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Results (displaying all 8 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.4.756680642578125.1 | x12 - 7x9 + 14x6 - 8x3 + 1 | \( 3^{18}\cdot 5^{9} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.4.756680642578125.3 | x12 - x9 - 4x6 + 4x3 + 1 | \( 3^{18}\cdot 5^{9} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.0.6643012500000000.1 | x12 - 135x6 - 270x5 + 225x4 + 1040x3 + 1080x2 + 480x + 80 | \( 2^{8}\cdot 3^{12}\cdot 5^{11} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.0.6643012500000000.2 | x12 - 15x10 + 90x8 - 290x6 - 90x5 + 405x4 + 730x3 + 1620x2 + 2040x + 880 | \( 2^{8}\cdot 3^{12}\cdot 5^{11} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.0.15196929064453125.1 | x12 - 11x9 + 51x6 - 121x3 + 121 | \( 3^{12}\cdot 5^{9}\cdot 11^{4} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.0.15196929064453125.2 | x12 - 28x9 + 259x6 - 902x3 + 1331 | \( 3^{12}\cdot 5^{9}\cdot 11^{4} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial |
| 12.12.1556165536200000000000.1 | x12 - 90x10 - 120x9 + 3015x8 + 8040x7 - 39450x6 - 178200x5 + 17985x4 + 1215280x3 + 2504700x2 + 2032800x + 590480 | \( 2^{12}\cdot 3^{12}\cdot 5^{11}\cdot 11^{4} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial (GRH) |
| 12.12.137007575440204500000000.1 | x12 - 78x10 - 90x9 + 2124x8 + 4830x7 - 20347x6 - 73080x5 + 2001x4 + 213150x3 + 151380x2 - 100920x - 67280 | \( 2^{8}\cdot 3^{18}\cdot 5^{9}\cdot 29^{4} \) | $S_3\times C_3:S_3.C_2$ (as 12T119) | Trivial (GRH) |