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 |
---|---|---|---|---|
8.6.65106259.1 | $x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 4 x^{2} - 2 x + 1$ | $-\,89\cdot 731531$ | $S_8$ (as 8T50) | trivial |
8.6.68494627.1 | $x^{8} - 2 x^{7} - 3 x^{6} + 10 x^{5} - 2 x^{4} - 11 x^{3} + 5 x^{2} + 2 x - 1$ | $-\,811\cdot 84457$ | $S_8$ (as 8T50) | trivial |
8.6.68856875.1 | $x^{8} - 2 x^{7} - 2 x^{6} + x^{5} + x^{4} + 5 x^{3} - x^{2} - 3 x + 1$ | $-\,5^{4}\cdot 29^{2}\cdot 131$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.69367411.1 | $x^{8} - x^{6} - 3 x^{5} - 3 x^{4} + 6 x^{3} + 4 x^{2} - 2 x - 1$ | $-\,69367411$ | $S_8$ (as 8T50) | trivial |
8.6.73061875.1 | $x^{8} - 4 x^{6} - 3 x^{4} - 5 x^{3} + 4 x^{2} + 5 x + 1$ | $-\,5^{4}\cdot 29^{2}\cdot 139$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.74671875.1 | $x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - 6 x^{4} + 9 x^{3} - 4 x + 1$ | $-\,3^{4}\cdot 5^{6}\cdot 59$ | $((C_8 : C_2):C_2):C_2$ (as 8T27) | trivial |
8.6.74906875.1 | $x^{8} - 3 x^{6} - 3 x^{5} + 3 x^{4} + 7 x^{3} - 2 x^{2} - 3 x + 1$ | $-\,5^{4}\cdot 119851$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.75272867.1 | $x^{8} - 2 x^{7} - 3 x^{6} + 9 x^{5} - x^{4} - 10 x^{3} + 3 x^{2} + 3 x - 1$ | $-\,31\cdot 2428157$ | $S_8$ (as 8T50) | trivial |
8.6.83260171.1 | $x^{8} - 2 x^{7} - 3 x^{6} + 4 x^{5} + 3 x^{4} + x^{3} - x^{2} - 3 x - 1$ | $-\,47\cdot 1771493$ | $S_8$ (as 8T50) | trivial |
8.6.84356875.1 | $x^{8} - 3 x^{6} - x^{5} + 4 x^{3} + 3 x^{2} - 2 x - 1$ | $-\,5^{4}\cdot 71\cdot 1901$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.86606875.1 | $x^{8} - x^{7} - 3 x^{6} + 2 x^{5} - x^{4} + 6 x^{3} + 3 x^{2} - 7 x - 1$ | $-\,5^{4}\cdot 138571$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.93594547.1 | $x^{8} - x^{7} - 6 x^{6} + 4 x^{5} + 11 x^{4} - 3 x^{3} - 7 x^{2} + x + 1$ | $-\,1117\cdot 83791$ | $S_8$ (as 8T50) | trivial |
8.6.94086875.1 | $x^{8} - 2 x^{7} + x^{6} + 4 x^{5} - 12 x^{4} + 3 x^{3} + 9 x^{2} - 6 x + 1$ | $-\,5^{4}\cdot 29^{2}\cdot 179$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.94156147.1 | $x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$ | $-\,94156147$ | $S_8$ (as 8T50) | trivial |
8.6.94856875.1 | $x^{8} - x^{7} - x^{6} + 3 x^{5} - 5 x^{4} - 2 x^{3} + 6 x^{2} + x - 1$ | $-\,5^{4}\cdot 151771$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.95029219.1 | $x^{8} - x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 2 x^{3} + 4 x^{2} + x - 1$ | $-\,1291\cdot 73609$ | $S_8$ (as 8T50) | trivial |
8.6.96530491.1 | $x^{8} - 2 x^{7} - 3 x^{6} + 7 x^{5} - 6 x^{3} + 4 x^{2} + x - 1$ | $-\,96530491$ | $S_8$ (as 8T50) | trivial |
8.6.96598171.1 | $x^{8} - 3 x^{7} + x^{6} + 4 x^{5} - 7 x^{4} + 5 x^{3} + 5 x^{2} - 6 x + 1$ | $-\,53\cdot 1229\cdot 1483$ | $S_8$ (as 8T50) | trivial |
8.6.97161811.1 | $x^{8} - 5 x^{6} - x^{5} + 6 x^{4} + 3 x^{3} - 2 x - 1$ | $-\,43\cdot 521\cdot 4337$ | $S_8$ (as 8T50) | trivial |
8.6.98070859.1 | $x^{8} - 2 x^{7} - x^{6} + 3 x^{5} - 5 x^{4} + 10 x^{3} - 4 x^{2} - 2 x + 1$ | $-\,61\cdot 263\cdot 6113$ | $S_8$ (as 8T50) | trivial |
8.6.98151947.1 | $x^{8} - 4 x^{6} - x^{5} + 3 x^{4} + 3 x^{3} + 2 x^{2} - 2 x - 1$ | $-\,7297\cdot 13451$ | $S_8$ (as 8T50) | trivial |
8.6.98915419.1 | $x^{8} - 4 x^{6} - x^{5} + 2 x^{4} + x^{3} + 3 x^{2} - 1$ | $-\,151\cdot 655069$ | $S_8$ (as 8T50) | trivial |
8.6.103405923.1 | $x^{8} - x^{7} + x^{5} - 8 x^{4} + x^{3} + 8 x^{2} - 2 x - 1$ | $-\,3^{3}\cdot 19^{2}\cdot 103^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.6.104081867.1 | $x^{8} - 3 x^{7} - x^{6} + 10 x^{5} - 5 x^{4} - 10 x^{3} + 7 x^{2} + 3 x - 1$ | $-\,19\cdot 73\cdot 75041$ | $S_8$ (as 8T50) | trivial |
8.6.104429827.1 | $x^{8} - x^{7} - 2 x^{6} + x^{5} - 2 x^{4} + 5 x^{3} + 2 x^{2} - 4 x + 1$ | $-\,17\cdot 199\cdot 30869$ | $S_8$ (as 8T50) | trivial |
8.6.106143931.1 | $x^{8} - 4 x^{7} + 3 x^{6} + 5 x^{5} - 8 x^{4} + 2 x^{3} + 5 x^{2} - 2 x - 1$ | $-\,3659\cdot 29009$ | $S_8$ (as 8T50) | trivial |
8.6.106899371.1 | $x^{8} - 3 x^{7} + 3 x^{5} + 3 x^{4} - 6 x^{2} + 1$ | $-\,67\cdot 1595513$ | $S_8$ (as 8T50) | trivial |
8.6.107555299.1 | $x^{8} - 3 x^{7} - x^{6} + 9 x^{5} - 5 x^{4} - 5 x^{3} + 6 x^{2} - 1$ | $-\,1153\cdot 93283$ | $S_8$ (as 8T50) | trivial |
8.6.107781875.1 | $x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 5 x^{4} - 3 x^{3} + 5 x^{2} + x - 1$ | $-\,5^{4}\cdot 331\cdot 521$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.108493747.1 | $x^{8} - x^{7} - 5 x^{6} + 5 x^{5} + 7 x^{4} - 8 x^{3} - 3 x^{2} + 4 x + 1$ | $-\,108493747$ | $S_8$ (as 8T50) | trivial |
8.6.108714131.1 | $x^{8} - x^{7} - 4 x^{6} + 5 x^{5} + 3 x^{4} - 9 x^{3} + x^{2} + 4 x - 1$ | $-\,103\cdot 971\cdot 1087$ | $S_8$ (as 8T50) | trivial |
8.6.109020787.1 | $x^{8} - 5 x^{6} - 3 x^{5} + 8 x^{4} + 9 x^{3} - 4 x^{2} - 6 x - 1$ | $-\,109020787$ | $S_8$ (as 8T50) | trivial |
8.6.109380619.1 | $x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} + x^{4} + 5 x^{3} + x^{2} - 4 x - 1$ | $-\,109380619$ | $S_8$ (as 8T50) | trivial |
8.6.110906875.1 | $x^{8} - 2 x^{7} - 4 x^{6} + 9 x^{5} - 9 x^{3} + 4 x^{2} + 3 x - 1$ | $-\,5^{4}\cdot 29^{2}\cdot 211$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.111219379.1 | $x^{8} - 2 x^{7} - 2 x^{6} + 7 x^{5} - 3 x^{4} - 7 x^{3} + 4 x^{2} + 2 x - 1$ | $-\,29\cdot 389\cdot 9859$ | $S_8$ (as 8T50) | trivial |
8.6.112129379.1 | $x^{8} - x^{7} - 4 x^{6} + 2 x^{5} + 4 x^{4} + 3 x^{3} - x^{2} - 4 x - 1$ | $-\,1427\cdot 78577$ | $S_8$ (as 8T50) | trivial |
8.6.114655339.1 | $x^{8} - 4 x^{7} + 3 x^{6} + 4 x^{5} - 5 x^{4} + 3 x^{3} - x^{2} - 3 x + 1$ | $-\,233\cdot 492083$ | $S_8$ (as 8T50) | trivial |
8.6.118871243.1 | $x^{8} - 2 x^{6} - 2 x^{5} - 3 x^{4} + 5 x^{3} + 5 x^{2} - 2 x - 1$ | $-\,101\cdot 1176943$ | $S_8$ (as 8T50) | trivial |
8.6.119649419.1 | $x^{8} - x^{7} - 4 x^{6} + 6 x^{5} + 6 x^{4} - 9 x^{3} - 4 x^{2} + 3 x + 1$ | $-\,119649419$ | $S_8$ (as 8T50) | trivial |
8.6.121587131.1 | $x^{8} - 2 x^{7} - x^{6} + 7 x^{5} - 7 x^{4} - 5 x^{3} + 8 x^{2} + x - 1$ | $-\,23\cdot 271\cdot 19507$ | $S_8$ (as 8T50) | trivial |
8.6.123531875.1 | $x^{8} - 5 x^{6} - 3 x^{5} + 8 x^{4} + 10 x^{3} - 4 x^{2} - 7 x + 1$ | $-\,5^{4}\cdot 197651$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.128782547.1 | $x^{8} - 2 x^{7} + 5 x^{5} - 8 x^{4} - 3 x^{3} + 8 x^{2} - x - 1$ | $-\,157\cdot 820271$ | $S_8$ (as 8T50) | trivial |
8.6.129062827.1 | $x^{8} - 2 x^{7} - 4 x^{6} + 5 x^{5} + 8 x^{4} - 3 x^{3} - 6 x^{2} + x + 1$ | $-\,17\cdot 31\cdot 244901$ | $S_8$ (as 8T50) | trivial |
8.6.131931875.1 | $x^{8} - x^{7} - 5 x^{6} + 5 x^{5} + 3 x^{4} - 3 x + 1$ | $-\,5^{4}\cdot 29^{2}\cdot 251$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.132655867.1 | $x^{8} - 2 x^{6} - 2 x^{5} - 3 x^{4} + 3 x^{3} + 4 x^{2} - x - 1$ | $-\,137\cdot 968291$ | $S_8$ (as 8T50) | trivial |
8.6.132761875.1 | $x^{8} - x^{7} - 5 x^{6} + 2 x^{5} + 11 x^{4} - x^{3} - 9 x^{2} + 1$ | $-\,5^{4}\cdot 212419$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.6.134560000.1 | $x^{8} - 3 x^{6} + 4 x^{2} - 1$ | $-\,2^{8}\cdot 5^{4}\cdot 29^{2}$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.134560000.2 | $x^{8} - 6 x^{4} + 5 x^{2} - 1$ | $-\,2^{8}\cdot 5^{4}\cdot 29^{2}$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.6.135123147.1 | $x^{8} - 4 x^{6} - 4 x^{5} + 9 x^{4} + 5 x^{3} - 6 x^{2} - x + 1$ | $-\,3^{4}\cdot 257\cdot 6491$ | $S_8$ (as 8T50) | trivial |
8.6.136128151.1 | $x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 7 x^{4} + 2 x^{3} + 6 x^{2} - x - 1$ | $-\,97\cdot 1403383$ | $S_8$ (as 8T50) | trivial |