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Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 12.4.2282521714753536.1 | x12 - 8x9 - 18x8 - 24x7 - 28x6 - 24x5 + 30x4 + 32x3 + 48x2 - 32 | \( 2^{32}\cdot 3^{12} \) | $PSU(3,2)$ (as 12T47) | Trivial |
| 12.4.3782285936100000000.1 | x12 - x11 + 2x10 + 15x9 - 146x8 + 373x7 - 587x6 + 568x5 - 506x4 + 480x3 - 484x2 + 320x - 80 | \( 2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8} \) | $PSU(3,2)$ (as 12T47) | $[3]$ |
| 12.12.16256901690906219140625.1 | x12 - 45x10 - 6x9 + 702x8 + 174x7 - 4822x6 - 1551x5 + 14679x4 + 5097x3 - 16002x2 - 5667x - 341 | \( 3^{12}\cdot 5^{8}\cdot 23^{8} \) | $PSU(3,2)$ (as 12T47) | Trivial (GRH) |
| 12.12.108315244054645124890624.1 | x12 - 4x11 - 46x10 + 276x9 + 124x8 - 3712x7 + 6880x6 + 7856x5 - 41606x4 + 52664x3 - 22620x2 - 3720x + 3844 | \( 2^{32}\cdot 7^{6}\cdot 11^{8} \) | $PSU(3,2)$ (as 12T47) | $[3]$ (GRH) |