Note: Search results may be incomplete due to uncomputed quantities: local_algs (140954 objects)

## Results (1-50 of at least 1000)

Label Polynomial Discriminant Galois group Class group
6.0.16807.1 x6 - x5 + x4 - x3 + x2 - x + 1 $-\,7^{5}$ $C_6$ (as 6T1) trivial
6.6.453789.1 x6 - x5 - 6x4 + 6x3 + 8x2 - 8x + 1 $3^{3}\cdot 7^{5}$ $C_6$ (as 6T1) trivial
6.4.487403.1 x6 - 2x5 - 3x4 + 6x3 - 5x2 + 3x + 1 $-\,7^{5}\cdot 29$ $A_4\times C_2$ (as 6T6) trivial
6.4.1075648.1 x6 - 7x2 + 7 $-\,2^{6}\cdot 7^{5}$ $A_4\times C_2$ (as 6T6) trivial
6.2.1394981.1 x6 - 2x5 + 4x4 - x3 + 2x2 - 4x - 13 $7^{5}\cdot 83$ $A_4\times C_2$ (as 6T6) trivial
6.4.1899191.1 x6 - x5 - 6x4 - x3 - 6x2 - 8x + 8 $-\,7^{5}\cdot 113$ $A_4\times C_2$ (as 6T6) trivial
6.2.2336173.1 x6 - x5 + x4 - 8x3 - 6x2 - 15x - 13 $7^{5}\cdot 139$ $A_4\times C_2$ (as 6T6) trivial
6.6.2806769.1 x6 - 3x5 - 5x4 + 15x3 + 11x2 - 19x - 13 $7^{5}\cdot 167$ $A_4\times C_2$ (as 6T6) trivial
6.4.2840383.1 x6 - 2x5 - 3x4 - x3 + 2x2 + 24x + 8 $-\,7^{5}\cdot 13^{2}$ $A_4\times C_2$ (as 6T6) trivial
6.4.3310979.1 x6 - 2x5 - 3x4 + 13x3 - 12x2 - 25x + 29 $-\,7^{5}\cdot 197$ $A_4\times C_2$ (as 6T6) trivial
6.2.3747961.1 x6 - x5 + x4 + 13x3 - 27x2 + 27x - 27 $7^{5}\cdot 223$ $A_4\times C_2$ (as 6T6) trivial
6.6.4218557.1 x6 - 2x5 - 10x4 + 20x3 + 16x2 - 25x - 13 $7^{5}\cdot 251$ $A_4\times C_2$ (as 6T6) trivial
6.4.4722767.1 x6 - x5 + x4 + 13x3 - 27x2 - 15x + 29 $-\,7^{5}\cdot 281$ $A_4\times C_2$ (as 6T6) trivial
6.0.4974872.1 x6 - 2x5 - 3x4 + 6x3 + 2x2 - 4x + 8 $-\,2^{3}\cdot 7^{5}\cdot 37$ $C_3^2:D_4$ (as 6T13) $[3]$
6.2.5159749.1 x6 - 3x5 + 2x4 + x3 - 31x2 + 30x - 41 $7^{5}\cdot 307$ $A_4\times C_2$ (as 6T6) trivial
6.4.5663959.1 x6 - x5 - 6x4 + 13x3 - 6x2 - 36x + 43 $-\,7^{5}\cdot 337$ $A_4\times C_2$ (as 6T6) trivial
6.0.5916064.1 x6 - x5 + 8x4 - 8x3 + 15x2 - 15x + 8 $-\,2^{5}\cdot 7^{5}\cdot 11$ $C_3^2:D_4$ (as 6T13) $[3]$
6.2.7042133.1 x6 - x5 + 8x4 + 6x3 + x2 + 55x - 41 $7^{5}\cdot 419$ $A_4\times C_2$ (as 6T6) trivial
6.4.7075747.1 x6 - x5 - 6x4 - 8x3 + x2 + 41x + 43 $-\,7^{5}\cdot 421$ $A_4\times C_2$ (as 6T6) trivial
6.4.7546343.1 x6 - 2x5 - 3x4 + 6x3 - 26x2 + 24x + 29 $-\,7^{5}\cdot 449$ $A_4\times C_2$ (as 6T6) trivial
6.2.8453921.1 x6 - 2x5 + 4x4 - 15x3 - 12x2 - 39x - 41 $7^{5}\cdot 503$ $A_4\times C_2$ (as 6T6) trivial
6.4.8605184.1 x6 - 28x2 + 56 $-\,2^{9}\cdot 7^{5}$ $A_4\times C_2$ (as 6T6) trivial
6.0.8605184.1 x6 + 14x4 + 56x2 + 56 $-\,2^{9}\cdot 7^{5}$ $C_6$ (as 6T1) $[4]$
6.4.8958131.1 x6 - x5 - 6x4 + 6x3 - 20x2 + 6x + 43 $-\,7^{5}\cdot 13\cdot 41$ $A_4\times C_2$ (as 6T6) trivial
6.0.8958131.1 x6 - 3x5 + 16x4 - 27x3 + 67x2 - 54x + 71 $-\,7^{5}\cdot 13\cdot 41$ $A_4\times C_2$ (as 6T6) $[2, 2]$
6.4.8958131.2 x6 - 2x5 - 3x4 + 20x3 - 33x2 - 25x + 71 $-\,7^{5}\cdot 13\cdot 41$ $A_4\times C_2$ (as 6T6) trivial
6.2.9395113.1 x6 - x5 + x4 - x3 - 13x2 - x - 83 $7^{5}\cdot 13\cdot 43$ $A_4\times C_2$ (as 6T6) $[2]$
6.6.9395113.1 x6 - x5 - 13x4 + 13x3 + 43x2 - 29x - 41 $7^{5}\cdot 13\cdot 43$ $A_4\times C_2$ (as 6T6) trivial
6.2.9395113.2 x6 - x5 + 8x4 - 15x3 + 8x2 - 64x - 41 $7^{5}\cdot 13\cdot 43$ $A_4\times C_2$ (as 6T6) $[2]$
6.2.9865709.1 x6 - 2x5 + 4x4 + 6x3 - 40x2 + 87x - 97 $7^{5}\cdot 587$ $A_4\times C_2$ (as 6T6) trivial
6.4.10369919.1 x6 - 3x5 - 5x4 + 15x3 - 24x2 + 16x + 64 $-\,7^{5}\cdot 617$ $A_4\times C_2$ (as 6T6) trivial
6.0.10504375.1 x6 - x5 + x4 + 6x3 + 8x2 - 29x + 22 $-\,5^{4}\cdot 7^{5}$ $S_3\times C_3$ (as 6T5) $[3]$
6.2.10806901.1 x6 - 2x5 + 11x4 - 29x3 + 30x2 - 81x - 27 $7^{5}\cdot 643$ $A_4\times C_2$ (as 6T6) trivial
6.4.11311111.1 x6 - 2x5 + 4x4 - 22x3 - 19x2 + 66x + 43 $-\,7^{5}\cdot 673$ $A_4\times C_2$ (as 6T6) trivial
6.0.11781707.1 x6 - x5 + 15x4 - 22x3 + 78x2 - 71x + 113 $-\,7^{5}\cdot 701$ $A_4\times C_2$ (as 6T6) $[4]$
6.2.12218689.1 x6 - x5 + 8x4 - 15x3 + 8x2 + 20x - 104 $7^{5}\cdot 727$ $A_4\times C_2$ (as 6T6) trivial
6.0.12252303.1 x6 + 7 $-\,3^{6}\cdot 7^{5}$ $D_{6}$ (as 6T3) $[3]$
6.4.12722899.1 x6 - x5 - 13x4 + 20x3 + 22x2 - 99x + 113 $-\,7^{5}\cdot 757$ $A_4\times C_2$ (as 6T6) trivial
6.0.12975004.2 x6 - x5 + x4 - 8x3 + 8x2 + 20x + 8 $-\,2^{2}\cdot 7^{5}\cdot 193$ $C_3^2:D_4$ (as 6T13) $[3]$
6.2.13159881.1 x6 - 2x5 + 11x4 - 15x3 + 30x2 - 4x - 104 $3^{3}\cdot 7^{5}\cdot 29$ $A_4\times C_2$ (as 6T6) $[2]$
6.2.13630477.1 x6 - 3x5 + 16x4 - 27x3 + 39x2 - 26x - 83 $7^{5}\cdot 811$ $A_4\times C_2$ (as 6T6) trivial
6.6.13983424.1 x6 - 14x4 + 63x2 - 91 $2^{6}\cdot 7^{5}\cdot 13$ $A_4\times C_2$ (as 6T6) trivial
6.2.13983424.1 x6 - 49x2 - 91 $2^{6}\cdot 7^{5}\cdot 13$ $A_4\times C_2$ (as 6T6) $[2]$
6.2.13983424.2 x6 + 7x4 - 21x2 - 91 $2^{6}\cdot 7^{5}\cdot 13$ $A_4\times C_2$ (as 6T6) $[2]$
6.2.13983424.3 x6 + 7x4 - 14x2 - 91 $2^{6}\cdot 7^{5}\cdot 13$ $A_4\times C_2$ (as 6T6) $[2]$
6.2.14101073.1 x6 - 2x5 + 11x4 - x3 + 2x2 + 80x - 104 $7^{5}\cdot 839$ $A_4\times C_2$ (as 6T6) trivial
6.4.14134687.1 x6 - x5 - 6x4 - x3 - 34x2 - 22x + 71 $-\,7^{5}\cdot 29^{2}$ $A_4\times C_2$ (as 6T6) trivial
6.0.14605283.1 x6 + 7x4 + 14x2 - 7x + 7 $-\,7^{5}\cdot 11\cdot 79$ $C_3^2:D_4$ (as 6T13) $[3]$
6.6.15512861.1 x6 - 3x5 - 12x4 + 29x3 + 53x2 - 68x - 83 $7^{5}\cdot 13\cdot 71$ $A_4\times C_2$ (as 6T6) trivial
6.2.15512861.1 x6 - 2x5 + 4x4 + 6x3 - 40x2 - 25x - 125 $7^{5}\cdot 13\cdot 71$ $A_4\times C_2$ (as 6T6) $[2]$