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Label Polynomial Discriminant Galois group Class group
6.0.270848.1 x6 - 2x4 + 8 \( -\,2^{9}\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.278016.1 x6 - 2x3 - x2 - 2x - 1 \( 2^{9}\cdot 3\cdot 181 \) $S_6$ (as 6T16) trivial
6.0.492032.2 x6 + 4x2 + 8 \( -\,2^{9}\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.740864.1 x6 - 6x3 - 3x2 + 2x + 1 \( 2^{9}\cdot 1447 \) $S_6$ (as 6T16) trivial
6.2.876032.1 x6 - 4x4 - 2x3 + 5x2 + 2x + 1 \( 2^{9}\cdot 29\cdot 59 \) $S_6$ (as 6T16) trivial
6.2.908800.1 x6 - 2x5 + 3x4 - 2x3 - 4x + 1 \( 2^{9}\cdot 5^{2}\cdot 71 \) $S_6$ (as 6T16) trivial
6.2.957952.1 x6 - 2x5 + x4 - 2x3 + 4x2 - 1 \( 2^{9}\cdot 1871 \) $S_6$ (as 6T16) trivial
6.2.1121792.1 x6 - 2x5 + x4 - 2x3 + 2x2 - 4x - 1 \( 2^{9}\cdot 7\cdot 313 \) $S_6$ (as 6T16) trivial
6.4.1176064.1 x6 - 2x5 - x4 + 6x3 - 2x2 - 4x + 1 \( -\,2^{9}\cdot 2297 \) $S_6$ (as 6T16) trivial
6.2.1183232.1 x6 - 2x4 - 2x3 + 3x2 - 2x + 1 \( 2^{9}\cdot 2311 \) $S_6$ (as 6T16) trivial
6.4.1229312.1 x6 - 2x4 - 8x2 + 8 \( -\,2^{9}\cdot 7^{4} \) $A_4\times C_2$ (as 6T6) trivial
6.2.1625600.1 x6 - 2x4 - 6x3 - x2 - 2x - 1 \( 2^{9}\cdot 5^{2}\cdot 127 \) $S_6$ (as 6T16) trivial
6.2.1678848.1 x6 + 2x4 - 2x3 + x2 - 6x + 3 \( 2^{9}\cdot 3\cdot 1093 \) $S_6$ (as 6T16) trivial
6.2.1809920.1 x6 - 2x5 + x4 + 6x3 - 12x2 + 8x - 3 \( 2^{9}\cdot 5\cdot 7\cdot 101 \) $S_6$ (as 6T16) trivial
6.2.1822208.1 x6 - 4x4 - 2x3 + x2 - 2x - 1 \( 2^{9}\cdot 3559 \) $S_6$ (as 6T16) trivial
6.2.1867264.1 x6 - 2x4 - 2x3 - x2 + 2x + 3 \( 2^{9}\cdot 7\cdot 521 \) $S_6$ (as 6T16) trivial
6.2.1895936.1 x6 - 2x4 - 4x2 - 56 \( 2^{9}\cdot 7\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.1895936.2 x6 - 2x4 + 8x2 - 56 \( 2^{9}\cdot 7\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.1991168.1 x6 - 2x3 + x2 + 2x + 3 \( -\,2^{9}\cdot 3889 \) $S_6$ (as 6T16) trivial
6.2.2121216.1 x6 - 2x4 - 2x3 - x2 + 2x - 1 \( 2^{9}\cdot 3\cdot 1381 \) $S_6$ (as 6T16) trivial
6.2.2248192.2 x6 - 2x5 - x4 + 6x3 - 4x2 - 1 \( 2^{9}\cdot 4391 \) $S_6$ (as 6T16) trivial
6.0.2273792.1 x6 - 2x5 + 7x4 - 10x3 + 14x2 - 12x + 9 \( -\,2^{9}\cdot 4441 \) $S_6$ (as 6T16) trivial
6.4.2507264.1 x6 - 2x5 - x4 + 6x3 - 4x2 - 4x + 3 \( -\,2^{9}\cdot 59\cdot 83 \) $S_6$ (as 6T16) trivial
6.2.2612736.1 x6 - 6x4 - 2x3 + 15x2 + 6x - 17 \( 2^{9}\cdot 3^{6}\cdot 7 \) $S_6$ (as 6T16) trivial
6.2.2625024.1 x6 + 2x4 - 6x3 - x2 + 6x - 3 \( 2^{9}\cdot 3\cdot 1709 \) $S_6$ (as 6T16) trivial
6.2.2629120.1 x6 - 2x5 + x4 + 2x3 - 10x2 + 4x - 1 \( 2^{9}\cdot 5\cdot 13\cdot 79 \) $S_6$ (as 6T16) trivial
6.2.2723328.1 x6 - 2x5 - x4 + 6x3 - 6x2 + 3 \( 2^{9}\cdot 3^{3}\cdot 197 \) $S_6$ (as 6T16) trivial
6.2.2948608.1 x6 - 2x5 + x4 + 2x3 - 2x2 - 4x - 1 \( 2^{9}\cdot 13\cdot 443 \) $S_6$ (as 6T16) trivial
6.2.3010048.1 x6 - 2x5 + x4 + 2x3 - 6x2 - 8x - 1 \( 2^{9}\cdot 5879 \) $S_6$ (as 6T16) trivial
6.2.3091968.1 x6 - 2x5 - x4 - 2x3 - 4x2 + 4x - 5 \( 2^{9}\cdot 3^{2}\cdot 11\cdot 61 \) $S_6$ (as 6T16) trivial
6.2.3137024.1 x6 - 2x5 + x4 - 2x3 - 4x2 + 8x - 3 \( 2^{9}\cdot 11\cdot 557 \) $S_6$ (as 6T16) trivial
6.2.3276288.1 x6 - 2x5 + 5x4 - 6x3 + 4x2 - 4x - 1 \( 2^{9}\cdot 3^{4}\cdot 79 \) $S_6$ (as 6T16) trivial
6.4.3359232.1 x6 - 12x2 + 8 \( -\,2^{9}\cdot 3^{8} \) $A_4\times C_2$ (as 6T6) trivial
6.2.3419648.1 x6 + 4x4 - 2x3 + x2 - 2x - 5 \( 2^{9}\cdot 6679 \) $S_6$ (as 6T16) trivial
6.2.3681792.1 x6 - 2x5 + 3x4 + 2x3 - 6x2 + 8x - 3 \( 2^{9}\cdot 3^{2}\cdot 17\cdot 47 \) $S_6$ (as 6T16) trivial
6.2.3689984.1 x6 - 2x4 - 2x3 - 5x2 - 2x - 1 \( 2^{9}\cdot 7207 \) $S_6$ (as 6T16) trivial
6.2.3689984.3 x6 - 2x5 + 3x4 - 6x3 - 8x + 21 \( 2^{9}\cdot 7207 \) $S_6$ (as 6T16) trivial
6.4.3699200.1 x6 - 2x5 - x4 + 10x3 - 14x2 + 4x + 1 \( -\,2^{9}\cdot 5^{2}\cdot 17^{2} \) $S_6$ (as 6T16) trivial
6.0.3719680.1 x6 + 6x4 - 2x3 + 9x2 - 2x + 3 \( -\,2^{9}\cdot 5\cdot 1453 \) $S_6$ (as 6T16) trivial
6.2.3796480.1 x6 - 2x5 + x4 - 2x3 + 8x2 - 1 \( 2^{9}\cdot 5\cdot 1483 \) $S_6$ (as 6T16) trivial
6.0.3813888.1 x6 - 2x5 + 7x4 - 10x3 + 2x2 + 3 \( -\,2^{9}\cdot 3\cdot 13\cdot 191 \) $S_6$ (as 6T16) trivial
6.0.3875328.2 x6 - 2x4 + 8x2 + 8 \( -\,2^{9}\cdot 3^{2}\cdot 29^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.3943936.1 x6 - 4x4 - 10x3 - 9x2 - 2x - 1 \( 2^{9}\cdot 7703 \) $S_6$ (as 6T16) trivial
6.2.4279808.1 x6 - 2x5 + x4 - 6x3 - 2x2 - 4x - 1 \( 2^{9}\cdot 13\cdot 643 \) $S_6$ (as 6T16) trivial
6.2.4288000.1 x6 - 2x5 - 5x4 + 6x3 + 10x2 - 5 \( 2^{9}\cdot 5^{3}\cdot 67 \) $S_6$ (as 6T16) trivial
6.4.4309504.1 x6 - 2x5 + x4 + 2x3 - 10x2 + 8x + 1 \( -\,2^{9}\cdot 19\cdot 443 \) $S_6$ (as 6T16) trivial
6.0.4350464.1 x6 - 2x5 + 3x4 - 2x3 + 2x2 - 4x + 3 \( -\,2^{9}\cdot 29\cdot 293 \) $S_6$ (as 6T16) trivial
6.0.4350464.2 x6 - 2x5 + 5x4 - 6x3 + 14x2 - 16x + 15 \( -\,2^{9}\cdot 29\cdot 293 \) $S_6$ (as 6T16) trivial
6.2.4382208.1 x6 + 4x4 - 2x3 + 3x2 - 2x - 3 \( 2^{9}\cdot 3^{3}\cdot 317 \) $S_6$ (as 6T16) trivial
6.0.4428288.2 x6 - 2x4 - 24x2 + 72 \( -\,2^{9}\cdot 3^{2}\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
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