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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 6.0.273375.1 | x6 - 3x5 + 3x4 - x3 + 3x2 - 3x + 1 | \( -\,3^{7}\cdot 5^{3} \) | $S_3$ (as 6T2) | $[2]$ |
| 6.0.381391.1 | x6 - 2x5 + x3 + 3x2 - 3x + 1 | \( -\,109\cdot 3499 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.391127.1 | x6 - x5 - x4 + x3 + 5x2 - 13x + 9 | \( -\,11\cdot 31^{2}\cdot 37 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.392000.1 | x6 - 2x5 + 3x4 + 4x2 + 2x + 1 | \( -\,2^{6}\cdot 5^{3}\cdot 7^{2} \) | $S_3\times C_3$ (as 6T5) | $[2]$ |
| 6.0.440896.1 | x6 - x4 - 3x2 + 4 | \( -\,2^{6}\cdot 83^{2} \) | $D_{6}$ (as 6T3) | $[2]$ |
| 6.0.447471.1 | x6 - x5 - 5x4 + 5x3 + 14x2 + 6x + 1 | \( -\,3^{3}\cdot 16573 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.451116.1 | x6 + 2x4 - x3 + 4x2 - x + 1 | \( -\,2^{2}\cdot 3^{3}\cdot 4177 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.473416.1 | x6 - x5 + x4 - 2x3 + 5x2 + 3x + 1 | \( -\,2^{3}\cdot 17\cdot 59^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.508707.1 | x6 - 2x5 + x4 - 2x3 + 5x2 - 3x + 1 | \( -\,3^{3}\cdot 83\cdot 227 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.513932.1 | x6 - x5 + 2x4 + x3 + 4x2 + 2x + 1 | \( -\,2^{2}\cdot 128483 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.532703.1 | x6 - 2x4 - 6x3 - 3x2 + 18x + 17 | \( -\,19\cdot 23^{2}\cdot 53 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.560263.1 | x6 + 2x4 - 2x3 + 5x2 - 14x + 9 | \( -\,11\cdot 31^{2}\cdot 53 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.596375.1 | x6 - x5 - x3 + 3x2 + x + 1 | \( -\,5^{3}\cdot 13\cdot 367 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.597248.1 | x6 + 3x4 - 2x3 + 5x2 - 2x + 1 | \( -\,2^{8}\cdot 2333 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.599103.1 | x6 - 3x5 - x4 + x3 + 10x2 + 4x + 1 | \( -\,3^{3}\cdot 22189 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.603500.1 | x6 - x5 + 4x4 - 3x3 + 4x2 + 1 | \( -\,2^{2}\cdot 5^{3}\cdot 17\cdot 71 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.607000.1 | x6 - x5 + x4 + 3x2 - 4x + 4 | \( -\,2^{3}\cdot 5^{3}\cdot 607 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.613111.1 | x6 - 2x5 + 7x4 - 2x3 + 12x2 + 10x + 11 | \( -\,19\cdot 23^{2}\cdot 61 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.617584.1 | x6 - 3x5 + 3x4 - x3 - 4x2 + 4x + 4 | \( -\,2^{4}\cdot 11^{3}\cdot 29 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.641144.1 | x6 - x5 + x4 + 2x3 + 5x2 - x + 1 | \( -\,2^{3}\cdot 7\cdot 107^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.643264.1 | x6 + 5x4 + 15x2 + 19 | \( -\,2^{6}\cdot 19\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.644463.1 | x6 + x4 - x3 + 4x2 - 2x + 1 | \( -\,3^{3}\cdot 23869 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.644851.1 | x6 - x5 + 2x4 - 8x3 + 9x2 - 3x + 25 | \( -\,23^{3}\cdot 53 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.648000.1 | x6 - 2x5 + 2x4 - 4x3 + 7x2 - 4x + 1 | \( -\,2^{6}\cdot 3^{4}\cdot 5^{3} \) | $S_3\times C_3$ (as 6T5) | $[2]$ |
| 6.0.658503.1 | x6 - 2x5 + 4x4 - 9x3 + 30x2 - 9x + 9 | \( -\,3^{3}\cdot 29^{3} \) | $S_3$ (as 6T2) | $[2]$ |
| 6.0.658503.2 | x6 - 3x5 + 5x4 - 5x3 + x2 + x + 1 | \( -\,3^{3}\cdot 29^{3} \) | $S_4$ (as 6T8) | $[2]$ |
| 6.0.676544.1 | x6 - 2x4 - x2 + 11 | \( -\,2^{6}\cdot 11\cdot 31^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.677376.1 | x6 - 2x5 + 3x4 - 6x3 + 8x2 - 4x + 1 | \( -\,2^{9}\cdot 3^{3}\cdot 7^{2} \) | $S_3\times C_3$ (as 6T5) | $[2]$ |
| 6.0.686000.1 | x6 - 3x5 + 8x4 - 11x3 + 8x2 - 3x + 1 | \( -\,2^{4}\cdot 5^{3}\cdot 7^{3} \) | $S_3$ (as 6T2) | $[2]$ |
| 6.0.699840.1 | x6 + 3x4 - 2x3 + 3x2 + 1 | \( -\,2^{6}\cdot 3^{7}\cdot 5 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.706023.1 | x6 - x5 + 7x4 - 7x3 + 14x2 - 12x + 7 | \( -\,3^{3}\cdot 79\cdot 331 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.711232.1 | x6 - 2x4 + 10x2 - 6x + 1 | \( -\,2^{6}\cdot 11113 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.711511.1 | x6 - 2x5 + 3x4 - 5x3 + 3x2 + 1 | \( -\,181\cdot 3931 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.719104.1 | x6 - 2x5 + x4 + 4x3 + x2 - 2x + 1 | \( -\,2^{8}\cdot 53^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.729399.1 | x6 - x5 - 3x4 + 9x3 - x2 - 21x + 17 | \( -\,3\cdot 11\cdot 23\cdot 31^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.732024.1 | x6 - 2x5 + 5x4 - 9x3 + 12x2 - 10x + 4 | \( -\,2^{3}\cdot 3^{3}\cdot 3389 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.739071.1 | x6 - x5 + 7x4 - 7x3 + 17x2 - 12x + 16 | \( -\,3^{3}\cdot 31\cdot 883 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.742187.1 | x6 - 2x5 + 10x4 - 13x3 + 30x2 - 18x + 27 | \( -\,23^{3}\cdot 61 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.756999.1 | x6 - 2x5 + 10x4 - 16x3 + 31x2 - 30x + 25 | \( -\,3^{3}\cdot 23^{2}\cdot 53 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.771471.1 | x6 - 4x4 - 3x3 + 7x2 + 15x + 9 | \( -\,3^{3}\cdot 28573 \) | $C_3^2:D_4$ (as 6T13) | $[2]$ |
| 6.0.771683.1 | x6 - 2x5 + x4 - 6x3 + 11x2 + 5x + 17 | \( -\,11\cdot 31^{2}\cdot 73 \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.773927.1 | x6 - 3x5 + 5x4 - 5x3 + 11x2 - 9x + 25 | \( -\,7\cdot 11\cdot 19\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.778688.1 | x6 + 3x4 + 8x2 + 23 | \( -\,2^{6}\cdot 23^{3} \) | $S_4$ (as 6T8) | $[2]$ |
| 6.0.783875.1 | x6 - x5 - 2x4 + x3 + 5x2 - 4x + 1 | \( -\,5^{3}\cdot 6271 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.797375.1 | x6 - 3x5 + 5x4 - 3x3 + 2x2 + x + 1 | \( -\,5^{3}\cdot 6379 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.805111.1 | x6 - x5 - x4 - x3 + 4x2 - 2x + 1 | \( -\,805111 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.817711.1 | x6 - 2x4 - x3 + 3x2 - x + 1 | \( -\,817711 \) | $S_6$ (as 6T16) | $[2]$ |
| 6.0.839056.1 | x6 + 6x4 + 8x2 + 1 | \( -\,2^{4}\cdot 229^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.854335.1 | x6 - x5 + 5x4 + 5x3 + 9x2 + 17x + 23 | \( -\,5\cdot 17\cdot 19\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
| 6.0.861184.2 | x6 - 3x4 + 5x2 + 1 | \( -\,2^{10}\cdot 29^{2} \) | $S_4\times C_2$ (as 6T11) | $[2]$ |
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