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Label Polynomial Discriminant Galois group Class group
6.2.270848.2 x6 + 2x4 - 8 \( 2^{9}\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.355840.1 x6 - 2x5 + 3x4 - 2x3 + 4x2 + 1 \( -\,2^{9}\cdot 5\cdot 139 \) $S_6$ (as 6T16) trivial
6.2.414208.1 x6 - 2x5 + x4 - 2x3 + 4x2 - 4x + 1 \( 2^{9}\cdot 809 \) $S_6$ (as 6T16) trivial
6.2.492032.1 x6 + 4x2 - 8 \( 2^{9}\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.594432.1 x6 + 2x4 - 6x3 + 3x2 + 2x - 1 \( 2^{9}\cdot 3^{3}\cdot 43 \) $S_6$ (as 6T16) trivial
6.0.781824.1 x6 - 2x5 + x4 + 2x3 - 4x2 + 3 \( -\,2^{9}\cdot 3\cdot 509 \) $S_6$ (as 6T16) trivial
6.0.810496.1 x6 + 2x4 - 2x3 - x2 + 2x + 1 \( -\,2^{9}\cdot 1583 \) $S_6$ (as 6T16) trivial
6.2.1036800.1 x6 - 2x5 - x4 + 6x3 - 2x2 - 4x - 1 \( 2^{9}\cdot 3^{4}\cdot 5^{2} \) $S_6$ (as 6T16) trivial
6.2.1229312.1 x6 + 2x4 - 8x2 - 8 \( 2^{9}\cdot 7^{4} \) $A_4\times C_2$ (as 6T6) trivial
6.2.1561088.2 x6 - 2x5 - x4 + 2x3 - 2x2 - 4x - 1 \( 2^{9}\cdot 3049 \) $S_6$ (as 6T16) trivial
6.2.1712640.1 x6 - 2x5 - x4 + 2x3 + 4x2 - 1 \( 2^{9}\cdot 3\cdot 5\cdot 223 \) $S_6$ (as 6T16) trivial
6.2.1716736.2 x6 - 4x4 - 2x3 + 5x2 + 6x + 1 \( 2^{9}\cdot 7\cdot 479 \) $S_6$ (as 6T16) trivial
6.2.1733120.1 x6 - 2x3 + 9x2 - 10x + 3 \( 2^{9}\cdot 5\cdot 677 \) $S_6$ (as 6T16) trivial
6.2.1761792.1 x6 + 2x4 - 2x3 + x2 + 2x - 1 \( 2^{9}\cdot 3\cdot 31\cdot 37 \) $S_6$ (as 6T16) trivial
6.2.1839616.1 x6 + 4x4 - 2x3 - x2 + 2x - 3 \( 2^{9}\cdot 3593 \) $S_6$ (as 6T16) trivial
6.0.1895936.1 x6 + 2x4 - 4x2 + 56 \( -\,2^{9}\cdot 7\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.1895936.2 x6 + 2x4 + 8x2 + 56 \( -\,2^{9}\cdot 7\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.2003456.1 x6 - 4x4 - 2x3 + 3x2 + 6x + 1 \( 2^{9}\cdot 7\cdot 13\cdot 43 \) $S_6$ (as 6T16) trivial
6.2.2040320.1 x6 - 2x5 + 3x4 - 2x3 - 2x2 - 1 \( 2^{9}\cdot 5\cdot 797 \) $S_6$ (as 6T16) trivial
6.4.2051584.1 x6 - 2x3 - 3x2 + 2x + 1 \( -\,2^{9}\cdot 4007 \) $S_6$ (as 6T16) trivial
6.2.2142720.1 x6 - 2x5 + 3x4 - 6x3 + 2x2 - 4x + 1 \( 2^{9}\cdot 3^{3}\cdot 5\cdot 31 \) $S_6$ (as 6T16) trivial
6.4.2215424.1 x6 - 2x5 - 3x4 + 6x3 - 4x + 3 \( -\,2^{9}\cdot 4327 \) $S_6$ (as 6T16) trivial
6.0.2215424.1 x6 + 2x4 - 2x3 + 3x2 - 2x + 3 \( -\,2^{9}\cdot 4327 \) $S_6$ (as 6T16) trivial
6.2.2368000.1 x6 - 2x5 + 3x4 + 2x3 - 4x2 + 4x - 1 \( 2^{9}\cdot 5^{3}\cdot 37 \) $S_6$ (as 6T16) trivial
6.2.2560512.1 x6 - 2x3 + x2 - 2x - 1 \( 2^{9}\cdot 3\cdot 1667 \) $S_6$ (as 6T16) trivial
6.2.2724352.1 x6 + 4x4 - 2x3 + 3x2 - 2x - 1 \( 2^{9}\cdot 17\cdot 313 \) $S_6$ (as 6T16) trivial
6.4.2788864.1 x6 - 2x5 - 5x4 + 6x3 + 8x2 - 4x - 3 \( -\,2^{9}\cdot 13\cdot 419 \) $S_6$ (as 6T16) trivial
6.2.3006976.1 x6 - 2x5 + 5x4 - 6x3 + 2x2 - 1 \( 2^{9}\cdot 7\cdot 839 \) $S_6$ (as 6T16) trivial
6.0.3169792.1 x6 - 2x5 + 3x4 - 6x3 + 12x2 - 12x + 5 \( -\,2^{9}\cdot 41\cdot 151 \) $S_6$ (as 6T16) trivial
6.2.3240448.1 x6 - 2x3 - 11x2 - 6x - 7 \( 2^{9}\cdot 6329 \) $S_6$ (as 6T16) trivial
6.0.3321344.1 x6 - 2x5 + 7x4 - 6x3 + 12x2 - 4x + 5 \( -\,2^{9}\cdot 13\cdot 499 \) $S_6$ (as 6T16) trivial
6.2.3359232.2 x6 - 12x2 - 8 \( 2^{9}\cdot 3^{8} \) $A_4\times C_2$ (as 6T6) trivial
6.2.3359232.3 x6 - 2x3 - 3x2 + 6x - 3 \( 2^{9}\cdot 3^{8} \) $S_6$ (as 6T16) trivial
6.0.3419648.1 x6 - 4x4 - 2x3 + 11x2 + 6x + 1 \( -\,2^{9}\cdot 6679 \) $S_6$ (as 6T16) trivial
6.0.3431936.1 x6 - 2x5 + x4 + 2x3 - 4x + 5 \( -\,2^{9}\cdot 6703 \) $S_6$ (as 6T16) trivial
6.2.3875328.4 x6 + 2x4 + 8x2 - 8 \( 2^{9}\cdot 3^{2}\cdot 29^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.4030976.1 x6 - 2x5 + 3x4 - 6x3 + 6x2 - 1 \( 2^{9}\cdot 7873 \) $S_6$ (as 6T16) trivial
6.2.4035072.1 x6 - 2x5 - 3x4 - 6x3 - 2x2 - 4x + 1 \( 2^{9}\cdot 3\cdot 37\cdot 71 \) $S_6$ (as 6T16) trivial
6.4.4263424.1 x6 - 2x5 + x4 - 2x3 - 2x2 + 4x - 1 \( -\,2^{9}\cdot 11\cdot 757 \) $S_6$ (as 6T16) trivial
6.2.4284928.1 x6 - 2x4 - 2x3 - x2 - 2x + 1 \( 2^{9}\cdot 8369 \) $S_6$ (as 6T16) trivial
6.2.4293120.1 x6 - 2x5 + x4 - 2x3 + 6x2 - 4x - 1 \( 2^{9}\cdot 3\cdot 5\cdot 13\cdot 43 \) $S_6$ (as 6T16) trivial
6.2.4305408.1 x6 - 6x3 + x2 + 2x + 3 \( 2^{9}\cdot 3\cdot 2803 \) $S_6$ (as 6T16) trivial
6.2.4379136.1 x6 - 6x4 - 2x3 + 5x2 - 2x - 1 \( 2^{9}\cdot 3\cdot 2851 \) $S_6$ (as 6T16) trivial
6.2.4428288.1 x6 + 2x4 - 24x2 - 72 \( 2^{9}\cdot 3^{2}\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.4428288.2 x6 - 8x4 + 36x2 - 72 \( 2^{9}\cdot 3^{2}\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.4436480.1 x6 - 2x5 - x4 + 2x3 + 4x2 + 4x - 3 \( 2^{9}\cdot 5\cdot 1733 \) $S_6$ (as 6T16) trivial
6.2.4461056.1 x6 - 2x4 - 2x3 + x2 - 2x - 1 \( 2^{9}\cdot 8713 \) $S_6$ (as 6T16) trivial
6.0.4500992.1 x6 - 2x5 + 7x4 - 10x3 + 16x2 - 12x + 11 \( -\,2^{9}\cdot 59\cdot 149 \) $S_6$ (as 6T16) trivial
6.0.4541952.1 x6 + 4x4 - 6x3 + x2 + 6x + 3 \( -\,2^{9}\cdot 3\cdot 2957 \) $S_6$ (as 6T16) trivial
6.0.4603392.1 x6 - 2x5 + 5x4 - 2x3 + 4x2 - 4x + 3 \( -\,2^{9}\cdot 3^{5}\cdot 37 \) $S_6$ (as 6T16) trivial
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