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Label Polynomial Discriminant Galois group Class group
6.2.324608.1 x6 - 2x5 + 4x3 - 6x2 + 4x - 2 \( 2^{10}\cdot 317 \) $S_6$ (as 6T16) trivial
6.0.379904.1 x6 - 2x5 + 4x4 - 4x3 + 4x2 - 4x + 2 \( -\,2^{10}\cdot 7\cdot 53 \) $S_6$ (as 6T16) trivial
6.2.390144.1 x6 - 2x5 + 4x - 2 \( 2^{10}\cdot 3\cdot 127 \) $S_6$ (as 6T16) trivial
6.0.1362944.1 x6 + 3x4 + 11x2 + 11 \( -\,2^{10}\cdot 11^{3} \) $S_4$ (as 6T8) trivial
6.2.1471488.1 x6 - 2x5 - 2x2 - 4x - 2 \( 2^{10}\cdot 3\cdot 479 \) $S_6$ (as 6T16) trivial
6.0.1592320.1 x6 - 2x5 + 6x4 - 4x3 + 6x2 + 2 \( -\,2^{10}\cdot 5\cdot 311 \) $S_6$ (as 6T16) trivial
6.2.1610752.1 x6 - 7x4 + 17x2 - 13 \( 2^{10}\cdot 11^{2}\cdot 13 \) $S_4\times C_2$ (as 6T11) trivial
6.2.1807360.1 x6 + x4 + 3x2 - 4x + 1 \( 2^{10}\cdot 5\cdot 353 \) $S_6$ (as 6T16) trivial
6.0.2239488.1 x6 + 3x4 + 3x2 + 3 \( -\,2^{10}\cdot 3^{7} \) $S_4$ (as 6T8) $[2]$
6.0.2354176.1 x6 - x4 - 5x2 + 19 \( -\,2^{10}\cdot 11^{2}\cdot 19 \) $S_4\times C_2$ (as 6T11) trivial
6.2.2364416.1 x6 - 2x5 + 2x4 - 8x3 + 4x2 + 2 \( 2^{10}\cdot 2309 \) $S_6$ (as 6T16) trivial
6.2.2536448.1 x6 - 2x5 + 4x3 - 2x2 - 4x + 2 \( 2^{10}\cdot 2477 \) $S_6$ (as 6T16) trivial
6.2.2593792.1 x6 - 2x5 + 2x2 - 4x + 2 \( 2^{10}\cdot 17\cdot 149 \) $S_6$ (as 6T16) trivial
6.2.2733056.1 x6 - 2x5 + x4 + 4x3 - 13x2 + 14x - 9 \( 2^{10}\cdot 17\cdot 157 \) $S_6$ (as 6T16) trivial
6.2.2929664.1 x6 - 2x5 + 2x4 + 4x3 - 8x2 + 8x - 2 \( 2^{10}\cdot 2861 \) $S_6$ (as 6T16) trivial
6.0.3116032.1 x6 - 3x4 - 4x3 + 3x2 + 8x + 5 \( -\,2^{10}\cdot 17\cdot 179 \) $S_6$ (as 6T16) trivial
6.2.3200000.1 x6 - 2x5 + 4x + 2 \( 2^{10}\cdot 5^{5} \) $\PGL(2,5)$ (as 6T14) trivial
6.0.3632128.1 x6 + x4 - 4x3 + 5x2 - 4x + 3 \( -\,2^{10}\cdot 3547 \) $S_6$ (as 6T16) trivial
6.2.3879936.1 x6 - 2x5 + 4x4 - 4x3 - 4x2 + 4x + 2 \( 2^{10}\cdot 3^{2}\cdot 421 \) $S_6$ (as 6T16) trivial
6.2.3937280.1 x6 - 2x5 - 2x2 + 4x - 2 \( 2^{10}\cdot 5\cdot 769 \) $S_6$ (as 6T16) trivial
6.2.4436992.1 x6 - 2x5 + 2x4 - 4x2 + 2 \( 2^{10}\cdot 7\cdot 619 \) $S_6$ (as 6T16) trivial
6.2.4805632.1 x6 + x4 + 5x2 - 13 \( 2^{10}\cdot 13\cdot 19^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
6.2.4862976.1 x6 - 7x4 - 4x3 + 13x2 + 12x + 3 \( 2^{10}\cdot 3\cdot 1583 \) $S_6$ (as 6T16) trivial
6.2.5035008.1 x6 - 2x5 + 2x4 - 2x2 - 2 \( 2^{10}\cdot 3\cdot 11\cdot 149 \) $S_6$ (as 6T16) trivial
6.2.5288960.1 x6 - x4 - 4x3 + x2 + 5 \( 2^{10}\cdot 5\cdot 1033 \) $S_6$ (as 6T16) trivial
6.0.5680128.2 x6 + 6x4 + 16x2 + 12 \( -\,2^{10}\cdot 3\cdot 43^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.6272000.2 x6 + 7x4 + 11x2 - 5 \( 2^{10}\cdot 5^{3}\cdot 7^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
6.2.6534144.1 x6 - 2x5 + 4x4 + 4x3 - 4x2 + 4x + 2 \( 2^{10}\cdot 3^{2}\cdot 709 \) $S_6$ (as 6T16) trivial
6.2.6566912.1 x6 - x4 - 29x2 - 53 \( 2^{10}\cdot 11^{2}\cdot 53 \) $S_4\times C_2$ (as 6T11) trivial
6.2.6566912.2 x6 - 9x4 + 35x2 - 53 \( 2^{10}\cdot 11^{2}\cdot 53 \) $S_4\times C_2$ (as 6T11) trivial
6.0.6884352.1 x6 - 2x5 + 5x4 - 4x3 + 3x2 + 6x + 3 \( -\,2^{10}\cdot 3^{4}\cdot 83 \) $S_6$ (as 6T16) trivial
6.2.6943744.1 x6 - 2x5 - 2x4 + 4x2 - 2 \( 2^{10}\cdot 6781 \) $S_6$ (as 6T16) trivial
6.6.7009280.1 x6 - 7x4 + 13x2 - 5 \( 2^{10}\cdot 5\cdot 37^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.7023616.1 x6 + 7x4 + 19x2 + 19 \( -\,2^{10}\cdot 19^{3} \) $S_4$ (as 6T8) $[2]$
6.0.7023616.2 x6 + 9x4 + 25x2 + 19 \( -\,2^{10}\cdot 19^{3} \) $S_4$ (as 6T8) $[2]$
6.4.7113728.1 x6 - 7x4 - 4x3 + 5x2 + 4x + 3 \( -\,2^{10}\cdot 6947 \) $S_6$ (as 6T16) trivial
6.2.7140352.1 x6 - 2x5 + 2x2 + 4x - 6 \( 2^{10}\cdot 19\cdot 367 \) $S_6$ (as 6T16) trivial
6.2.7173120.1 x6 - 2x5 - 6x4 + 12x3 + 10x2 - 24x + 6 \( 2^{10}\cdot 3\cdot 5\cdot 467 \) $S_6$ (as 6T16) trivial
6.0.7236608.1 x6 - 2x5 + 2x2 + 4x + 2 \( -\,2^{10}\cdot 37\cdot 191 \) $S_6$ (as 6T16) trivial
6.2.7271424.1 x6 - 2x4 - 8x3 + 8x + 4 \( 2^{10}\cdot 3^{3}\cdot 263 \) $S_6$ (as 6T16) trivial
6.0.7646208.1 x6 + 3x4 + 5x2 - 4x + 1 \( -\,2^{10}\cdot 3\cdot 19\cdot 131 \) $S_6$ (as 6T16) $[3]$
6.0.7990272.1 x6 + x4 + x2 + 3 \( -\,2^{10}\cdot 3^{3}\cdot 17^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
6.4.8047616.1 x6 - 2x5 - 2x4 + 4x3 - 2x2 + 2 \( -\,2^{10}\cdot 29\cdot 271 \) $S_6$ (as 6T16) trivial
6.2.8467456.1 x6 - 2x5 + 8x3 - 6x2 - 4x + 10 \( 2^{10}\cdot 8269 \) $S_6$ (as 6T16) trivial
6.2.8614912.1 x6 - 2x5 + 20x - 18 \( 2^{10}\cdot 47\cdot 179 \) $S_6$ (as 6T16) $[3]$
6.2.8631296.1 x6 - 2x5 - 2x4 + 4x3 + 6x2 - 8x + 2 \( 2^{10}\cdot 8429 \) $S_6$ (as 6T16) trivial
6.2.8827904.1 x6 - 2x5 - 3x4 + 4x3 + 7x2 + 6x - 1 \( 2^{10}\cdot 37\cdot 233 \) $S_6$ (as 6T16) trivial
6.2.8860672.1 x6 - x4 - 4x3 + 3x2 + 12x - 1 \( 2^{10}\cdot 17\cdot 509 \) $S_6$ (as 6T16) trivial
6.2.8950784.1 x6 - 2x5 + 2x4 - 4x3 - 2 \( 2^{10}\cdot 8741 \) $S_6$ (as 6T16) trivial
6.0.9096192.1 x6 + x4 + 3x2 - 12x + 9 \( -\,2^{10}\cdot 3^{3}\cdot 7\cdot 47 \) $S_6$ (as 6T16) trivial
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