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Results (displaying all 8 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.4.1785233613312000.1 | x12 - 10x9 + 3x8 - 18x7 + 18x6 + 18x5 + 30x3 + 18x2 - 3 | \( 2^{12}\cdot 3^{20}\cdot 5^{3} \) | $A_4\wr C_2$ (as 12T129) | Trivial |
| 12.6.2611367412498432.1 | x12 - 2x10 - 12x9 - 7x8 + 16x7 + 50x6 + 24x5 - 46x4 - 40x3 + 8x2 + 8x - 1 | \( -\,2^{24}\cdot 3^{3}\cdot 7^{8} \) | $A_4\wr C_2$ (as 12T129) | Trivial |
| 12.4.3515376756641792.1 | x12 - 6x11 + 13x10 - 56x8 + 100x7 - 81x6 + 2x5 + 34x4 + 8x3 - 40x2 + 40x - 8 | \( 2^{12}\cdot 7^{8}\cdot 53^{3} \) | $A_4\wr C_2$ (as 12T129) | Trivial |
| 12.6.5777633090469888.1 | x12 - 6x10 - 3x8 - 48x7 - 40x6 + 24x5 + 12x4 - 16x3 + 6x2 + 12x + 1 | \( -\,2^{27}\cdot 3^{16} \) | $A_4\wr C_2$ (as 12T129) | Trivial |
| 12.0.224984112425074688.1 | x12 - 4x11 + 6x10 + 11x8 - 50x7 + 72x6 - 130x5 - 38x4 + 48x3 + 608x2 - 266x + 29 | \( 2^{18}\cdot 7^{8}\cdot 53^{3} \) | $A_4\wr C_2$ (as 12T129) | $[2]$ |
| 12.0.224984112425074688.2 | x12 - 4x11 + 10x10 - 22x9 + 69x8 - 136x7 + 86x6 + 30x5 + 202x4 - 262x3 + 440x2 - 254x + 43 | \( 2^{18}\cdot 7^{8}\cdot 53^{3} \) | $A_4\wr C_2$ (as 12T129) | $[2]$ |
| 12.12.3162650245232620032000.1 | x12 - 6x11 - 36x10 + 138x9 + 675x8 - 432x7 - 4536x6 - 3816x5 + 7551x4 + 16014x3 + 11196x2 + 3294x + 333 | \( 2^{12}\cdot 3^{20}\cdot 5^{3}\cdot 11^{6} \) | $A_4\wr C_2$ (as 12T129) | Trivial (GRH) |
| 12.12.12739284620584026624000.1 | x12 - 6x11 - 21x10 + 152x9 + 111x8 - 1194x7 + 131x6 + 2802x5 - 1887x4 - 906x3 + 843x2 + 60x - 89 | \( 2^{12}\cdot 3^{16}\cdot 5^{3}\cdot 7^{6}\cdot 17^{3} \) | $A_4\wr C_2$ (as 12T129) | Trivial (GRH) |