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Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.0.12548716987355136.1 | x12 - 2x11 + x10 + 10x9 + 14x8 + 56x7 + 101x6 + 124x5 + 193x4 + 180x3 + 142x2 + 112x + 41 | \( 2^{12}\cdot 3^{12}\cdot 7^{8} \) | $C_3\times A_4$ (as 12T20) | $[2]$ |
| 12.0.13289296949899369.2 | x12 - 4x11 + 20x10 - 54x9 + 135x8 - 252x7 + 386x6 - 490x5 + 508x4 - 394x3 + 276x2 - 90x + 29 | \( 7^{10}\cdot 19^{6} \) | $C_3\times A_4$ (as 12T20) | $[4]$ |
| 12.12.3729769656536978649.1 | x12 - 21x10 - 16x9 + 119x8 + 112x7 - 253x6 - 238x5 + 203x4 + 176x3 - 49x2 - 28x + 7 | \( 3^{6}\cdot 7^{8}\cdot 31^{6} \) | $C_3\times A_4$ (as 12T20) | Trivial (GRH) |
| 12.12.4801917846986704129.1 | x12 - 4x11 - 20x10 + 88x9 + 115x8 - 661x7 - 50x6 + 1945x5 - 970x4 - 1927x3 + 1427x2 + 518x - 461 | \( 7^{8}\cdot 97^{6} \) | $C_3\times A_4$ (as 12T20) | Trivial (GRH) |