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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 6.0.1778112.1 | x6 + 3x4 - 2x3 + 6x2 + 1 | \( -\,2^{6}\cdot 3^{4}\cdot 7^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.2177712.1 | x6 - x5 - 4x2 + 8 | \( -\,2^{4}\cdot 3^{3}\cdot 71^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.2299968.1 | x6 - 2x5 - x4 + 4x3 - 4x2 + 4x + 1 | \( 2^{6}\cdot 3^{3}\cdot 11^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.2611467.1 | x6 - 3x5 + 7x4 - 6x3 + 6x2 - 7x + 5 | \( -\,3^{3}\cdot 311^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.2725888.1 | x6 - x5 + 2x4 - 4x3 + 4x2 + 4x + 8 | \( -\,2^{11}\cdot 11^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.2725888.5 | x6 - x5 - x4 + 2x3 - 5x2 - x - 3 | \( 2^{11}\cdot 11^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.3200000.1 | x6 - 2x5 + 4x + 2 | \( 2^{10}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.3421872.4 | x6 - 2x5 + 6x4 - 12x3 + 14x2 - 10x + 4 | \( -\,2^{4}\cdot 3^{3}\cdot 89^{2} \) | $\PGL(2,5)$ (as 6T14) | $[4]$ |
| 6.0.3479787.1 | x6 - 3x5 + 4x4 - 3x2 + 3x + 3 | \( -\,3^{3}\cdot 359^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.3786752.3 | x6 - x5 + 3x4 - 4x3 + 2x2 - 6x + 10 | \( -\,2^{11}\cdot 43^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.3895843.1 | x6 - x5 + x4 - 2x3 + 2x2 - x + 3 | \( -\,7^{2}\cdot 43^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.5000000.1 | x6 - 2x5 - 8x - 4 | \( 2^{6}\cdot 5^{7} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.5256144.1 | x6 - x5 - 2x4 - 2x3 + x2 + 5x + 4 | \( 2^{4}\cdot 3^{3}\cdot 23^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.5400000.3 | x6 - 2x5 + 5x2 + 2x + 1 | \( -\,2^{6}\cdot 3^{3}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.0.5400000.4 | x6 - 2x5 + 5x4 + 6x + 3 | \( -\,2^{6}\cdot 3^{3}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.5778125.2 | x6 - 5x2 - 6x - 5 | \( 5^{5}\cdot 43^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.5787963.1 | x6 - x5 + 4x4 - 12x3 + 15x2 - 9x + 3 | \( -\,3^{3}\cdot 463^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.6154544.2 | x6 - 2x5 + 5x4 - 2x3 + 6x2 + 12x + 4 | \( -\,2^{4}\cdot 11^{3}\cdot 17^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.6627103.2 | x6 - 2x5 - 8x3 + 21x2 - 8x + 1 | \( -\,7^{3}\cdot 139^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.6750000.1 | x6 - x5 + 5x2 + 3x + 2 | \( -\,2^{4}\cdot 3^{3}\cdot 5^{6} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.7129088.4 | x6 - 3x5 + 7x4 - 4x3 + 8x2 - 4x + 4 | \( -\,2^{11}\cdot 59^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.8108208.2 | x6 - 3x5 + 4x4 - 2x + 2 | \( -\,2^{4}\cdot 3^{3}\cdot 137^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.9148592.2 | x6 - x5 + 4x4 + x2 + 3x + 2 | \( -\,2^{4}\cdot 83^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.9483264.1 | x6 - 2x5 + x4 - 4x3 + 7x2 - 2x - 5 | \( 2^{10}\cdot 3^{3}\cdot 7^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.9590832.1 | x6 - x5 + 4x4 + 4x3 + x2 + 3x + 10 | \( -\,2^{4}\cdot 3^{3}\cdot 149^{2} \) | $\PGL(2,5)$ (as 6T14) | $[4]$ |
| 6.2.9800000.2 | x6 - 10x3 - 4x + 5 | \( 2^{6}\cdot 5^{5}\cdot 7^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.9834496.1 | x6 - 2x5 + 3x4 - 4x3 + 5x2 - 6x + 7 | \( -\,2^{12}\cdot 7^{4} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.10209375.1 | x6 - 2x5 + 5x4 + 9x + 12 | \( -\,3^{3}\cdot 5^{5}\cdot 11^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.10368000.1 | x6 - 2x5 + 4x4 - 4x3 + 2x2 - 4x - 6 | \( 2^{10}\cdot 3^{4}\cdot 5^{3} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.0.10546875.1 | x6 - 5x4 + 15x2 - 11x + 5 | \( -\,3^{3}\cdot 5^{8} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.10731125.1 | x6 - x5 + 2x4 + 4x3 - 3x2 - 3x + 1 | \( 5^{3}\cdot 293^{2} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.0.10784448.3 | x6 - 2x5 + 4x4 - 4x3 + 4x2 + 4x + 4 | \( -\,2^{6}\cdot 3^{3}\cdot 79^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.10916416.1 | x6 - 2x5 + 2x4 + 7x2 + 1 | \( -\,2^{6}\cdot 7^{2}\cdot 59^{2} \) | $\PGL(2,5)$ (as 6T14) | $[4]$ |
| 6.2.11366912.2 | x6 - 2x5 + 7x4 - 10x3 + 12x2 - 8x + 1 | \( 2^{9}\cdot 149^{2} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.0.12800000.1 | x6 - 2x5 + 5x4 + 4x + 2 | \( -\,2^{12}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.12869712.1 | x6 - x5 - x3 + 4x2 + 3x - 9 | \( 2^{4}\cdot 3^{3}\cdot 31^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.13203125.1 | x6 - x5 - 4x - 1 | \( 5^{7}\cdot 13^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.13530125.1 | x6 - 2x5 + 3x4 - x3 + 2x2 + 3x - 1 | \( 5^{3}\cdot 7^{2}\cdot 47^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.13530125.2 | x6 - 3x4 - 2x3 + 11x2 - 7x + 1 | \( 5^{3}\cdot 7^{2}\cdot 47^{2} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.0.13687488.1 | x6 - x5 + x4 + x3 + x2 - x + 4 | \( -\,2^{6}\cdot 3^{3}\cdot 89^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.13841712.3 | x6 - 2x5 + 8x4 - 12x3 + 12x2 - 10x + 4 | \( -\,2^{4}\cdot 3^{3}\cdot 179^{2} \) | $\PGL(2,5)$ (as 6T14) | $[4]$ |
| 6.0.14625792.2 | x6 - 2x5 + 5x4 - 12x3 + 15x2 - 18x + 15 | \( -\,2^{10}\cdot 3^{3}\cdot 23^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.14697207.1 | x6 - x5 + 3x4 + 6x2 + 3 | \( -\,3^{4}\cdot 7^{3}\cdot 23^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.14792000.2 | x6 - 3x4 - 8x3 - 9x2 - 8x - 4 | \( 2^{6}\cdot 5^{3}\cdot 43^{2} \) | $\PGL(2,5)$ (as 6T14) | $[2]$ |
| 6.2.15000633.1 | x6 - 3x5 - 3x4 + 4x3 - 12x2 + 6x - 5 | \( 3^{7}\cdot 19^{3} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.15106608.2 | x6 - 3x5 + 4x4 + 6x2 + 2x + 2 | \( -\,2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 17^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.15268608.1 | x6 - 2x5 + 2x4 + 3x2 - 18x + 18 | \( -\,2^{8}\cdot 3^{3}\cdot 47^{2} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.0.16133283.3 | x6 - x5 + 3x4 + 9x3 + 5x2 - 2x + 1 | \( -\,3^{3}\cdot 773^{2} \) | $\PGL(2,5)$ (as 6T14) | $[4]$ |
| 6.2.16200000.1 | x6 - 2x5 - 6x - 3 | \( 2^{6}\cdot 3^{4}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
| 6.2.16200000.2 | x6 - 2x5 + 5x4 - 5x2 + 8x - 1 | \( 2^{6}\cdot 3^{4}\cdot 5^{5} \) | $\PGL(2,5)$ (as 6T14) | Trivial |
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