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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.2.171382426877952.1 | x12 + 6x10 - 4x9 + 18x8 - 18x7 + 30x6 - 54x5 + 36x4 - 50x3 + 36x2 - 12x + 2 | \( -\,2^{14}\cdot 3^{21} \) | $C_3:S_4$ (as 12T44) | Trivial |
| 12.2.385610460475392.1 | x12 - 6x11 + 12x10 - 2x9 - 27x8 + 36x7 - 36x5 + 18x4 + 20x3 - 12x2 - 12x - 4 | \( -\,2^{12}\cdot 3^{23} \) | $C_3:S_4$ (as 12T44) | Trivial |
| 12.0.4308890951402024256.1 | x12 - 3x11 + 12x10 - 50x9 + 171x8 - 423x7 + 918x6 - 1404x5 + 1845x4 - 1663x3 + 786x2 - 84x + 8 | \( 2^{6}\cdot 3^{21}\cdot 23^{5} \) | $C_3:S_4$ (as 12T44) | Trivial |
| 12.0.7582118806327332096.1 | x12 - 3x11 + 6x10 - 3x9 + 18x8 - 27x7 + 65x6 - 72x5 + 396x4 + 492x3 + 216x2 + 432x + 288 | \( 2^{8}\cdot 3^{17}\cdot 47^{5} \) | $C_3:S_4$ (as 12T44) | Trivial |
| 12.12.285365713943624384512.1 | x12 - 4x11 - 26x10 + 130x9 + 74x8 - 972x7 + 795x6 + 1612x5 - 2180x4 - 288x3 + 1356x2 - 560x + 64 | \( 2^{15}\cdot 13^{6}\cdot 71^{5} \) | $C_3:S_4$ (as 12T44) | Trivial |
| 12.12.1941022414419797016576.1 | x12 - 6x11 - 21x10 + 142x9 + 90x8 - 990x7 + 303x6 + 1980x5 - 756x4 - 1372x3 + 105x2 + 300x + 53 | \( 2^{16}\cdot 3^{17}\cdot 47^{5} \) | $C_3:S_4$ (as 12T44) | Trivial |