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 |
---|---|---|---|---|
10.6.14002335917.1 | $x^{10} - x^{9} - x^{8} + 4 x^{7} - 4 x^{6} + 8 x^{4} - 3 x^{3} - 5 x^{2} + x + 1$ | $43\cdot 325635719$ | $S_{10}$ (as 10T45) | trivial |
10.6.14339628125.1 | $x^{10} - 2 x^{8} - 4 x^{7} - 4 x^{6} + 6 x^{5} + 9 x^{4} + 3 x^{3} - 4 x^{2} - 5 x + 1$ | $5^{5}\cdot 4588681$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.6.14478216461.1 | $x^{10} - 2 x^{9} - x^{8} + 4 x^{7} - 3 x^{6} - 4 x^{5} + 7 x^{4} + 4 x^{3} - 5 x^{2} - x + 1$ | $67\cdot 216092783$ | $S_{10}$ (as 10T45) | trivial |
10.6.14517675917.1 | $x^{10} - 4 x^{8} - 2 x^{7} + 4 x^{6} + 6 x^{5} - 4 x^{4} - 7 x^{3} + 2 x^{2} + 4 x + 1$ | $14517675917$ | $S_{10}$ (as 10T45) | trivial |
10.6.14791763533.1 | $x^{10} - 2 x^{9} + x^{8} + 4 x^{7} - 8 x^{6} + 6 x^{5} - 9 x^{3} + 6 x^{2} + x - 1$ | $127\cdot 4831\cdot 24109$ | $S_{10}$ (as 10T45) | trivial |
10.6.14805034037.1 | $x^{10} - x^{9} - 5 x^{8} + 7 x^{7} + 5 x^{6} - 15 x^{5} + 5 x^{4} + 11 x^{3} - 7 x^{2} - x + 1$ | $131\cdot 431\cdot 262217$ | $S_{10}$ (as 10T45) | trivial |
10.6.15051339509.1 | $x^{10} - 2 x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} + 2 x^{4} - x^{3} + x^{2} - 3 x + 1$ | $73^{2}\cdot 2824421$ | $S_{10}$ (as 10T45) | trivial |
10.6.15170413373.1 | $x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - 2 x^{6} - 8 x^{5} + 7 x^{4} + 8 x^{3} - 5 x^{2} - 2 x + 1$ | $43\cdot 5867\cdot 60133$ | $S_{10}$ (as 10T45) | trivial |
10.6.15248763469.1 | $x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + x^{5} + 5 x^{4} - 6 x^{3} - 4 x^{2} + 2 x + 1$ | $61\cdot 89\cdot 2808761$ | $S_{10}$ (as 10T45) | trivial |
10.6.15279193421.1 | $x^{10} - 4 x^{8} - 2 x^{7} + x^{6} + 7 x^{4} + 4 x^{3} - 6 x^{2} - x + 1$ | $67\cdot 228047663$ | $S_{10}$ (as 10T45) | trivial |
10.6.15310032229.1 | $x^{10} - 5 x^{8} - 2 x^{7} + 9 x^{6} + 4 x^{5} - 6 x^{4} + 2 x^{3} + x^{2} - 4 x - 1$ | $15310032229$ | $S_{10}$ (as 10T45) | trivial |
10.6.15370981037.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 6 x^{7} - 3 x^{6} - 5 x^{5} + 10 x^{4} + 2 x^{3} - 8 x^{2} - x + 1$ | $81701\cdot 188137$ | $S_{10}$ (as 10T45) | trivial |
10.6.15414254509.1 | $x^{10} - x^{9} - 5 x^{8} + 8 x^{7} + x^{6} - 9 x^{5} + 5 x^{4} + x^{3} - 3 x^{2} + 2 x + 1$ | $59\cdot 261258551$ | $S_{10}$ (as 10T45) | trivial |
10.6.15417264029.1 | $x^{10} - x^{9} - 3 x^{8} + 5 x^{7} + x^{6} - 7 x^{5} - x^{4} + 5 x^{3} + 3 x^{2} - x - 1$ | $461\cdot 5783^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.15485789357.1 | $x^{10} - x^{9} - 2 x^{8} - 3 x^{6} + 5 x^{5} + 7 x^{4} - x^{3} - 2 x^{2} - 2 x - 1$ | $157\cdot 2531\cdot 38971$ | $S_{10}$ (as 10T45) | trivial |
10.6.15570809981.1 | $x^{10} - 3 x^{9} + 6 x^{7} - 3 x^{6} + x^{5} - 5 x^{4} - 3 x^{3} + 8 x^{2} - 1$ | $127\cdot 6133\cdot 19991$ | $S_{10}$ (as 10T45) | trivial |
10.6.15625169689.1 | $x^{10} - x^{9} - 3 x^{8} - x^{7} + 5 x^{6} + 6 x^{5} - x^{4} - 7 x^{3} - x^{2} + 4 x - 1$ | $241\cdot 64834729$ | $S_{10}$ (as 10T45) | trivial |
10.6.15632169373.1 | $x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 2 x^{5} - 3 x^{4} - 2 x^{3} + 6 x^{2} - x - 1$ | $63727\cdot 245299$ | $S_{10}$ (as 10T45) | trivial |
10.6.15655427257.1 | $x^{10} - x^{9} - 2 x^{8} - 3 x^{7} + 3 x^{6} + 7 x^{5} + 3 x^{4} - 3 x^{3} - 6 x^{2} - x + 1$ | $109\cdot 1447\cdot 99259$ | $S_{10}$ (as 10T45) | trivial |
10.6.15671976301.1 | $x^{10} - 2 x^{8} - x^{7} - x^{6} + 3 x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} - 1$ | $149\cdot 641\cdot 164089$ | $S_{10}$ (as 10T45) | trivial |
10.6.15692318461.1 | $x^{10} - 3 x^{9} + 3 x^{8} - x^{7} - 6 x^{6} + 12 x^{5} - 4 x^{4} - 3 x^{3} + 5 x^{2} - 4 x + 1$ | $157\cdot 2833\cdot 35281$ | $S_{10}$ (as 10T45) | trivial |
10.6.15844129541.1 | $x^{10} - 2 x^{9} + x^{8} - x^{7} + 4 x^{5} - 7 x^{4} + x^{3} + 6 x^{2} - x - 1$ | $83\cdot 190893127$ | $S_{10}$ (as 10T45) | trivial |
10.6.16034047037.1 | $x^{10} - x^{9} - 3 x^{8} - 2 x^{7} + 3 x^{6} + 6 x^{5} - x^{4} - x^{2} - 2 x + 1$ | $16034047037$ | $S_{10}$ (as 10T45) | trivial |
10.6.16085091221.1 | $x^{10} - x^{9} - 3 x^{8} + 4 x^{7} - 2 x^{6} - 6 x^{5} + 8 x^{4} - x^{3} - 3 x^{2} + 5 x - 1$ | $16085091221$ | $S_{10}$ (as 10T45) | trivial |
10.6.16178522257.1 | $x^{10} - 3 x^{9} - 2 x^{8} + 14 x^{7} - 7 x^{6} - 19 x^{5} + 19 x^{4} + 2 x^{3} - 11 x^{2} + 6 x - 1$ | $673\cdot 4903^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.16247003125.1 | $x^{10} - x^{9} - x^{8} + 4 x^{7} - 4 x^{6} - 5 x^{5} + 2 x^{4} + x^{3} + 4 x^{2} + x - 1$ | $5^{5}\cdot 31\cdot 167711$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.6.16247108237.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} - x^{6} + 7 x^{5} - 13 x^{4} + 5 x^{3} + 6 x^{2} - 5 x + 1$ | $131\cdot 124023727$ | $S_{10}$ (as 10T45) | trivial |
10.6.16288734493.1 | $x^{10} - x^{9} - 2 x^{8} + 2 x^{7} - x^{6} - 4 x^{5} + 6 x^{4} + 8 x^{3} - 4 x^{2} - 5 x - 1$ | $47\cdot 7321\cdot 47339$ | $S_{10}$ (as 10T45) | trivial |
10.6.16296015389.1 | $x^{10} - 3 x^{9} + 5 x^{7} - 5 x^{6} + 5 x^{5} + 5 x^{4} - 10 x^{3} - 3 x^{2} + 3 x + 1$ | $457\cdot 35658677$ | $S_{10}$ (as 10T45) | trivial |
10.6.16297628125.1 | $x^{10} - 3 x^{8} - 2 x^{7} - x^{6} + x^{5} + 4 x^{4} + 5 x^{3} - 2 x^{2} - 3 x + 1$ | $5^{5}\cdot 41\cdot 131\cdot 971$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.6.16329970477.1 | $x^{10} - 2 x^{9} - x^{8} + 3 x^{7} - 3 x^{5} + 2 x^{4} + 6 x^{3} - 4 x^{2} - 4 x + 1$ | $16329970477$ | $S_{10}$ (as 10T45) | trivial |
10.6.16377200813.1 | $x^{10} - 3 x^{9} + 3 x^{8} - x^{7} - 4 x^{6} + 6 x^{5} - 2 x^{4} - 2 x^{3} + 4 x^{2} - 1$ | $37\cdot 442627049$ | $S_{10}$ (as 10T45) | trivial |
10.6.16454730077.1 | $x^{10} - 3 x^{9} - x^{8} + 11 x^{7} - 9 x^{6} - 9 x^{5} + 15 x^{4} + x^{3} - 7 x^{2} + x + 1$ | $239\cdot 523\cdot 131641$ | $S_{10}$ (as 10T45) | trivial |
10.6.16469469197.1 | $x^{10} - 6 x^{8} - x^{7} + 13 x^{6} + 7 x^{5} - 10 x^{4} - 11 x^{3} + x^{2} + 4 x + 1$ | $12601\cdot 1306997$ | $S_{10}$ (as 10T45) | trivial |
10.6.16513512157.1 | $x^{10} - 2 x^{9} - x^{8} - x^{7} + 5 x^{6} + 6 x^{5} - 10 x^{4} - 2 x^{3} + 6 x^{2} - 1$ | $16513512157$ | $S_{10}$ (as 10T45) | trivial |
10.6.16596688733.1 | $x^{10} - x^{9} - 4 x^{8} + 4 x^{7} + 5 x^{6} - 6 x^{5} - 4 x^{4} + 4 x^{3} + 4 x^{2} - x - 1$ | $16596688733$ | $S_{10}$ (as 10T45) | trivial |
10.6.16656903125.1 | $x^{10} - 6 x^{8} - 2 x^{7} + 12 x^{6} + 8 x^{5} - 8 x^{4} - 9 x^{3} - x^{2} + 3 x + 1$ | $5^{5}\cdot 79\cdot 109\cdot 619$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.6.16780434029.1 | $x^{10} - 2 x^{9} - 2 x^{8} + 5 x^{7} - x^{6} - 7 x^{5} + x^{4} + 7 x^{3} - x^{2} - 3 x + 1$ | $1657\cdot 2239\cdot 4523$ | $S_{10}$ (as 10T45) | trivial |
10.6.16798253125.1 | $x^{10} - 4 x^{9} + 2 x^{8} + 9 x^{7} - 10 x^{6} - 6 x^{5} + 12 x^{4} + 3 x^{3} - 6 x^{2} - x + 1$ | $5^{5}\cdot 5375441$ | $S_5^2 \wr C_2$ (as 10T43) | trivial |
10.6.16822229077.1 | $x^{10} - x^{9} - x^{8} + x^{6} + x^{5} - 7 x^{4} + x^{3} + 6 x^{2} - x - 1$ | $659\cdot 859\cdot 29717$ | $S_{10}$ (as 10T45) | trivial |
10.6.16851625709.1 | $x^{10} - x^{9} - 2 x^{8} - 6 x^{6} + 9 x^{4} + 2 x^{3} - 3 x^{2} - 2 x + 1$ | $701\cdot 4903^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.16898485501.1 | $x^{10} - 3 x^{9} + 3 x^{8} + 2 x^{7} - 7 x^{6} + 5 x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 2 x - 1$ | $82051\cdot 205951$ | $S_{10}$ (as 10T45) | trivial |
10.6.16964142281.1 | $x^{10} - 2 x^{9} - x^{8} + 3 x^{7} - 5 x^{6} + 8 x^{5} + x^{4} - 5 x^{3} + 3 x^{2} - 3 x + 1$ | $271\cdot 62598311$ | $S_{10}$ (as 10T45) | trivial |
10.6.16965864077.1 | $x^{10} - x^{9} - 4 x^{8} + 4 x^{7} + x^{6} - x^{5} + 11 x^{4} - 9 x^{3} - 9 x^{2} + 7 x - 1$ | $557\cdot 5519^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.16987351657.1 | $x^{10} - x^{9} - 6 x^{8} + 7 x^{7} + 12 x^{6} - 16 x^{5} - 12 x^{4} + 18 x^{3} + 4 x^{2} - 7 x + 1$ | $53^{2}\cdot 139^{2}\cdot 313$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.17007429581.1 | $x^{10} - 2 x^{9} + x^{8} - 5 x^{7} + 7 x^{6} + 3 x^{5} - 7 x^{4} + 7 x^{3} - 4 x^{2} - 3 x + 1$ | $29\cdot 61^{2}\cdot 397^{2}$ | $C_2 \wr S_5$ (as 10T39) | trivial |
10.6.17094519053.1 | $x^{10} - x^{9} + 4 x^{7} - 3 x^{6} - 6 x^{5} - 3 x^{4} + 4 x^{3} + 6 x^{2} - 2 x - 1$ | $17094519053$ | $S_{10}$ (as 10T45) | trivial |
10.6.17114203661.1 | $x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} + 5 x^{6} - 15 x^{5} - 6 x^{4} + 13 x^{3} + 4 x^{2} - 3 x - 1$ | $101\cdot 3041\cdot 55721$ | $S_{10}$ (as 10T45) | trivial |
10.6.17177053693.1 | $x^{10} - 2 x^{9} - 4 x^{8} + 10 x^{7} + 3 x^{6} - 14 x^{5} + 3 x^{4} + 2 x^{3} - 2 x^{2} + 3 x - 1$ | $1109\cdot 15488777$ | $S_{10}$ (as 10T45) | trivial |
10.6.17186031773.1 | $x^{10} - 2 x^{9} - 3 x^{8} + 10 x^{7} - 4 x^{6} - 13 x^{5} + 16 x^{4} - 8 x^{2} + 5 x - 1$ | $17186031773$ | $S_{10}$ (as 10T45) | trivial |