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Label Polynomial Discriminant Galois group Class group
6.0.10051.1 x6 - x5 + 2x4 - 2x3 + 2x2 - 2x + 1 \( -\,19\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.10571.1 x6 - x5 - x4 + 2x3 - x + 1 \( -\,11\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.0.18515.1 x6 + 2x4 - x3 + 2x2 + 1 \( -\,5\cdot 7\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.22747.1 x6 - x5 - 2x3 + x2 + x + 1 \( -\,23^{2}\cdot 43 \) $S_4\times C_2$ Trivial
6.0.27556.1 x6 - x5 + 2x3 - x + 1 \( -\,2^{2}\cdot 83^{2} \) $S_4\times C_2$ Trivial
6.0.27848.1 x6 - x5 + 2x4 + 2x2 - x + 1 \( -\,2^{3}\cdot 59^{2} \) $S_4\times C_2$ Trivial
6.2.28037.1 x6 - 2x5 + 3x3 - 2x - 1 \( 23^{2}\cdot 53 \) $S_4\times C_2$ Trivial
6.0.29095.1 x6 - x5 + 3x4 - x3 + 3x2 - x + 1 \( -\,5\cdot 11\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.31211.1 x6 - x4 - x3 + 2x2 + 3x + 1 \( -\,23^{2}\cdot 59 \) $S_4\times C_2$ Trivial
6.2.32269.1 x6 - 3x5 + 4x4 - 3x3 + x2 - 1 \( 23^{2}\cdot 61 \) $S_4\times C_2$ Trivial
6.0.33856.1 x6 - x4 + 1 \( -\,2^{6}\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.2.35557.1 x6 - 2x4 - x3 + 2x2 - 1 \( 31^{2}\cdot 37 \) $S_4\times C_2$ Trivial
6.0.37479.1 x6 - x5 + 3x4 - 3x3 + 3x2 - x + 1 \( -\,3\cdot 13\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.2.40733.1 x6 - 2x5 + 3x4 - 2x3 - 3x2 + 3x - 1 \( 7\cdot 11\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.41791.1 x6 - 3x5 + 3x4 - x3 - x2 + x + 1 \( -\,23^{2}\cdot 79 \) $S_4\times C_2$ Trivial
6.2.44965.1 x6 - 2x4 - 3x - 1 \( 5\cdot 17\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.45167.1 x6 - x5 + x4 - x3 + 3x2 - 3x + 1 \( -\,31^{2}\cdot 47 \) $S_4\times C_2$ Trivial
6.2.47081.1 x6 - x5 - 3x4 + 3x3 + 3x2 - x - 1 \( 23^{2}\cdot 89 \) $S_4\times C_2$ Trivial
6.0.49011.1 x6 - 2x5 + 4x4 - 3x3 + 4x2 - 2x + 1 \( -\,3\cdot 17\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.2.50933.1 x6 - 2x5 - x4 + 4x3 - 3x2 + 3x - 1 \( 31^{2}\cdot 53 \) $S_4\times C_2$ Trivial
6.2.53429.1 x6 - 3x5 + 2x4 + x3 + x2 - 2x - 1 \( 23^{2}\cdot 101 \) $S_4\times C_2$ Trivial
6.0.54208.1 x6 - 2x5 + 3x4 - 2x3 + 3x2 - 2x + 1 \( -\,2^{6}\cdot 7\cdot 11^{2} \) $S_4\times C_2$ Trivial
6.0.55696.1 x6 + 2x2 + 1 \( -\,2^{4}\cdot 59^{2} \) $S_4\times C_2$ Trivial
6.2.56144.1 x6 - x5 - 2x4 + 3x3 - 3x + 1 \( 2^{4}\cdot 11^{2}\cdot 29 \) $S_4\times C_2$ Trivial
6.0.56603.1 x6 - 2x5 + 3x4 + x2 + 3x + 1 \( -\,23^{2}\cdot 107 \) $S_4\times C_2$ Trivial
6.2.57661.1 x6 - x5 + 4x3 - 3x2 + x - 1 \( 23^{2}\cdot 109 \) $S_4\times C_2$ Trivial
6.2.59177.1 x6 - x4 - x3 + x2 - 1 \( 17\cdot 59^{2} \) $S_4\times C_2$ Trivial
6.0.60835.1 x6 - x5 + 4x4 + 3x2 + 3x + 1 \( -\,5\cdot 23^{3} \) $S_4\times C_2$ Trivial
6.0.61504.1 x6 + x2 + 1 \( -\,2^{6}\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.0.62951.1 x6 - x5 + 2x4 - x3 + 4x2 + 2x + 1 \( -\,7\cdot 17\cdot 23^{2} \) $S_4\times C_2$ Trivial
6.0.64387.1 x6 - 2x5 - 2x3 + 4x2 + x + 1 \( -\,31^{2}\cdot 67 \) $S_4\times C_2$ Trivial
6.0.64387.2 x6 - 3x5 + 4x4 - 3x3 + x2 + 1 \( -\,31^{2}\cdot 67 \) $S_4\times C_2$ Trivial
6.0.64387.3 x6 - 2x5 + 4x4 - 6x3 + 6x2 - 5x + 3 \( -\,31^{2}\cdot 67 \) $S_4\times C_2$ Trivial
6.2.66309.1 x6 + x4 - x3 - 2x2 + 3x - 1 \( 3\cdot 23\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.0.69312.1 x6 + x4 - 2x3 + x2 + 1 \( -\,2^{6}\cdot 3\cdot 19^{2} \) $S_4\times C_2$ Trivial
6.2.70153.1 x6 - 3x5 + 5x4 - 5x3 + 3x2 - x - 1 \( 31^{2}\cdot 73 \) $S_4\times C_2$ Trivial
6.2.72473.1 x6 - 2x5 - 2x3 + 5x2 - 2x - 1 \( 23^{2}\cdot 137 \) $S_4\times C_2$ Trivial
6.2.75088.1 x6 - x5 + x3 - x - 1 \( 2^{4}\cdot 13\cdot 19^{2} \) $S_4\times C_2$ Trivial
6.2.78821.1 x6 - x5 + 2x4 - 4x2 - 2x - 1 \( 23^{2}\cdot 149 \) $S_4\times C_2$ Trivial
6.0.79763.1 x6 - x5 - 2x4 + 4x3 - 4x + 3 \( -\,31^{2}\cdot 83 \) $S_4\times C_2$ Trivial
6.0.80143.1 x6 - 2x5 + x4 + x3 + x2 - 2x + 1 \( -\,7\cdot 107^{2} \) $S_4\times C_2$ Trivial
6.2.83053.1 x6 - 2x5 - x4 + x3 + 4x2 + x - 5 \( 23^{2}\cdot 157 \) $S_4\times C_2$ Trivial
6.0.83248.1 x6 - x5 + x3 + 2x2 - 3x + 1 \( -\,2^{4}\cdot 11^{2}\cdot 43 \) $S_4\times C_2$ Trivial
6.0.83607.1 x6 - 2x5 + 2x4 - 4x3 + 3x2 + 2x + 1 \( -\,3\cdot 29\cdot 31^{2} \) $S_4\times C_2$ Trivial
6.2.85169.1 x6 - 3x4 - 2x3 + 6x2 - 2x - 1 \( 7\cdot 23^{3} \) $S_4\times C_2$ Trivial
6.0.88343.1 x6 - 2x5 + 4x3 - 3x2 - 4x + 5 \( -\,23^{2}\cdot 167 \) $S_4\times C_2$ Trivial
6.2.89373.1 x6 - x5 - 4x4 + 4x3 + 3x2 - 5x + 1 \( 3\cdot 31^{3} \) $S_4\times C_2$ Trivial
6.0.90992.1 x6 - x5 + x4 + x3 + 2 \( -\,2^{4}\cdot 11^{2}\cdot 47 \) $S_4\times C_2$ Trivial
6.2.91517.1 x6 - 2x5 - x4 + 4x3 - x2 - 5x - 1 \( 23^{2}\cdot 173 \) $S_4\times C_2$ Trivial
6.2.91592.1 x6 - x5 - x - 1 \( 2^{3}\cdot 107^{2} \) $S_4\times C_2$ Trivial

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