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Results (displaying all 8 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.4.31336408949981184.1 | x12 - 6x10 - 4x9 + 21x8 + 16x7 + 36x6 + 16x5 - 97x4 - 38x2 + 20x - 1 | \( 2^{26}\cdot 3^{4}\cdot 7^{8} \) | $A_4\wr C_2$ (as 12T128) | $[3]$ |
| 12.4.35704672266240000.1 | x12 - 6x11 + 12x10 - 2x9 - 36x8 + 72x7 - 48x6 - 54x5 + 180x4 - 146x3 - 6x2 + 12x - 2 | \( 2^{14}\cdot 3^{20}\cdot 5^{4} \) | $A_4\wr C_2$ (as 12T128) | Trivial |
| 12.4.46221064723759104.1 | x12 - 12x10 - 24x9 + 48x7 + 32x6 - 24x5 - 30x4 - 64x3 - 96x2 - 48x - 8 | \( 2^{30}\cdot 3^{16} \) | $A_4\wr C_2$ (as 12T128) | $[3]$ |
| 12.4.173911685539840000.1 | x12 - 4x11 - 6x10 + 48x9 - 26x8 - 192x7 + 216x6 + 400x5 - 416x4 - 394x3 + 314x2 + 120x - 106 | \( 2^{14}\cdot 5^{4}\cdot 19^{8} \) | $A_4\wr C_2$ (as 12T128) | $[3]$ |
| 12.0.6524405577830560000.1 | x12 - x11 + 2x10 - 2x9 + 36x8 - 10x7 + 60x6 - 40x5 + 165x4 - 185x3 + 310x2 - 146x + 170 | \( 2^{8}\cdot 5^{4}\cdot 7^{4}\cdot 19^{8} \) | $A_4\wr C_2$ (as 12T128) | $[6]$ |
| 12.0.11924157958528958464.1 | x12 - 6x11 + 18x10 - 8x9 - 4x8 - 56x7 + 232x6 - 218x5 + 300x4 - 412x3 + 448x2 - 224x + 63 | \( 2^{18}\cdot 7^{8}\cdot 53^{4} \) | $A_4\wr C_2$ (as 12T128) | $[6]$ |
| 12.12.63253004904652400640000.1 | x12 - 48x10 - 24x9 + 807x8 + 624x7 - 6174x6 - 6234x5 + 21795x4 + 27658x3 - 26418x2 - 45504x - 11073 | \( 2^{14}\cdot 3^{20}\cdot 5^{4}\cdot 11^{6} \) | $A_4\wr C_2$ (as 12T128) | Trivial (GRH) |
| 12.12.1082839192749642263040000.1 | x12 - 6x11 - 27x10 + 169x9 + 225x8 - 1308x7 - 952x6 + 2796x5 + 1572x4 - 1616x3 - 420x2 + 252x - 12 | \( 2^{12}\cdot 3^{16}\cdot 5^{4}\cdot 7^{6}\cdot 17^{4} \) | $A_4\wr C_2$ (as 12T128) | $[3]$ (GRH) |