \) | $A_4 \times C_3$ (as 18T8) | Trivial (GRH) |
| 18.18.578700169474787302846561871409.1 | x18 - 42x16 - 28x15 + 630x14 + 714x13 - 4107x12 - 5880x11 + 12159x10 + 20818x9 - 13965x8 - 32634x7 - 435x6 + 19026x5 + 7182x4 - 1512x3 - 945x2 + 27 | \( 3^{24}\cdot 7^{12}\cdot 23^{6} \) | $A_4 \times C_3$ (as 18T8) | Trivial (GRH) |