## Results (displaying matches 1-50 of 24493) Next

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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