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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
6.0.54691.1 | $ x^{6} - x^{5} - 2 x^{3} + 2 x^{2} + 1 $ | $-\,7\cdot 13\cdot 601$ | $S_6$ (as 6T16) | trivial |
6.2.70629.1 | $ x^{6} - x^{3} + 2 x^{2} + 2 x - 1 $ | $3\cdot 13\cdot 1811$ | $S_6$ (as 6T16) | trivial |
6.2.70837.1 | $ x^{6} + 2 x^{4} - x^{3} - 2 x - 1 $ | $13\cdot 5449$ | $S_6$ (as 6T16) | trivial |
6.0.70967.1 | $ x^{6} - x^{5} + 3 x^{3} - x^{2} - x + 2 $ | $-\,13\cdot 53\cdot 103$ | $S_6$ (as 6T16) | trivial |
6.2.75088.1 | $ x^{6} - x^{5} + x^{3} - x - 1 $ | $2^{4}\cdot 13\cdot 19^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.95667.1 | $ x^{6} - x^{5} + x^{4} + x + 1 $ | $-\,3\cdot 11\cdot 13\cdot 223$ | $S_6$ (as 6T16) | trivial |
6.2.100672.1 | $ x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + x^{2} - 2 x - 1 $ | $2^{6}\cdot 11^{2}\cdot 13$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.123344.1 | $ x^{6} - x^{5} + 2 x^{4} - x^{3} - x - 1 $ | $2^{4}\cdot 13\cdot 593$ | $S_6$ (as 6T16) | trivial |
6.0.176176.1 | $ x^{6} - x^{5} + 4 x^{4} - x^{3} + 4 x^{2} - x + 1 $ | $-\,2^{4}\cdot 7\cdot 11^{2}\cdot 13$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.190528.1 | $ x^{6} - 2 x^{4} + x^{2} - 2 x + 1 $ | $2^{6}\cdot 13\cdot 229$ | $S_6$ (as 6T16) | trivial |
6.2.199004.1 | $ x^{6} - x^{5} - 3 x^{4} + x^{3} + 5 x^{2} - 2 $ | $2^{2}\cdot 13\cdot 43\cdot 89$ | $S_6$ (as 6T16) | trivial |
6.2.212381.1 | $ x^{6} - 2 x^{5} - 4 x^{4} + 7 x^{3} + 4 x^{2} - 2 x - 1 $ | $13\cdot 17\cdot 31^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.4.214747.1 | $ x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x + 1 $ | $-\,13\cdot 16519$ | $S_6$ (as 6T16) | trivial |
6.0.221299.1 | $ x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + 4 x^{2} - x + 1 $ | $-\,13\cdot 29\cdot 587$ | $S_6$ (as 6T16) | trivial |
6.2.234793.1 | $ x^{6} - 2 x^{5} - x^{3} + 3 x^{2} - x + 1 $ | $13\cdot 18061$ | $S_6$ (as 6T16) | trivial |
6.2.246857.1 | $ x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - x^{2} - 4 x + 1 $ | $13\cdot 17\cdot 1117$ | $S_6$ (as 6T16) | trivial |
6.0.276848.1 | $ x^{6} - x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - 4 x + 4 $ | $-\,2^{4}\cdot 11^{3}\cdot 13$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.287339.1 | $ x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + 10 x^{2} - x + 3 $ | $-\,13\cdot 23\cdot 31^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.302965.1 | $ x^{6} + x^{4} - 2 x^{3} + 5 x^{2} - 5 x + 1 $ | $5\cdot 13\cdot 59\cdot 79$ | $S_6$ (as 6T16) | trivial |
6.2.303381.1 | $ x^{6} - 2 x^{5} + x^{4} - x^{3} + 2 x^{2} + x - 1 $ | $3^{2}\cdot 13\cdot 2593$ | $S_6$ (as 6T16) | trivial |
6.2.338897.1 | $ x^{6} - x^{5} + 3 x^{3} - 5 x^{2} + 5 x - 2 $ | $13\cdot 131\cdot 199$ | $S_6$ (as 6T16) | trivial |
6.2.353288.1 | $ x^{6} - 3 x^{5} + 3 x^{4} + x^{3} - 5 x^{2} + 2 x + 2 $ | $2^{3}\cdot 13\cdot 43\cdot 79$ | $S_6$ (as 6T16) | trivial |
6.2.362297.1 | $ x^{6} - x^{5} - 4 x^{4} + 3 x^{3} + 4 x^{2} - 10 x - 1 $ | $13\cdot 29\cdot 31^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.389831.1 | $ x^{6} - x^{5} - x^{4} + 3 x^{3} + x^{2} - x + 1 $ | $-\,13\cdot 157\cdot 191$ | $S_6$ (as 6T16) | trivial |
6.0.402688.1 | $ x^{6} - 2 x^{5} + 6 x^{4} - 2 x^{3} + 2 x^{2} + 4 x + 2 $ | $-\,2^{8}\cdot 11^{2}\cdot 13$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.405353.1 | $ x^{6} - x^{5} + x^{4} + 3 x^{3} - x^{2} + x + 1 $ | $13\cdot 31181$ | $S_6$ (as 6T16) | trivial |
6.2.407693.1 | $ x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 3 x^{2} + 3 x + 1 $ | $11\cdot 13\cdot 2851$ | $S_6$ (as 6T16) | trivial |
6.2.408629.1 | $ x^{6} - 2 x^{5} + 4 x^{3} - 2 x^{2} - 3 x + 1 $ | $13\cdot 17\cdot 43^{2}$ | $S_6$ (as 6T16) | trivial |
6.0.427440.1 | $ x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 3 x + 1 $ | $-\,2^{4}\cdot 3\cdot 5\cdot 13\cdot 137$ | $S_6$ (as 6T16) | trivial |
6.0.435136.1 | $ x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 2 $ | $-\,2^{6}\cdot 13\cdot 523$ | $S_6$ (as 6T16) | trivial |
6.0.435968.1 | $ x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 2 $ | $-\,2^{8}\cdot 13\cdot 131$ | $S_6$ (as 6T16) | trivial |
6.2.441168.1 | $ x^{6} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 3 x + 3 $ | $2^{4}\cdot 3\cdot 7\cdot 13\cdot 101$ | $S_6$ (as 6T16) | trivial |
6.2.462137.1 | $ x^{6} - x^{5} - 2 x^{4} + x^{3} - x^{2} + 3 x + 1 $ | $13\cdot 19\cdot 1871$ | $S_6$ (as 6T16) | trivial |
6.0.468416.1 | $ x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 3 $ | $-\,2^{6}\cdot 13\cdot 563$ | $S_6$ (as 6T16) | trivial |
6.0.471536.1 | $ x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 4 x + 2 $ | $-\,2^{4}\cdot 13\cdot 2267$ | $S_6$ (as 6T16) | trivial |
6.2.487513.1 | $ x^{6} - x^{5} + x^{4} + 3 x^{3} - 4 x^{2} + 5 x - 1 $ | $13\cdot 37501$ | $S_6$ (as 6T16) | trivial |
6.0.496704.1 | $ x^{6} - 2 x^{5} + 2 x^{4} - x^{2} - 2 x + 3 $ | $-\,2^{6}\cdot 3\cdot 13\cdot 199$ | $S_6$ (as 6T16) | trivial |
6.0.497783.1 | $ x^{6} + 5 x^{4} - x^{3} + 5 x^{2} + 1 $ | $-\,11\cdot 13\cdot 59^{2}$ | $S_4\times C_2$ (as 6T11) | trivial |
6.2.504517.1 | $ x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 1 $ | $13\cdot 197^{2}$ | $S_6$ (as 6T16) | trivial |
6.2.508885.1 | $ x^{6} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 2 x^{2} - 2 x + 1 $ | $5\cdot 13\cdot 7829$ | $S_6$ (as 6T16) | trivial |
6.2.513344.1 | $ x^{6} - x^{4} - 2 x^{3} - 3 x^{2} + 4 x - 1 $ | $2^{6}\cdot 13\cdot 617$ | $S_6$ (as 6T16) | trivial |
6.4.519051.1 | $ x^{6} - 2 x^{5} + 4 x^{3} - 4 x^{2} - x + 1 $ | $-\,3\cdot 13\cdot 13309$ | $S_6$ (as 6T16) | trivial |
6.2.519285.1 | $ x^{6} - x^{5} + x^{4} + 2 x^{3} - 5 x - 1 $ | $3\cdot 5\cdot 13\cdot 2663$ | $S_6$ (as 6T16) | trivial |
6.4.533923.1 | $ x^{6} - x^{5} - x^{4} - 2 x^{2} + x + 1 $ | $-\,13\cdot 67\cdot 613$ | $S_6$ (as 6T16) | trivial |
6.0.537199.1 | $ x^{6} - 3 x^{5} + 6 x^{4} - x^{3} - 2 x^{2} + 8 x + 8 $ | $-\,13\cdot 31^{2}\cdot 43$ | $S_4\times C_2$ (as 6T11) | trivial |
6.0.541372.1 | $ x^{6} - 2 x^{4} - 3 x^{3} + 2 x^{2} + 4 x + 2 $ | $-\,2^{2}\cdot 13\cdot 29\cdot 359$ | $S_6$ (as 6T16) | trivial |
6.0.542984.1 | $ x^{6} - 3 x^{5} + 6 x^{4} - 6 x^{3} + 7 x^{2} - 4 x + 2 $ | $-\,2^{3}\cdot 13\cdot 23\cdot 227$ | $S_6$ (as 6T16) | trivial |
6.0.548899.1 | $ x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} + x + 1 $ | $-\,13\cdot 42223$ | $S_6$ (as 6T16) | trivial |
6.2.560144.1 | $ x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 4 x - 4 $ | $2^{4}\cdot 13\cdot 2693$ | $S_6$ (as 6T16) | trivial |
6.2.560625.1 | $ x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + 3 x^{2} - 3 x - 2 $ | $3\cdot 5^{4}\cdot 13\cdot 23$ | $S_6$ (as 6T16) | trivial |