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Label Polynomial Discriminant Galois group Class group
6.0.214375.1 x6 - 3x5 + x4 + 3x3 + x2 - 3x + 1 \( -\,5^{4}\cdot 7^{3} \) $S_3$ (as 6T2) trivial
6.0.270000.1 x6 - 3x5 + 4x4 - 3x3 - 2x2 + 3x + 3 \( -\,2^{4}\cdot 3^{3}\cdot 5^{4} \) $S_3$ (as 6T2) trivial
6.0.320000.1 x6 + 4x4 - 3x2 + 2 \( -\,2^{9}\cdot 5^{4} \) $S_3$ (as 6T2) trivial
6.2.520625.1 x6 - x5 - x4 - x3 + x2 - x - 1 \( 5^{4}\cdot 7^{2}\cdot 17 \) $S_4\times C_2$ (as 6T11) trivial
6.0.826875.1 x6 - x5 - x4 + 4x3 + x2 - 6x + 9 \( -\,3^{3}\cdot 5^{4}\cdot 7^{2} \) $D_{6}$ (as 6T3) trivial
6.0.920000.1 x6 - x5 - x4 - x3 + x2 - x + 4 \( -\,2^{6}\cdot 5^{4}\cdot 23 \) $S_4\times C_2$ (as 6T11) trivial
6.0.1080000.1 x6 - 2x5 + x4 + 2x3 + x2 - 2x + 1 \( -\,2^{6}\cdot 3^{3}\cdot 5^{4} \) $S_4$ (as 6T8) trivial
6.0.1080000.2 x6 - x5 - x4 - 6x3 + 6x2 + 4x + 4 \( -\,2^{6}\cdot 3^{3}\cdot 5^{4} \) $D_{6}$ (as 6T3) trivial
6.0.1120000.1 x6 - x5 + 4x4 - 6x3 + 6x2 - 6x + 4 \( -\,2^{8}\cdot 5^{4}\cdot 7 \) $S_4\times C_2$ (as 6T11) trivial
6.2.1120000.1 x6 + x4 - 3x2 - 10x - 2 \( 2^{8}\cdot 5^{4}\cdot 7 \) $S_4\times C_2$ (as 6T11) trivial
6.0.1280000.1 x6 - x4 + 2x2 + 2 \( -\,2^{11}\cdot 5^{4} \) $S_4$ (as 6T8) trivial
6.2.1280000.1 x6 - 4x4 - 3x2 - 2 \( 2^{11}\cdot 5^{4} \) $D_{6}$ (as 6T3) trivial
6.2.1280000.2 x6 + 4x4 + 2x2 - 8 \( 2^{11}\cdot 5^{4} \) $S_4\times C_2$ (as 6T11) trivial
6.0.1366875.1 x6 - 3x5 + 6x4 + 3x3 - 9x2 - 18x + 36 \( -\,3^{7}\cdot 5^{4} \) $S_3$ (as 6T2) trivial
6.0.1439375.1 x6 + x4 - 5x3 + 2x2 + 8 \( -\,5^{4}\cdot 7^{2}\cdot 47 \) $S_4\times C_2$ (as 6T11) trivial
6.2.1623125.1 x6 - 4x4 + 2x2 - 5x + 3 \( 5^{4}\cdot 7^{2}\cdot 53 \) $S_4\times C_2$ (as 6T11) trivial
6.0.1720000.1 x6 - x5 + x4 - 4x3 + 3x2 + x + 7 \( -\,2^{6}\cdot 5^{4}\cdot 43 \) $S_4\times C_2$ (as 6T11) trivial
6.0.1929375.1 x6 - 3x5 + 4x4 - 3x3 + 8x2 - 2x + 3 \( -\,3^{2}\cdot 5^{4}\cdot 7^{3} \) $S_4$ (as 6T8) trivial
6.0.2080000.1 x6 - 2x5 + 6x4 - 8x3 + 6x2 - 2x + 1 \( -\,2^{8}\cdot 5^{4}\cdot 13 \) $S_4\times C_2$ (as 6T11) trivial
6.2.2080000.1 x6 - x5 - x4 + 4x3 + x2 - x - 1 \( 2^{8}\cdot 5^{4}\cdot 13 \) $S_4\times C_2$ (as 6T11) trivial
6.2.2120000.1 x6 - x5 - 4x4 + x3 + 3x2 + 6x + 2 \( 2^{6}\cdot 5^{4}\cdot 53 \) $S_4\times C_2$ (as 6T11) trivial
6.2.2848125.1 x6 - 2x5 + 6x4 - 13x3 + 6x2 - 2x + 1 \( 3\cdot 5^{4}\cdot 7^{2}\cdot 31 \) $S_4\times C_2$ (as 6T11) trivial
6.0.2851875.1 x6 - 3x5 + 4x4 + 2x3 - 2x2 - 2x + 13 \( -\,3^{3}\cdot 5^{4}\cdot 13^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.2.2860625.1 x6 - x5 - 4x4 + x3 + 3x2 + x + 2 \( 5^{4}\cdot 23\cdot 199 \) $S_6$ (as 6T16) trivial
6.2.2970000.1 x6 - x5 + x4 + x3 - 2x2 - 4x - 8 \( 2^{4}\cdot 3^{3}\cdot 5^{4}\cdot 11 \) $S_4\times C_2$ (as 6T11) trivial
6.0.3154375.1 x6 - 3x5 + 9x4 - 13x3 + 13x2 - 7x + 3 \( -\,5^{4}\cdot 7^{2}\cdot 103 \) $S_4\times C_2$ (as 6T11) trivial
6.0.3276875.1 x6 - 2x5 + 6x4 - 8x3 + 16x2 - 7x + 1 \( -\,5^{4}\cdot 7^{2}\cdot 107 \) $S_4\times C_2$ (as 6T11) trivial
6.0.3276875.2 x6 - 3x5 + 6x4 - 7x3 + x2 + 2x + 1 \( -\,5^{4}\cdot 7^{2}\cdot 107 \) $S_4\times C_2$ (as 6T11) trivial
6.0.3276875.3 x6 + x4 - 5x3 + 12x2 - 5x + 3 \( -\,5^{4}\cdot 7^{2}\cdot 107 \) $S_4\times C_2$ (as 6T11) trivial
6.2.3330000.1 x6 - x5 + 4x4 - x3 - 4x2 - x - 1 \( 2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 37 \) $S_4\times C_2$ (as 6T11) trivial
6.2.3583125.1 x6 - 2x5 - x4 + 3x3 - 2x2 + 7x - 7 \( 3^{2}\cdot 5^{4}\cdot 7^{2}\cdot 13 \) $S_4\times C_2$ (as 6T11) trivial
6.2.3645000.1 x6 - 3x5 + 6x4 - 2x3 - 9x2 + 12x - 4 \( 2^{3}\cdot 3^{6}\cdot 5^{4} \) $S_4\times C_2$ (as 6T11) trivial
6.0.3766875.1 x6 - 3x5 - x4 + 2x3 + 8x2 + 3x + 3 \( -\,3\cdot 5^{4}\cdot 7^{2}\cdot 41 \) $S_4\times C_2$ (as 6T11) trivial
6.2.3880000.1 x6 - 3x5 - x4 + 7x3 - 7x2 + 3x - 2 \( 2^{6}\cdot 5^{4}\cdot 97 \) $S_4\times C_2$ (as 6T11) trivial
6.2.3910625.1 x6 - 2x5 + x4 + 2x3 - 4x2 + 3x - 4 \( 5^{4}\cdot 6257 \) $S_6$ (as 6T16) trivial
6.2.4008125.1 x6 - 2x5 + 4x4 - 7x3 + 8x2 - 8x + 3 \( 5^{4}\cdot 11^{2}\cdot 53 \) $S_6$ (as 6T16) trivial
6.2.4073125.1 x6 - 2x5 + x4 + 2x3 - 9x2 - 7x + 1 \( 5^{4}\cdot 7^{3}\cdot 19 \) $S_4\times C_2$ (as 6T11) trivial
6.2.4195625.1 x6 - x5 - x4 + 9x3 + x2 - x - 1 \( 5^{4}\cdot 7^{2}\cdot 137 \) $S_4\times C_2$ (as 6T11) trivial
6.0.4230000.1 x6 - 2x5 + 4x4 - 2x3 + 8x2 - 8x + 8 \( -\,2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 47 \) $S_4\times C_2$ (as 6T11) trivial
6.2.4320000.1 x6 - 4x4 + 12x2 - 12 \( 2^{8}\cdot 3^{3}\cdot 5^{4} \) $S_4\times C_2$ (as 6T11) trivial
6.2.4320000.2 x6 - x4 + 7x2 - 3 \( 2^{8}\cdot 3^{3}\cdot 5^{4} \) $D_{6}$ (as 6T3) trivial
6.2.4480000.1 x6 + x4 - 3x2 - 7 \( 2^{10}\cdot 5^{4}\cdot 7 \) $S_4\times C_2$ (as 6T11) trivial
6.0.4501875.1 x6 - 2x5 + 6x4 - 3x3 + 6x2 - 2x + 1 \( -\,3\cdot 5^{4}\cdot 7^{4} \) $S_4\times C_2$ (as 6T11) $[2]$
6.0.4991875.1 x6 - 3x5 + 4x4 - 3x3 + 3x2 - 2x + 3 \( -\,5^{4}\cdot 7^{2}\cdot 163 \) $S_4\times C_2$ (as 6T11) trivial
6.0.5080000.1 x6 - x5 + 4x4 + 4x3 + 11x2 + 9x + 4 \( -\,2^{6}\cdot 5^{4}\cdot 127 \) $S_4\times C_2$ (as 6T11) trivial
6.0.5120000.1 x6 + 4x4 + 7x2 + 2 \( -\,2^{13}\cdot 5^{4} \) $S_4$ (as 6T8) trivial
6.0.5120000.2 x6 - 4x4 + 2x2 + 8 \( -\,2^{13}\cdot 5^{4} \) $S_4$ (as 6T8) trivial
6.2.5120000.1 x6 + x4 + 2x2 - 2 \( 2^{13}\cdot 5^{4} \) $S_4\times C_2$ (as 6T11) trivial
6.2.5120000.2 x6 - 4x4 + 7x2 - 2 \( 2^{13}\cdot 5^{4} \) $S_4\times C_2$ (as 6T11) trivial
6.2.5298125.1 x6 - 3x5 - 4x4 + 8x3 + 11x2 + 7x + 1 \( 5^{4}\cdot 7^{2}\cdot 173 \) $S_4\times C_2$ (as 6T11) trivial
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