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Label Polynomial Discriminant Galois group Class group
6.2.57152.1 x6 - 2x5 + 2x4 - 2x3 + x2 - 1 \( 2^{6}\cdot 19\cdot 47 \) $S_6$ (as 6T16) trivial
6.2.99136.1 x6 - 2x5 + 2x3 - 3x2 + 2x + 1 \( 2^{6}\cdot 1549 \) $S_6$ (as 6T16) trivial
6.2.119104.1 x6 - 2x5 + 2x4 - 2x3 + x2 - 2x + 1 \( 2^{6}\cdot 1861 \) $S_6$ (as 6T16) trivial
6.0.123072.1 x6 - 2x5 + x4 + 2x + 1 \( -\,2^{6}\cdot 3\cdot 641 \) $S_6$ (as 6T16) trivial
6.0.147136.1 x6 - 2x5 + 2x3 + x2 - 2x + 1 \( -\,2^{6}\cdot 11^{2}\cdot 19 \) $S_6$ (as 6T16) trivial
6.2.169280.1 x6 + x4 - 4x2 - 5 \( 2^{6}\cdot 5\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.169280.2 x6 - 4x4 + 7x2 - 5 \( 2^{6}\cdot 5\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.179008.1 x6 + x4 - 2x2 - 2x - 1 \( 2^{6}\cdot 2797 \) $S_6$ (as 6T16) trivial
6.2.180032.1 x6 - 2x5 + x4 - 2x + 1 \( 2^{6}\cdot 29\cdot 97 \) $S_6$ (as 6T16) trivial
6.0.184512.1 x6 + 3x4 + 4x2 + 3 \( -\,2^{6}\cdot 3\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.184512.2 x6 - 2x4 - x2 + 3 \( -\,2^{6}\cdot 3\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.186560.1 x6 - 2x5 + 5x4 - 6x3 + 6x2 - 2x + 1 \( -\,2^{6}\cdot 5\cdot 11\cdot 53 \) $S_6$ (as 6T16) trivial
6.2.188736.1 x6 + x4 - 4x3 + 4x2 - 1 \( 2^{6}\cdot 3\cdot 983 \) $S_6$ (as 6T16) trivial
6.2.190784.1 x6 - 2x5 + 3x4 - 4x3 + 2x2 - 1 \( 2^{6}\cdot 11\cdot 271 \) $S_6$ (as 6T16) trivial
6.2.222016.1 x6 - 2x5 + x4 + 2x - 1 \( 2^{6}\cdot 3469 \) $S_6$ (as 6T16) trivial
6.4.228544.1 x6 - 2x5 + 4x3 - 3x2 - 2x + 1 \( -\,2^{6}\cdot 3571 \) $S_6$ (as 6T16) trivial
6.2.236864.1 x6 - 2x4 - 2x3 + 3x2 + 4x + 1 \( 2^{6}\cdot 3701 \) $S_6$ (as 6T16) trivial
6.2.237376.1 x6 - x4 - 2x3 - 2x2 + 1 \( 2^{6}\cdot 3709 \) $S_6$ (as 6T16) trivial
6.0.242368.1 x6 + 3x2 - 2x + 1 \( -\,2^{6}\cdot 7\cdot 541 \) $S_6$ (as 6T16) trivial
6.2.282944.1 x6 - 2x5 - x4 + 4x3 - 2x2 - 1 \( 2^{6}\cdot 4421 \) $S_6$ (as 6T16) trivial
6.2.293696.1 x6 - 2x5 + 3x4 - 4x3 + 4x2 - 4x + 1 \( 2^{6}\cdot 13\cdot 353 \) $S_6$ (as 6T16) trivial
6.0.300224.1 x6 + 2x4 + x2 - 2x + 1 \( -\,2^{6}\cdot 4691 \) $S_6$ (as 6T16) trivial
6.2.303936.1 x6 - 4x4 - 2x3 + 5x2 - 1 \( 2^{6}\cdot 3\cdot 1583 \) $S_6$ (as 6T16) trivial
6.2.317248.1 x6 - x4 - 2x + 1 \( 2^{6}\cdot 4957 \) $S_6$ (as 6T16) trivial
6.2.342848.1 x6 - 2x5 + 2x4 + 2x3 - 7x2 + 4x - 1 \( 2^{6}\cdot 11\cdot 487 \) $S_6$ (as 6T16) trivial
6.2.352064.1 x6 - 2x5 + 4x3 - 5x2 + 2x - 1 \( 2^{6}\cdot 5501 \) $S_6$ (as 6T16) trivial
6.2.363328.1 x6 - 2x5 - x4 + 4x3 - 4x + 1 \( 2^{6}\cdot 7\cdot 811 \) $S_6$ (as 6T16) trivial
6.0.372416.1 x6 + 4x4 + 7x2 + 11 \( -\,2^{6}\cdot 11\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.372416.2 x6 + 4x4 + 9x2 + 11 \( -\,2^{6}\cdot 11\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.377152.2 x6 - 2x5 + 2x4 - 3x2 + 4x - 1 \( 2^{6}\cdot 71\cdot 83 \) $S_6$ (as 6T16) trivial
6.0.380096.1 x6 - x4 - 2x3 + 2x2 + 1 \( -\,2^{6}\cdot 5939 \) $S_6$ (as 6T16) trivial
6.0.397504.1 x6 - x4 - 2x3 + 2x2 + 2x + 1 \( -\,2^{6}\cdot 6211 \) $S_6$ (as 6T16) trivial
6.2.398656.1 x6 - x4 - 2x3 + 2x2 + 2x - 1 \( 2^{6}\cdot 6229 \) $S_6$ (as 6T16) trivial
6.0.402624.1 x6 - 2x5 + 3x4 - 4x3 + 6x2 - 6x + 3 \( -\,2^{6}\cdot 3^{3}\cdot 233 \) $S_6$ (as 6T16) trivial
6.0.402624.2 x6 - 2x5 + 6x4 - 8x3 + 9x2 - 6x + 3 \( -\,2^{6}\cdot 3^{3}\cdot 233 \) $S_6$ (as 6T16) trivial
6.2.516928.1 x6 - 2x5 + 2x4 - 2x3 + x2 + 4x - 3 \( 2^{6}\cdot 41\cdot 197 \) $S_6$ (as 6T16) trivial
6.2.516928.2 x6 - 2x5 + x4 - 2x - 1 \( 2^{6}\cdot 41\cdot 197 \) $S_6$ (as 6T16) trivial
6.2.536384.1 x6 - 2x5 + x4 + 2x3 - 4x2 + 2x + 1 \( 2^{6}\cdot 17^{2}\cdot 29 \) $S_6$ (as 6T16) trivial
6.2.596800.1 x6 - 2x5 - 2x4 + 4x3 + 5x2 - 1 \( 2^{6}\cdot 5^{2}\cdot 373 \) $S_6$ (as 6T16) trivial
6.2.606528.1 x6 + 3x4 - 2x3 + 6x2 - 1 \( 2^{6}\cdot 3^{6}\cdot 13 \) $S_6$ (as 6T16) trivial
6.4.629952.1 x6 - 2x5 + 6x3 - 3x2 - 2x + 1 \( -\,2^{6}\cdot 3\cdot 17\cdot 193 \) $S_6$ (as 6T16) trivial
6.0.643264.1 x6 + 5x4 + 15x2 + 19 \( -\,2^{6}\cdot 19\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
6.2.648000.1 x6 + 2x4 - 2x3 - 3x2 - 6x - 3 \( 2^{6}\cdot 3^{4}\cdot 5^{3} \) $S_6$ (as 6T16) trivial
6.2.650048.1 x6 - 2x5 + 2x4 - 4x3 + 3x2 - 1 \( 2^{6}\cdot 7\cdot 1451 \) $S_6$ (as 6T16) trivial
6.2.674624.1 x6 - 4x3 - 3x2 - 4x - 1 \( 2^{6}\cdot 83\cdot 127 \) $S_6$ (as 6T16) trivial
6.0.676544.1 x6 - 2x4 - x2 + 11 \( -\,2^{6}\cdot 11\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
6.2.701248.1 x6 - x4 - 2x3 - 4x2 - 4x - 1 \( 2^{6}\cdot 10957 \) $S_6$ (as 6T16) trivial
6.2.704832.1 x6 - 2x5 - 2x4 + 2x3 + 5x2 - 1 \( 2^{6}\cdot 3\cdot 3671 \) $S_6$ (as 6T16) trivial
6.0.733376.1 x6 - 2x5 + x4 - 4x3 + 4x2 + 2x + 1 \( -\,2^{6}\cdot 7\cdot 1637 \) $S_6$ (as 6T16) trivial
6.2.737088.1 x6 - 4x3 - 5x2 - 4x - 1 \( 2^{6}\cdot 3\cdot 11\cdot 349 \) $S_6$ (as 6T16) trivial
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