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Label Polynomial Discriminant Galois group Class group
6.6.300125.1 x6 - x5 - 7x4 + 2x3 + 7x2 - 2x - 1 \( 5^{3}\cdot 7^{4} \) $C_6$ (as 6T1) trivial
6.6.371293.1 x6 - x5 - 5x4 + 4x3 + 6x2 - 3x - 1 \( 13^{5} \) $C_6$ (as 6T1) trivial
6.6.434581.1 x6 - 2x5 - 4x4 + 5x3 + 4x2 - 2x - 1 \( 7^{4}\cdot 181 \) $A_4\times C_2$ (as 6T6) trivial
6.6.453789.1 x6 - x5 - 6x4 + 6x3 + 8x2 - 8x + 1 \( 3^{3}\cdot 7^{5} \) $C_6$ (as 6T1) trivial
6.6.485125.1 x6 - 2x5 - 4x4 + 8x3 + 2x2 - 5x + 1 \( 5^{3}\cdot 3881 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.592661.1 x6 - x5 - 5x4 + 4x3 + 5x2 - 2x - 1 \( 592661 \) $S_6$ (as 6T16) trivial
6.6.703493.1 x6 - 2x5 - 5x4 + 11x3 + 2x2 - 9x + 1 \( 7^{4}\cdot 293 \) $A_4\times C_2$ (as 6T6) trivial
6.6.722000.1 x6 - x5 - 6x4 + 7x3 + 4x2 - 5x + 1 \( 2^{4}\cdot 5^{3}\cdot 19^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.6.810448.1 x6 - 3x5 - 2x4 + 9x3 - 5x + 1 \( 2^{4}\cdot 37^{3} \) $S_3$ (as 6T2) trivial
6.6.820125.1 x6 - 9x4 - 4x3 + 9x2 + 3x - 1 \( 3^{8}\cdot 5^{3} \) $C_6$ (as 6T1) trivial
6.6.905177.1 x6 - x5 - 7x4 + 9x3 + 7x2 - 9x - 1 \( 7^{4}\cdot 13\cdot 29 \) $A_4\times C_2$ (as 6T6) trivial
6.6.966125.1 x6 - x5 - 6x4 + 4x3 + 8x2 - 1 \( 5^{3}\cdot 59\cdot 131 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.980125.1 x6 - x5 - 6x4 + 6x3 + 7x2 - 5x - 1 \( 5^{3}\cdot 7841 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1075648.1 x6 - 7x4 + 14x2 - 7 \( 2^{6}\cdot 7^{5} \) $C_6$ (as 6T1) trivial
6.6.1081856.1 x6 - 6x4 - 2x3 + 7x2 + 2x - 1 \( 2^{9}\cdot 2113 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1134389.1 x6 - 2x5 - 4x4 + 6x3 + 4x2 - 3x - 1 \( 1134389 \) $S_6$ (as 6T16) trivial
6.6.1202933.1 x6 - 6x4 - 2x3 + 6x2 + x - 1 \( 79\cdot 15227 \) $S_6$ (as 6T16) trivial
6.6.1229312.1 x6 - 10x4 + 24x2 - 8 \( 2^{9}\cdot 7^{4} \) $C_6$ (as 6T1) trivial
6.6.1241125.1 x6 - 7x4 - 2x3 + 11x2 + 7x + 1 \( 5^{3}\cdot 9929 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1259712.1 x6 - 6x4 + 9x2 - 3 \( 2^{6}\cdot 3^{9} \) $C_6$ (as 6T1) trivial
6.6.1279733.1 x6 - 2x5 - 6x4 + 10x3 + 10x2 - 11x - 1 \( 7^{4}\cdot 13\cdot 41 \) $A_4\times C_2$ (as 6T6) trivial
6.6.1292517.1 x6 - 6x4 - x3 + 6x2 - 1 \( 3^{8}\cdot 197 \) $A_4\times C_2$ (as 6T6) trivial
6.6.1312625.1 x6 - x5 - 7x4 + 7x3 + 12x2 - 12x - 1 \( 5^{3}\cdot 10501 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1387029.1 x6 - 3x5 - 2x4 + 9x3 - x2 - 4x + 1 \( 3\cdot 7\cdot 257^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.6.1397493.1 x6 - 3x5 - 3x4 + 10x3 + 3x2 - 6x + 1 \( 3^{9}\cdot 71 \) $A_4\times C_2$ (as 6T6) trivial
6.6.1416125.1 x6 - 2x5 - 5x4 + 9x3 + 6x2 - 9x + 1 \( 5^{3}\cdot 11329 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1528713.1 x6 - 3x5 - 3x4 + 7x3 + 3x2 - 3x - 1 \( 3^{8}\cdot 233 \) $A_4\times C_2$ (as 6T6) trivial
6.6.1541581.1 x6 - x5 - 6x4 + 2x3 + 9x2 + x - 1 \( 1541581 \) $S_6$ (as 6T16) trivial
6.6.1683101.1 x6 - 3x5 - 4x4 + 13x3 + 7x2 - 14x - 7 \( 7^{4}\cdot 701 \) $A_4\times C_2$ (as 6T6) trivial
6.6.1767625.1 x6 - 7x4 - x3 + 11x2 + x - 1 \( 5^{3}\cdot 79\cdot 179 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1868969.1 x6 - 6x4 - x3 + 8x2 + x - 2 \( 107\cdot 17467 \) $S_6$ (as 6T16) trivial
6.6.1922000.1 x6 - x5 - 8x4 - x3 + 12x2 + 7x + 1 \( 2^{4}\cdot 5^{3}\cdot 31^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.6.1995125.1 x6 - 2x5 - 6x4 + 6x3 + 12x2 + x - 1 \( 5^{3}\cdot 11\cdot 1451 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.1997632.1 x6 - 8x4 + 19x2 - 13 \( 2^{6}\cdot 7^{4}\cdot 13 \) $A_4\times C_2$ (as 6T6) trivial
6.6.2115281.1 x6 - x5 - 8x4 + 5x3 + 16x2 - 4x - 8 \( 7^{4}\cdot 881 \) $A_4\times C_2$ (as 6T6) trivial
6.6.2235125.1 x6 - x5 - 7x4 + 2x3 + 12x2 + 3x - 1 \( 5^{3}\cdot 17881 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.2249737.1 x6 - 2x5 - 7x4 + 9x3 + 14x2 - 8x - 8 \( 7^{4}\cdot 937 \) $A_4\times C_2$ (as 6T6) trivial
6.6.2286997.1 x6 - 7x4 + 13x2 - x - 5 \( 349\cdot 6553 \) $S_6$ (as 6T16) trivial
6.6.2323397.1 x6 - 6x4 + 8x2 - x - 1 \( 2323397 \) $S_6$ (as 6T16) trivial
6.6.2415125.1 x6 - x5 - 8x4 + 5x3 + 19x2 - 4x - 11 \( 5^{3}\cdot 139^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.6.2460365.1 x6 - x5 - 6x4 + 6x3 + 7x2 - 7x + 1 \( 5\cdot 263\cdot 1871 \) $S_6$ (as 6T16) trivial
6.6.2495261.1 x6 - x5 - 6x4 + 6x3 + 6x2 - 6x + 1 \( 199\cdot 12539 \) $S_6$ (as 6T16) trivial
6.6.2501557.1 x6 - x5 - 6x4 + 3x3 + 9x2 - 2x - 3 \( 769\cdot 3253 \) $S_6$ (as 6T16) trivial
6.6.2540864.1 x6 - 8x4 - 4x3 + 12x2 + 10x + 2 \( 2^{6}\cdot 29\cdot 37^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.6.2565429.1 x6 - 6x4 - x3 + 8x2 + 2x - 1 \( 3\cdot 855143 \) $S_6$ (as 6T16) trivial
6.6.2591125.1 x6 - x5 - 7x4 + 6x3 + 10x2 - 9x + 1 \( 5^{3}\cdot 19\cdot 1091 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.2623625.1 x6 - x5 - 7x4 + 5x3 + 13x2 - 6x - 4 \( 5^{3}\cdot 139\cdot 151 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.2624293.1 x6 - x5 - 9x4 + 8x3 + 21x2 - 14x - 7 \( 7^{4}\cdot 1093 \) $A_4\times C_2$ (as 6T6) trivial
6.6.2661761.1 x6 - x5 - 6x4 + 3x3 + 9x2 - x - 1 \( 41\cdot 64921 \) $S_6$ (as 6T16) trivial
6.6.2666432.1 x6 - 2x5 - 6x4 + 4x3 + 7x2 - 2x - 1 \( 2^{6}\cdot 61\cdot 683 \) $S_6$ (as 6T16) trivial
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