Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
6.2.28037.1 | $x^{6} - 2 x^{5} + 3 x^{3} - 2 x - 1$ | $23^{2}\cdot 53$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.29077.1 | $x^{6} - x^{5} + x^{4} - x^{2} + 2 x - 1$ | $29077$ | $S_6$ (as 6T16) | trivial |
6.2.29189.1 | $x^{6} - 2 x^{5} + x^{4} + x^{3} - 2 x^{2} + x + 1$ | $17^{2}\cdot 101$ | $S_6$ (as 6T16) | trivial |
6.2.30125.1 | $x^{6} - x^{5} + x^{4} - 2 x^{2} + x - 1$ | $5^{3}\cdot 241$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.31133.1 | $x^{6} - 2 x^{4} - x^{3} + 2 x + 1$ | $163\cdot 191$ | $S_6$ (as 6T16) | trivial |
6.2.31213.1 | $x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ | $7^{4}\cdot 13$ | $A_4\times C_2$ (as 6T6) | trivial |
6.2.31709.1 | $x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + 1$ | $37\cdot 857$ | $S_6$ (as 6T16) | trivial |
6.2.32269.1 | $x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$ | $23^{2}\cdot 61$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.33856.1 | $x^{6} + x^{4} - 1$ | $2^{6}\cdot 23^{2}$ | $S_4$ (as 6T7) | trivial |
6.2.35125.1 | $x^{6} - x^{5} - x^{4} + 2 x^{3} - x^{2} + 1$ | $5^{3}\cdot 281$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.35557.1 | $x^{6} - 2 x^{4} - x^{3} + 2 x^{2} - 1$ | $31^{2}\cdot 37$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.37253.1 | $x^{6} - x^{4} + x^{2} - x - 1$ | $37253$ | $S_6$ (as 6T16) | trivial |
6.2.37568.1 | $x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 2 x - 1$ | $2^{6}\cdot 587$ | $S_6$ (as 6T16) | trivial |
6.2.39269.1 | $x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - 2 x + 1$ | $107\cdot 367$ | $S_6$ (as 6T16) | trivial |
6.2.40277.1 | $x^{6} - x^{5} + 2 x^{3} - 3 x^{2} + 3 x - 1$ | $40277$ | $S_6$ (as 6T16) | trivial |
6.2.40733.1 | $x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} + 3 x - 1$ | $7\cdot 11\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.41069.1 | $x^{6} - 2 x^{4} + 2 x^{2} - x - 1$ | $7\cdot 5867$ | $S_6$ (as 6T16) | trivial |
6.2.44965.1 | $x^{6} - 2 x^{4} - 3 x - 1$ | $5\cdot 17\cdot 23^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.45301.1 | $x^{6} - x^{5} + x^{4} + x - 1$ | $89\cdot 509$ | $S_6$ (as 6T16) | trivial |
6.2.46757.1 | $x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + 2 x - 1$ | $46757$ | $S_6$ (as 6T16) | trivial |
6.2.47081.1 | $x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$ | $23^{2}\cdot 89$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.47149.1 | $x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - 1$ | $47149$ | $S_6$ (as 6T16) | trivial |
6.2.47669.1 | $x^{6} - x^{5} + x^{4} - x^{2} - 1$ | $73\cdot 653$ | $S_6$ (as 6T16) | trivial |
6.2.47933.1 | $x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - 1$ | $47933$ | $S_6$ (as 6T16) | trivial |
6.2.49664.1 | $x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 1$ | $2^{9}\cdot 97$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.49781.1 | $x^{6} - x - 1$ | $67\cdot 743$ | $S_6$ (as 6T16) | trivial |
6.2.50173.1 | $x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 3 x - 1$ | $131\cdot 383$ | $S_6$ (as 6T16) | trivial |
6.2.50933.1 | $x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} + 3 x - 1$ | $31^{2}\cdot 53$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.51125.1 | $x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{2} + 3 x - 1$ | $5^{3}\cdot 409$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.51757.1 | $x^{6} - 2 x^{3} - 2 x^{2} + x + 1$ | $73\cdot 709$ | $S_6$ (as 6T16) | trivial |
6.2.51869.1 | $x^{6} - 2 x^{5} + x^{4} + x^{3} - 2 x^{2} + x - 1$ | $51869$ | $S_6$ (as 6T16) | trivial |
6.2.52441.1 | $x^{6} - x^{4} - x^{3} - x^{2} + 1$ | $229^{2}$ | $S_4$ (as 6T7) | trivial |
6.2.52625.1 | $x^{6} - 2 x^{4} - x^{3} + x^{2} + x - 1$ | $5^{3}\cdot 421$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.53429.1 | $x^{6} - 3 x^{5} + 2 x^{4} + x^{3} + x^{2} - 2 x - 1$ | $23^{2}\cdot 101$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.55376.1 | $x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - x + 1$ | $2^{4}\cdot 3461$ | $S_6$ (as 6T16) | trivial |
6.2.56125.1 | $x^{6} - x^{5} + x^{3} - 3 x^{2} + 2 x - 1$ | $5^{3}\cdot 449$ | $C_3^2:D_4$ (as 6T13) | trivial |
6.2.56144.1 | $x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 3 x + 1$ | $2^{4}\cdot 11^{2}\cdot 29$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.57152.1 | $x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} - 1$ | $2^{6}\cdot 19\cdot 47$ | $S_6$ (as 6T16) | trivial |
6.2.57661.1 | $x^{6} - x^{5} + 4 x^{3} - 3 x^{2} + x - 1$ | $23^{2}\cdot 109$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.58589.1 | $x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - 4 x^{2} + 4 x - 1$ | $41\cdot 1429$ | $S_6$ (as 6T16) | trivial |
6.2.58673.1 | $x^{6} - x^{3} + x^{2} + x - 1$ | $23\cdot 2551$ | $S_6$ (as 6T16) | trivial |
6.2.59177.1 | $x^{6} - x^{4} - x^{3} + x^{2} - 1$ | $17\cdot 59^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.61193.1 | $x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + x - 1$ | $11\cdot 5563$ | $S_6$ (as 6T16) | trivial |
6.2.61504.1 | $x^{6} + x^{2} - 1$ | $2^{6}\cdot 31^{2}$ | $S_4$ (as 6T7) | trivial |
6.2.62437.1 | $x^{6} - x^{4} - x^{3} + 2 x^{2} + x - 1$ | $29\cdot 2153$ | $S_6$ (as 6T16) | trivial |
6.2.63461.1 | $x^{6} - x^{3} + 2 x - 1$ | $17\cdot 3733$ | $S_6$ (as 6T16) | trivial |
6.2.63909.1 | $x^{6} + 2 x^{4} - x - 1$ | $3^{5}\cdot 263$ | $S_6$ (as 6T16) | trivial |
6.2.64829.1 | $x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$ | $241\cdot 269$ | $S_6$ (as 6T16) | trivial |
6.2.65405.1 | $x^{6} - x^{5} + 2 x^{4} - 2 x^{3} - 1$ | $5\cdot 103\cdot 127$ | $S_6$ (as 6T16) | trivial |
6.2.65797.1 | $x^{6} - 2 x^{4} - x + 1$ | $19\cdot 3463$ | $S_6$ (as 6T16) | trivial |