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Label Polynomial Discriminant Galois group Class group
6.0.12167.1 x6 - 3x5 + 5x4 - 5x3 + 5x2 - 3x + 1 \( -\,23^{3} \) $S_3$ Trivial
6.0.21296.1 x6 - x5 + 2x4 - 3x3 + 2x2 - x + 1 \( -\,2^{4}\cdot 11^{3} \) $S_3$ Trivial
6.0.29791.1 x6 - 3x5 + 7x4 - 9x3 + 7x2 - 3x + 1 \( -\,31^{3} \) $S_3$ Trivial
6.0.34992.1 x6 - 3x5 + 5x3 - 3x + 1 \( -\,2^{4}\cdot 3^{7} \) $S_3$ Trivial
6.0.109744.2 x6 - 3x5 + 4x4 - 3x3 + 4x2 - 3x + 1 \( -\,2^{4}\cdot 19^{3} \) $S_3$ Trivial
6.0.177147.2 x6 + 3 \( -\,3^{11} \) $S_3$ Trivial
6.0.205379.1 x6 - 3x5 + 10x4 - 15x3 + 21x2 - 14x + 4 \( -\,59^{3} \) $S_3$ Trivial
6.0.214375.1 x6 - 3x5 + x4 + 3x3 + x2 - 3x + 1 \( -\,5^{4}\cdot 7^{3} \) $S_3$ Trivial
6.0.270000.1 x6 - 3x5 + 4x4 - 3x3 - 2x2 + 3x + 3 \( -\,2^{4}\cdot 3^{3}\cdot 5^{4} \) $S_3$ Trivial
6.0.273375.1 x6 - 3x5 + 3x4 - x3 + 3x2 - 3x + 1 \( -\,3^{7}\cdot 5^{3} \) $S_3$ $[2]$
6.0.320000.1 x6 + 4x4 - 3x2 + 2 \( -\,2^{9}\cdot 5^{4} \) $S_3$ Trivial
6.0.419904.2 x6 - 2x3 + 9x2 + 6x + 2 \( -\,2^{6}\cdot 3^{8} \) $S_3$ Trivial
6.0.571787.1 x6 - x4 - 4x3 + 21x2 + 2x + 4 \( -\,83^{3} \) $S_3$ Trivial
6.0.658503.1 x6 - 2x5 + 4x4 - 9x3 + 30x2 - 9x + 9 \( -\,3^{3}\cdot 29^{3} \) $S_3$ $[2]$
6.0.686000.1 x6 - 3x5 + 8x4 - 11x3 + 8x2 - 3x + 1 \( -\,2^{4}\cdot 5^{3}\cdot 7^{3} \) $S_3$ $[2]$
6.6.810448.1 x6 - 3x5 - 2x4 + 9x3 - 5x + 1 \( 2^{4}\cdot 37^{3} \) $S_3$ Trivial
6.0.937024.1 x6 - 7x4 + 20x2 + 4 \( -\,2^{6}\cdot 11^{4} \) $S_3$ Trivial
6.0.1037232.1 x6 - 3x5 + 4x4 - 3x3 - 8x2 + 9x + 27 \( -\,2^{4}\cdot 3^{3}\cdot 7^{4} \) $S_3$ $[3]$
6.0.1119744.1 x6 - 3x2 + 6 \( -\,2^{9}\cdot 3^{7} \) $S_3$ $[2]$
6.0.1124864.1 x6 + 8x4 + 29x2 + 26 \( -\,2^{9}\cdot 13^{3} \) $S_3$ $[2]$
6.0.1225043.1 x6 - 2x5 - 2x3 + 30x2 - 52x + 29 \( -\,107^{3} \) $S_3$ Trivial
6.0.1272112.1 x6 - 3x5 + 10x4 - 15x3 + 10x2 - 3x + 1 \( -\,2^{4}\cdot 43^{3} \) $S_3$ Trivial
6.0.1366875.1 x6 - 3x5 + 6x4 + 3x3 - 9x2 - 18x + 36 \( -\,3^{7}\cdot 5^{4} \) $S_3$ Trivial
6.0.1560896.1 x6 - 2x5 - x4 + 10x3 + 22x2 - 8x + 16 \( -\,2^{6}\cdot 29^{3} \) $S_3$ $[2]$
6.0.1827904.2 x6 - 2x5 + 2x4 - 6x3 + 25x2 - 20x + 8 \( -\,2^{6}\cdot 13^{4} \) $S_3$ $[3]$
6.0.2122416.1 x6 - x5 + 4x4 - 15x3 + 30x2 - 27x + 9 \( -\,2^{4}\cdot 3^{3}\cdot 17^{3} \) $S_3$ $[2]$
6.0.2250423.3 x6 + 6x4 + 9x2 + 7 \( -\,3^{8}\cdot 7^{3} \) $S_3$ Trivial
6.0.2255067.2 x6 + x4 - 11x2 + 12 \( -\,3^{3}\cdot 17^{4} \) $S_3$ Trivial
6.0.2685619.1 x6 + 3x4 - 12x3 + 37x2 - 18x + 36 \( -\,139^{3} \) $S_3$ Trivial
6.0.2834352.1 x6 + 12 \( -\,2^{4}\cdot 3^{11} \) $S_3$ Trivial
6.0.2834352.2 x6 + 48 \( -\,2^{4}\cdot 3^{11} \) $S_3$ Trivial
6.0.3359232.4 x6 - 6x4 + 9x2 + 8 \( -\,2^{9}\cdot 3^{8} \) $S_3$ $[3]$
6.0.3511808.1 x6 - 2x5 + 5x4 + 4x3 + 34x2 + 16x + 16 \( -\,2^{9}\cdot 19^{3} \) $S_3$ $[2]$
6.0.3518667.2 x6 - 3x5 + 4x4 - 3x3 - 5x2 + 6x + 12 \( -\,3^{3}\cdot 19^{4} \) $S_3$ $[3]$
6.0.4804839.1 x6 - 3x5 + 9x4 - 13x3 + 9x2 - 3x + 1 \( -\,3^{7}\cdot 13^{3} \) $S_3$ $[4]$
6.0.4812208.1 x6 - x5 + 8x4 - 23x3 + 34x2 - 27x + 9 \( -\,2^{4}\cdot 67^{3} \) $S_3$ Trivial
6.0.5250987.1 x6 - 3x5 + 6x4 + 7x3 - 15x2 - 24x + 64 \( -\,3^{7}\cdot 7^{4} \) $S_3$ $[3]$
6.0.6324912.1 x6 + x4 - 29x2 + 75 \( -\,2^{4}\cdot 3^{3}\cdot 11^{4} \) $S_3$ Trivial
6.0.7880599.1 x6 - 3x4 - 5x3 + 52x2 - 92x + 56 \( -\,199^{3} \) $S_3$ $[3]$
6.0.8732691.5 x6 - 6x4 + 9x2 + 44 \( -\,3^{8}\cdot 11^{3} \) $S_3$ $[3]$
6.0.9393931.1 x6 - 2x5 + 4x4 - 18x3 + 70x2 - 128x + 109 \( -\,211^{3} \) $S_3$ Trivial
6.0.9528128.1 x6 - 4x4 - 6x3 + 57x2 - 94x + 62 \( -\,2^{6}\cdot 53^{3} \) $S_3$ $[2]$
6.0.10744731.1 x6 - 3x5 + 9x4 - 3x2 + 27x + 33 \( -\,3^{7}\cdot 17^{3} \) $S_3$ $[2]$
6.6.12002256.1 x6 - 3x5 - 6x4 + 17x3 - 6x2 - 3x + 1 \( 2^{4}\cdot 3^{7}\cdot 7^{3} \) $S_3$ Trivial
6.6.12008989.1 x6 - 2x5 - 14x4 + 14x2 - 2x - 1 \( 229^{3} \) $S_3$ Trivial
6.0.12057136.1 x6 - 3x5 + 14x4 - 23x3 + 44x2 - 33x + 9 \( -\,2^{4}\cdot 7^{3}\cdot 13^{3} \) $S_3$ $[2]$
6.0.12326391.1 x6 - 2x5 + 4x4 + 15x3 + 42x2 + 27x + 81 \( -\,3^{3}\cdot 7^{3}\cdot 11^{3} \) $S_3$ $[2, 2]$
6.0.12338352.2 x6 + x4 - 17x2 + 27 \( -\,2^{4}\cdot 3^{3}\cdot 13^{4} \) $S_3$ $[3]$
6.6.13122000.1 x6 - 12x4 + 36x2 - 20 \( 2^{4}\cdot 3^{8}\cdot 5^{3} \) $S_3$ Trivial
6.0.13651919.1 x6 - 2x5 + 8x4 + 11x3 + 54x2 + 63x + 81 \( -\,239^{3} \) $S_3$ $[5]$

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