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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
9.3.1735643790720.1 | $x^{9} - 9 x^{6} + 9 x^{5} - 6 x^{3} + 9 x^{2} - 2$ | $-\,2^{7}\cdot 3^{18}\cdot 5\cdot 7$ | $S_9$ (as 9T34) | trivial |
9.1.2539579392000.1 | $x^{9} - 3 x^{8} + 12 x^{7} - 20 x^{6} + 69 x^{5} - 99 x^{4} + 132 x^{3} - 72 x^{2} - 6 x + 10$ | $2^{14}\cdot 3^{11}\cdot 5^{3}\cdot 7$ | $S_9$ (as 9T34) | trivial |
9.3.34284321792000.1 | $x^{9} - 3 x^{8} - 6 x^{7} + 18 x^{6} - 36 x^{5} + 108 x^{4} - 174 x^{3} + 162 x^{2} - 81 x + 27$ | $-\,2^{13}\cdot 3^{14}\cdot 5^{3}\cdot 7$ | $S_9$ (as 9T34) | trivial |
9.1.49601160000000.1 | $x^{9} - 3 x^{8} - 9 x^{7} + 15 x^{6} + 150 x^{5} - 450 x^{4} + 300 x^{3} + 150 x^{2} - 100$ | $2^{9}\cdot 3^{11}\cdot 5^{7}\cdot 7$ | $S_9$ (as 9T34) | trivial |
9.1.4601270257436160.1 | $x^{9} - 3 x^{8} - 18 x^{7} + 76 x^{6} + 93 x^{5} - 495 x^{4} + 580 x^{3} + 1458 x^{2} - 1836 x + 4464$ | $2^{9}\cdot 3^{13}\cdot 5\cdot 7\cdot 11^{5}$ | $S_9$ (as 9T34) | $[2]$ |
10.0.967207171.1 | $x^{10} - x^{9} + 3 x^{8} - 5 x^{7} + 4 x^{6} - 6 x^{5} + 4 x^{4} - 2 x^{3} + 2 x^{2} + 1$ | $-\,7\cdot 138172453$ | $S_{10}$ (as 10T45) | trivial |
10.0.982312667.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 6 x^{6} - 6 x^{5} + 6 x^{4} - 2 x^{3} + 4 x^{2} + 1$ | $-\,7\cdot 37\cdot 919\cdot 4127$ | $S_{10}$ (as 10T45) | trivial |
10.0.1043341075.1 | $x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + x^{6} - 3 x^{5} + x^{4} + x^{3} - x^{2} + 1$ | $-\,5^{2}\cdot 7^{2}\cdot 103\cdot 8269$ | $S_{10}$ (as 10T45) | trivial |
10.0.1124443327.1 | $x^{10} - 2 x^{8} - 2 x^{7} + 3 x^{6} + 3 x^{5} - 2 x^{4} - 3 x^{3} + 2 x + 1$ | $-\,7^{2}\cdot 41\cdot 559703$ | $S_{10}$ (as 10T45) | trivial |
10.0.1251659171.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 3 x^{7} + 5 x^{6} - 7 x^{5} + 9 x^{4} - 9 x^{3} + 7 x^{2} - 3 x + 1$ | $-\,7\cdot 2557\cdot 69929$ | $S_{10}$ (as 10T45) | trivial |
10.0.1356935111.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - x^{5} + 3 x^{4} - x^{3} + 3 x^{2} + 1$ | $-\,7\cdot 193847873$ | $S_{10}$ (as 10T45) | trivial |
10.0.1530842075.1 | $x^{10} - 3 x^{9} + 3 x^{8} - 2 x^{6} + x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$ | $-\,5^{2}\cdot 7^{2}\cdot 113\cdot 11059$ | $S_{10}$ (as 10T45) | trivial |
10.0.1629148619.1 | $x^{10} - 2 x^{9} + 2 x^{8} + 2 x^{7} - 4 x^{6} + 2 x^{5} + 3 x^{4} - 3 x^{3} - x^{2} + 2 x + 1$ | $-\,7^{2}\cdot 131\cdot 253801$ | $S_{10}$ (as 10T45) | trivial |
10.0.1643385856.1 | $x^{10} + 2 x^{8} - x^{6} - x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ | $-\,2^{10}\cdot 7\cdot 229267$ | $S_{10}$ (as 10T45) | trivial |
10.0.1682646476.1 | $x^{10} + x^{8} - 2 x^{7} + x^{6} - 4 x^{5} + x^{4} - x^{3} + 3 x^{2} + x + 1$ | $-\,2^{2}\cdot 7^{2}\cdot 107\cdot 80233$ | $S_{10}$ (as 10T45) | trivial |
10.0.1795570847.1 | $x^{10} - x^{9} + x^{7} - 3 x^{6} + 2 x^{5} + x^{4} - 3 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,7^{2}\cdot 36644303$ | $S_{10}$ (as 10T45) | trivial |
10.2.1880601821.1 | $x^{10} - x^{8} - 3 x^{7} - 2 x^{6} + 5 x^{5} + 5 x^{4} - x^{3} - 4 x^{2} - 2 x + 1$ | $7^{2}\cdot 787\cdot 48767$ | $S_{10}$ (as 10T45) | trivial |
10.0.1887157027.1 | $x^{10} - x^{9} + 2 x^{8} + x^{6} + 4 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} + 1$ | $-\,7\cdot 491\cdot 549071$ | $S_{10}$ (as 10T45) | trivial |
10.0.1888076939.1 | $x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{4} + x^{2} + 1$ | $-\,7\cdot 269725277$ | $S_{10}$ (as 10T45) | trivial |
10.0.1896111791.1 | $x^{10} - x^{9} - x^{7} + x^{4} - x^{3} + x^{2} + 1$ | $-\,7^{2}\cdot 1009\cdot 38351$ | $S_{10}$ (as 10T45) | trivial |
10.0.1937783792.1 | $x^{10} - x^{9} + 2 x^{8} - x^{7} + 2 x^{6} + x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 7^{2}\cdot 2471663$ | $S_{10}$ (as 10T45) | trivial |
10.0.1979862311.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 11 x^{6} - 14 x^{5} + 15 x^{4} - 12 x^{3} + 8 x^{2} - 4 x + 1$ | $-\,7\cdot 6067\cdot 46619$ | $S_{10}$ (as 10T45) | trivial |
10.2.2012250709.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 7 x^{5} + 10 x^{4} - 10 x^{3} + 7 x^{2} - 4 x + 1$ | $7^{2}\cdot 229\cdot 389\cdot 461$ | $S_{10}$ (as 10T45) | trivial |
10.0.2038643719.1 | $x^{10} - x^{9} + x^{8} + 2 x^{6} - 3 x^{5} + x^{4} + 2 x^{3} - 2 x^{2} - x + 1$ | $-\,7\cdot 1039\cdot 280303$ | $S_{10}$ (as 10T45) | trivial |
10.0.2103848971.1 | $x^{10} - 3 x^{9} + 5 x^{8} - 2 x^{7} - 5 x^{6} + 10 x^{5} - 5 x^{4} - 4 x^{3} + 7 x^{2} - 4 x + 1$ | $-\,7\cdot 37\cdot 8122969$ | $S_{10}$ (as 10T45) | trivial |
10.0.2106354859.1 | $x^{10} - 2 x^{9} + 3 x^{8} - x^{7} + x^{6} + 2 x^{4} + 2 x^{3} - x^{2} + x + 1$ | $-\,7\cdot 17\cdot 17700461$ | $S_{10}$ (as 10T45) | trivial |
10.0.2113889743.1 | $x^{10} - x^{9} + 2 x^{8} - x^{7} + x^{6} + x^{5} + 2 x^{4} - x^{3} + 4 x^{2} - x + 1$ | $-\,7^{2}\cdot 43140607$ | $S_{10}$ (as 10T45) | trivial |
10.0.2288851495.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{2} + x + 1$ | $-\,5\cdot 7^{2}\cdot 71\cdot 131581$ | $S_{10}$ (as 10T45) | trivial |
10.2.2321314093.1 | $x^{10} - x^{9} - x^{8} + x^{7} - 2 x^{5} + x^{4} + 4 x^{3} - 6 x^{2} + 3 x - 1$ | $7^{2}\cdot 67\cdot 707071$ | $S_{10}$ (as 10T45) | trivial |
10.0.2340363151.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 3 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,7\cdot 334337593$ | $S_{10}$ (as 10T45) | trivial |
10.0.2343232031.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 3 x + 1$ | $-\,7\cdot 334747433$ | $S_{10}$ (as 10T45) | trivial |
10.0.2343831427.1 | $x^{10} + x^{4} - x^{3} + x^{2} - 2 x + 1$ | $-\,7\cdot 14551\cdot 23011$ | $S_{10}$ (as 10T45) | trivial |
10.2.2382678361.1 | $x^{10} - x^{8} - x^{7} - x^{6} - 2 x^{5} + x^{4} + x^{3} + 3 x^{2} - x + 1$ | $7^{2}\cdot 59^{2}\cdot 61\cdot 229$ | $S_{10}$ (as 10T45) | trivial |
10.0.2433240775.1 | $x^{10} - 2 x^{9} + x^{8} - x^{7} + 3 x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + x^{2} + 1$ | $-\,5^{2}\cdot 7^{2}\cdot 149\cdot 13331$ | $S_{10}$ (as 10T45) | trivial |
10.0.2448037907.1 | $x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} + 3 x^{6} - 2 x^{5} + x^{4} + 2 x^{2} - 2 x + 1$ | $-\,7\cdot 1747\cdot 200183$ | $S_{10}$ (as 10T45) | trivial |
10.0.2481749207.1 | $x^{10} - x^{9} + 3 x^{6} + 2 x^{5} - 4 x^{4} + 3 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,7^{2}\cdot 5647\cdot 8969$ | $S_{10}$ (as 10T45) | trivial |
10.2.2520749581.1 | $x^{10} - 2 x^{9} + 2 x^{8} + x^{7} - 5 x^{6} + 9 x^{5} - 12 x^{4} + 13 x^{3} - 9 x^{2} + 4 x - 1$ | $7^{2}\cdot 89\cdot 578021$ | $S_{10}$ (as 10T45) | trivial |
10.0.2539968116.1 | $x^{10} - x^{9} + x^{7} + 2 x^{6} - x^{5} + 2 x^{4} + x^{3} + 2 x + 1$ | $-\,2^{2}\cdot 7^{2}\cdot 12959021$ | $S_{10}$ (as 10T45) | trivial |
10.0.2632784896.1 | $x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{2} + 1$ | $-\,2^{10}\cdot 7^{2}\cdot 137\cdot 383$ | $S_{10}$ (as 10T45) | trivial |
10.0.2639232512.1 | $x^{10} - 2 x^{9} + 5 x^{8} - 7 x^{7} + 11 x^{6} - 11 x^{5} + 12 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$ | $-\,2^{9}\cdot 7^{2}\cdot 105199$ | $S_{10}$ (as 10T45) | trivial |
10.0.2659086731.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 5 x^{7} + 7 x^{6} - 6 x^{5} + 8 x^{4} - 4 x^{3} + 3 x^{2} - x + 1$ | $-\,7\cdot 89\cdot 4268197$ | $S_{10}$ (as 10T45) | trivial |
10.0.2673672491.1 | $x^{10} - x^{9} - 3 x^{8} + 4 x^{7} + 3 x^{6} - 6 x^{5} + 5 x^{3} - x^{2} - 2 x + 1$ | $-\,7\cdot 381953213$ | $S_{10}$ (as 10T45) | trivial |
10.2.2718826397.1 | $x^{10} - 5 x^{9} + 13 x^{8} - 22 x^{7} + 26 x^{6} - 21 x^{5} + 9 x^{4} + 2 x^{3} - 5 x^{2} + 2 x + 1$ | $7^{2}\cdot 701\cdot 79153$ | $S_{10}$ (as 10T45) | trivial |
10.2.2730344813.1 | $x^{10} - x^{9} - x^{8} + 4 x^{7} - 2 x^{6} - 4 x^{5} + 5 x^{4} - 4 x^{2} + 2 x + 1$ | $7\cdot 43\cdot 9070913$ | $S_{10}$ (as 10T45) | trivial |
10.0.2792932352.1 | $x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 7 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$ | $-\,2^{10}\cdot 7\cdot 31\cdot 12569$ | $S_{10}$ (as 10T45) | trivial |
10.0.2851952747.1 | $x^{10} - x^{9} + 3 x^{7} - 3 x^{6} + 2 x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ | $-\,7\cdot 743\cdot 548347$ | $S_{10}$ (as 10T45) | trivial |
10.0.2916205859.1 | $x^{10} + x^{8} - 2 x^{7} + x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} + 1$ | $-\,7\cdot 541\cdot 770057$ | $S_{10}$ (as 10T45) | trivial |
10.0.3076447367.1 | $x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ | $-\,7\cdot 13177\cdot 33353$ | $S_{10}$ (as 10T45) | trivial |
10.0.3099649987.1 | $x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 5 x^{4} - 2 x^{3} + 4 x^{2} + 1$ | $-\,7^{2}\cdot 19\cdot 3329377$ | $S_{10}$ (as 10T45) | trivial |
10.2.3113754889.1 | $x^{10} - 2 x^{9} + x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 3 x^{4} + 2 x^{2} - x - 1$ | $7\cdot 113\cdot 461\cdot 8539$ | $S_{10}$ (as 10T45) | trivial |