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Label Polynomial Discriminant Galois group Class group
6.0.10816.1 x6 - x4 - 2x3 + 2x + 1 \( -\,2^{6}\cdot 13^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.22592.1 x6 - 2x5 + 2x4 - x2 + 1 \( -\,2^{6}\cdot 353 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.33856.2 x6 + x4 + 2x2 + 1 \( -\,2^{6}\cdot 23^{2} \) $D_{6}$ (as 6T3) trivial
6.0.47680.1 x6 + x2 - 2x + 1 \( -\,2^{6}\cdot 5\cdot 149 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.60992.1 x6 + 3x4 - 2x3 + 4x2 - 2x + 1 \( -\,2^{6}\cdot 953 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.61504.2 x6 - 2x4 + x2 + 1 \( -\,2^{6}\cdot 31^{2} \) $D_{6}$ (as 6T3) trivial
6.0.65600.1 x6 - 2x5 - x4 + 2x3 + 2x2 - 2x + 1 \( -\,2^{6}\cdot 5^{2}\cdot 41 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.87616.1 x6 - 2x5 - 2x4 + 4x3 + 3x2 - 4x + 1 \( -\,2^{6}\cdot 37^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.96832.1 x6 - 2x5 + 2x4 - 2x3 - x2 + 2x + 1 \( -\,2^{6}\cdot 17\cdot 89 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.106560.1 x6 - 2x5 + 3x4 + 2x + 1 \( -\,2^{6}\cdot 3^{2}\cdot 5\cdot 37 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.147008.1 x6 - 4x4 - 2x3 + 5x2 + 4x + 1 \( -\,2^{6}\cdot 2297 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.147520.1 x6 - 2x5 - 2x3 + 3x2 + 4x + 1 \( -\,2^{6}\cdot 5\cdot 461 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.153664.1 x6 + 5x4 + 6x2 + 1 \( -\,2^{6}\cdot 7^{4} \) $C_6$ (as 6T1) trivial
6.0.202304.1 x6 - 4x4 + 5x2 - 2x + 1 \( -\,2^{6}\cdot 29\cdot 109 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.205376.1 x6 - x4 - 4x3 + 2x2 + 2x + 1 \( -\,2^{6}\cdot 3209 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.212032.1 x6 - 2x5 - x4 + 4x2 + 2x + 1 \( -\,2^{6}\cdot 3313 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.230464.1 x6 - 2x5 + 2x4 - x2 - 4x + 5 \( -\,2^{6}\cdot 13\cdot 277 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.238144.2 x6 - 2x5 + 5x4 - 8x3 + 12x2 - 12x + 5 \( -\,2^{6}\cdot 61^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.305728.1 x6 + 3x4 - 2x3 + 4x2 - 2x + 5 \( -\,2^{6}\cdot 17\cdot 281 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.308800.1 x6 - 2x5 + 2x4 - 4x3 + 11x2 - 12x + 5 \( -\,2^{6}\cdot 5^{2}\cdot 193 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.326720.1 x6 + 2x4 + 5x2 - 4x + 1 \( -\,2^{6}\cdot 5\cdot 1021 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.330304.1 x6 - 3x4 - 4x3 + 6x2 + 4x + 1 \( -\,2^{6}\cdot 13\cdot 397 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.341056.1 x6 - 5x4 + 10x2 - 6x + 1 \( -\,2^{6}\cdot 73^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.348736.1 x6 - 2x5 + 4x3 - 5x2 - 2x + 5 \( -\,2^{6}\cdot 5449 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.356416.1 x6 + 3x4 + 6x2 - 2x + 5 \( -\,2^{6}\cdot 5569 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.374336.1 x6 + x4 - 4x3 + 2x2 + 4x + 1 \( -\,2^{6}\cdot 5849 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.419904.1 x6 + 6x4 + 9x2 + 1 \( -\,2^{6}\cdot 3^{8} \) $C_6$ (as 6T1) trivial
6.0.419904.3 x6 - 2x3 + 9x2 - 12x + 5 \( -\,2^{6}\cdot 3^{8} \) $S_3\times C_3$ (as 6T5) trivial
6.0.424000.1 x6 - 2x5 + 4x4 - 8x3 + 11x2 - 10x + 5 \( -\,2^{6}\cdot 5^{3}\cdot 53 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.470080.1 x6 - 2x5 - 2x4 + 7x2 + 4x + 1 \( -\,2^{6}\cdot 5\cdot 13\cdot 113 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.476608.1 x6 + x4 - 2x3 - 4x2 + 1 \( 2^{6}\cdot 11\cdot 677 \) $S_6$ (as 6T16) trivial
6.0.484416.2 x6 - 3x4 + 6x2 + 1 \( -\,2^{6}\cdot 3^{2}\cdot 29^{2} \) $D_{6}$ (as 6T3) trivial
6.0.499264.1 x6 - 3x4 - 2x3 + 4x + 5 \( -\,2^{6}\cdot 29\cdot 269 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.516160.1 x6 - 2x5 + 3x4 - 6x3 + 6x2 - 6x + 5 \( -\,2^{6}\cdot 5\cdot 1613 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.516544.1 x6 - 2x5 + 2x4 - 6x3 + 7x2 - 2x + 1 \( 2^{6}\cdot 7\cdot 1153 \) $S_6$ (as 6T16) trivial
6.0.517184.1 x6 - 5x4 - 2x3 + 8x2 + 2x + 1 \( -\,2^{6}\cdot 8081 \) $C_3^2:D_4$ (as 6T13) trivial
6.4.526912.1 x6 - 3x4 - 4x3 + 2x2 + 4x + 1 \( -\,2^{6}\cdot 8233 \) $S_6$ (as 6T16) trivial
6.0.543296.1 x6 - 3x4 - 4x3 + 10x2 - 4x + 1 \( -\,2^{6}\cdot 13\cdot 653 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.549440.1 x6 - 2x5 + 3x4 - 6x3 + 14x2 - 10x + 5 \( -\,2^{6}\cdot 5\cdot 17\cdot 101 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.549440.2 x6 - 2x5 + 6x4 - 4x3 + 7x2 + 5 \( -\,2^{6}\cdot 5\cdot 17\cdot 101 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.557120.1 x6 - 5x4 - 2x3 + 8x2 + 10x + 5 \( -\,2^{6}\cdot 5\cdot 1741 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.580160.1 x6 - 2x5 - 2x4 + 4x3 - x2 + 5 \( -\,2^{6}\cdot 5\cdot 7^{2}\cdot 37 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.583232.1 x6 - 2x5 + 3x4 - 4x3 + 4x2 - 6x + 5 \( -\,2^{6}\cdot 13\cdot 701 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.586304.1 x6 - 3x4 - 4x3 + 2x2 + 8x + 5 \( -\,2^{6}\cdot 9161 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.586816.1 x6 - 2x5 + 6x3 + 3x2 - 4x + 1 \( -\,2^{6}\cdot 53\cdot 173 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.595008.1 x6 - 2x5 + x4 + 2x3 + 2x2 - 8x + 5 \( -\,2^{6}\cdot 3^{2}\cdot 1033 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.602176.1 x6 - 2x5 - 4x4 + 11x2 + 14x + 5 \( -\,2^{6}\cdot 97^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.603200.1 x6 - 4x4 - 4x3 + 5x2 + 10x + 5 \( -\,2^{6}\cdot 5^{2}\cdot 13\cdot 29 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.609344.1 x6 - 2x5 - 2x4 + 8x3 - x2 - 12x + 9 \( -\,2^{6}\cdot 9521 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.613952.1 x6 - 2x5 + 3x4 - 4x3 + 12x2 - 14x + 5 \( -\,2^{6}\cdot 53\cdot 181 \) $C_3^2:D_4$ (as 6T13) trivial
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