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Label Polynomial Discriminant Galois group Class group
6.2.236032.1 x6 - 2x5 + 3x4 - 2x3 + 2x2 - 1 \( 2^{9}\cdot 461 \) $S_6$ (as 6T16) trivial
6.0.243200.1 x6 + 4x4 - 2x3 + 5x2 - 2x + 1 \( -\,2^{9}\cdot 5^{2}\cdot 19 \) $S_6$ (as 6T16) trivial
6.2.363008.1 x6 - 2x4 - 2x3 + 3x2 + 2x - 1 \( 2^{9}\cdot 709 \) $S_6$ (as 6T16) trivial
6.2.477696.1 x6 - 2x5 - x4 + 2x3 + 2x2 - 3 \( 2^{9}\cdot 3\cdot 311 \) $S_6$ (as 6T16) trivial
6.2.866816.1 x6 - 6x3 + 3x2 - 2x + 1 \( 2^{9}\cdot 1693 \) $S_6$ (as 6T16) trivial
6.2.973312.2 x6 - 4x4 - 2x3 + 5x2 + 2x - 3 \( 2^{9}\cdot 1901 \) $S_6$ (as 6T16) trivial
6.2.1227264.1 x6 - 2x5 - 3x4 + 6x3 + 4x2 - 4x - 5 \( 2^{9}\cdot 3\cdot 17\cdot 47 \) $S_6$ (as 6T16) trivial
6.2.1354240.1 x6 + 2x4 - 16x2 - 40 \( 2^{9}\cdot 5\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.1354240.2 x6 - 8x4 + 28x2 - 40 \( 2^{9}\cdot 5\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.1476096.1 x6 - 4x4 - 4x2 + 24 \( -\,2^{9}\cdot 3\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.1476096.2 x6 + 6x4 + 16x2 + 24 \( -\,2^{9}\cdot 3\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.1690112.1 x6 - 2x5 + x4 - 2x3 + 10x2 - 8x + 1 \( 2^{9}\cdot 3301 \) $S_6$ (as 6T16) trivial
6.2.1755648.2 x6 - 2x5 + x4 - 6x3 + 4x2 - 8x + 5 \( 2^{9}\cdot 3^{3}\cdot 127 \) $S_6$ (as 6T16) trivial
6.0.1848832.1 x6 + 6x4 - 6x3 + 9x2 - 2x + 1 \( -\,2^{9}\cdot 23\cdot 157 \) $S_6$ (as 6T16) trivial
6.2.1907200.1 x6 - 2x5 - x4 + 2x3 + 4x2 - 8x + 5 \( 2^{9}\cdot 5^{2}\cdot 149 \) $S_6$ (as 6T16) trivial
6.2.1923584.1 x6 - 2x5 - 3x4 + 6x3 + 4x2 - 8x + 1 \( 2^{9}\cdot 13\cdot 17^{2} \) $S_6$ (as 6T16) trivial
6.4.2000384.1 x6 - 4x4 - 2x3 + x2 + 2x + 3 \( -\,2^{9}\cdot 3907 \) $S_6$ (as 6T16) trivial
6.0.2049536.1 x6 - 2x5 + 5x4 - 6x3 + 10x2 - 8x + 7 \( -\,2^{9}\cdot 4003 \) $S_6$ (as 6T16) trivial
6.2.2087424.3 x6 - 2x5 - x4 - 6x3 - 2x2 - 4x - 1 \( 2^{9}\cdot 3^{3}\cdot 151 \) $S_6$ (as 6T16) trivial
6.2.2423296.1 x6 - 2x5 + 3x4 - 2x3 - 2x2 + 4x - 3 \( 2^{9}\cdot 4733 \) $S_6$ (as 6T16) trivial
6.2.2484736.1 x6 - 2x4 - 2x3 + 3x2 + 2x - 3 \( 2^{9}\cdot 23\cdot 211 \) $S_6$ (as 6T16) trivial
6.2.2501120.1 x6 - 2x5 + 3x4 + 2x3 - 4x2 + 8x - 3 \( 2^{9}\cdot 5\cdot 977 \) $S_6$ (as 6T16) trivial
6.2.2529792.1 x6 - 4x4 - 2x3 + 3x2 + 6x + 3 \( 2^{9}\cdot 3^{4}\cdot 61 \) $S_6$ (as 6T16) trivial
6.2.2554368.1 x6 - 2x5 + 3x4 - 10x3 + 12x2 - 8x + 1 \( 2^{9}\cdot 3\cdot 1663 \) $S_6$ (as 6T16) trivial
6.0.2848256.1 x6 - 2x3 - x2 - 2x + 5 \( -\,2^{9}\cdot 5563 \) $S_6$ (as 6T16) trivial
6.0.2979328.1 x6 + 8x4 + 28x2 + 88 \( -\,2^{9}\cdot 11\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.2979328.2 x6 + 8x4 + 36x2 + 88 \( -\,2^{9}\cdot 11\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.2980352.1 x6 - 4x4 - 6x3 + x2 - 2x - 1 \( 2^{9}\cdot 5821 \) $S_6$ (as 6T16) trivial
6.4.3233280.1 x6 - 2x5 - 3x4 + 6x3 - 6x2 + 4x + 1 \( -\,2^{9}\cdot 3\cdot 5\cdot 421 \) $S_6$ (as 6T16) trivial
6.4.3245568.1 x6 - 4x4 - 2x3 - 3x2 - 2x + 1 \( -\,2^{9}\cdot 3\cdot 2113 \) $S_6$ (as 6T16) trivial
6.0.3307008.1 x6 + 4x4 - 2x3 + x2 - 6x + 11 \( -\,2^{9}\cdot 3\cdot 2153 \) $S_6$ (as 6T16) trivial
6.2.3566080.1 x6 - 2x5 + 3x4 - 6x3 + 2x2 - 4x + 5 \( 2^{9}\cdot 5\cdot 7\cdot 199 \) $S_6$ (as 6T16) trivial
6.2.3725824.1 x6 - 2x4 - 2x3 + 5x2 - 2x - 1 \( 2^{9}\cdot 19\cdot 383 \) $S_6$ (as 6T16) trivial
6.4.3728896.1 x6 - 2x5 - 3x4 + 2x3 + 10x2 - 9 \( -\,2^{9}\cdot 7283 \) $S_6$ (as 6T16) trivial
6.4.3757568.1 x6 - 2x5 - x4 + 2x3 - 2x2 + 4x - 1 \( -\,2^{9}\cdot 41\cdot 179 \) $S_6$ (as 6T16) trivial
6.0.3831296.1 x6 - 2x4 - 2x3 + 3x2 - 2x + 5 \( -\,2^{9}\cdot 7\cdot 1069 \) $S_6$ (as 6T16) trivial
6.0.3986944.1 x6 - 2x3 + 3x2 + 2x + 1 \( -\,2^{9}\cdot 13\cdot 599 \) $S_6$ (as 6T16) trivial
6.4.4150784.1 x6 - 6x4 - 2x3 + 5x2 + 2x - 1 \( -\,2^{9}\cdot 11^{2}\cdot 67 \) $S_6$ (as 6T16) trivial
6.2.4196864.1 x6 - 2x5 - 3x4 + 6x3 + 6x2 - 1 \( 2^{9}\cdot 7\cdot 1171 \) $S_6$ (as 6T16) trivial
6.2.4422144.1 x6 - 2x5 + x4 - 2x3 - 4x2 + 3 \( 2^{9}\cdot 3\cdot 2879 \) $S_6$ (as 6T16) trivial
6.2.4487680.1 x6 - 2x5 + x4 + 6x3 - 14x2 + 20x - 5 \( 2^{9}\cdot 5\cdot 1753 \) $S_6$ (as 6T16) trivial
6.2.4524544.1 x6 - 2x5 - 5x4 + 10x3 + 1 \( 2^{9}\cdot 8837 \) $S_6$ (as 6T16) trivial
6.2.4651520.1 x6 - 2x5 - x4 + 4x3 - 13x2 - 10x - 3 \( 2^{9}\cdot 5\cdot 23\cdot 79 \) $S_6$ (as 6T16) trivial
6.2.4655616.1 x6 - 2x5 + 5x4 - 2x3 - 2x2 + 8x - 9 \( 2^{9}\cdot 3\cdot 7\cdot 433 \) $S_6$ (as 6T16) trivial
6.0.4769280.1 x6 - 2x5 - x4 - 2x3 + 8x2 + 16x + 7 \( -\,2^{9}\cdot 3^{4}\cdot 5\cdot 23 \) $S_6$ (as 6T16) trivial
6.0.4834816.1 x6 - 2x5 - 3x4 + 2x3 + 8x2 + 1 \( -\,2^{9}\cdot 7\cdot 19\cdot 71 \) $S_6$ (as 6T16) trivial
6.2.4844032.1 x6 - 2x5 + 3x4 - 6x3 + 4x2 - 4x + 5 \( 2^{9}\cdot 9461 \) $S_6$ (as 6T16) trivial
6.2.4913664.1 x6 + 2x4 - 10x3 - 5x2 + 6x + 3 \( 2^{9}\cdot 3\cdot 7\cdot 457 \) $S_6$ (as 6T16) trivial
6.2.5040640.1 x6 - 2x5 + x4 + 6x3 - 8x2 + 11 \( 2^{9}\cdot 5\cdot 11\cdot 179 \) $S_6$ (as 6T16) trivial
6.0.5146112.2 x6 + 10x4 + 60x2 + 152 \( -\,2^{9}\cdot 19\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) $[2]$
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