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Label Polynomial Discriminant Galois group Class group
9.3.1735643790720.1 x9 - 9x6 + 9x5 - 6x3 + 9x2 - 2 \( -\,2^{7}\cdot 3^{18}\cdot 5\cdot 7 \) $S_9$ (as 9T34) trivial
9.1.2539579392000.1 x9 - 3x8 + 12x7 - 20x6 + 69x5 - 99x4 + 132x3 - 72x2 - 6x + 10 \( 2^{14}\cdot 3^{11}\cdot 5^{3}\cdot 7 \) $S_9$ (as 9T34) trivial
9.3.34284321792000.1 x9 - 3x8 - 6x7 + 18x6 - 36x5 + 108x4 - 174x3 + 162x2 - 81x + 27 \( -\,2^{13}\cdot 3^{14}\cdot 5^{3}\cdot 7 \) $S_9$ (as 9T34) trivial
9.1.49601160000000.1 x9 - 3x8 - 9x7 + 15x6 + 150x5 - 450x4 + 300x3 + 150x2 - 100 \( 2^{9}\cdot 3^{11}\cdot 5^{7}\cdot 7 \) $S_9$ (as 9T34) trivial
9.1.4601270257436160.1 x9 - 3x8 - 18x7 + 76x6 + 93x5 - 495x4 + 580x3 + 1458x2 - 1836x + 4464 \( 2^{9}\cdot 3^{13}\cdot 5\cdot 7\cdot 11^{5} \) $S_9$ (as 9T34) $[2]$ (GRH)
10.0.967207171.1 x10 - x9 + 3x8 - 5x7 + 4x6 - 6x5 + 4x4 - 2x3 + 2x2 + 1 \( -\,7\cdot 138172453 \) $S_{10}$ (as 10T45) trivial
10.0.982312667.1 x10 - 2x9 + 4x8 - 5x7 + 6x6 - 6x5 + 6x4 - 2x3 + 4x2 + 1 \( -\,7\cdot 37\cdot 919\cdot 4127 \) $S_{10}$ (as 10T45) trivial
10.0.1043341075.1 x10 - x9 - 2x8 + 3x7 + x6 - 3x5 + x4 + x3 - x2 + 1 \( -\,5^{2}\cdot 7^{2}\cdot 103\cdot 8269 \) $S_{10}$ (as 10T45) trivial
10.0.1124443327.1 x10 - 2x8 - 2x7 + 3x6 + 3x5 - 2x4 - 3x3 + 2x + 1 \( -\,7^{2}\cdot 41\cdot 559703 \) $S_{10}$ (as 10T45) trivial
10.0.1251659171.1 x10 - 2x9 + 2x8 - 3x7 + 5x6 - 7x5 + 9x4 - 9x3 + 7x2 - 3x + 1 \( -\,7\cdot 2557\cdot 69929 \) $S_{10}$ (as 10T45) trivial
10.0.1356935111.1 x10 - x9 + 2x8 - 2x7 + 2x6 - x5 + 3x4 - x3 + 3x2 + 1 \( -\,7\cdot 193847873 \) $S_{10}$ (as 10T45) trivial
10.0.1530842075.1 x10 - 3x9 + 3x8 - 2x6 + x5 + 2x4 - x3 - 2x2 + x + 1 \( -\,5^{2}\cdot 7^{2}\cdot 113\cdot 11059 \) $S_{10}$ (as 10T45) trivial
10.0.1629148619.1 x10 - 2x9 + 2x8 + 2x7 - 4x6 + 2x5 + 3x4 - 3x3 - x2 + 2x + 1 \( -\,7^{2}\cdot 131\cdot 253801 \) $S_{10}$ (as 10T45) trivial
10.0.1643385856.1 x10 + 2x8 - x6 - x4 - 2x3 + 3x2 - 2x + 1 \( -\,2^{10}\cdot 7\cdot 229267 \) $S_{10}$ (as 10T45) trivial
10.0.1682646476.1 x10 + x8 - 2x7 + x6 - 4x5 + x4 - x3 + 3x2 + x + 1 \( -\,2^{2}\cdot 7^{2}\cdot 107\cdot 80233 \) $S_{10}$ (as 10T45) trivial
10.0.1795570847.1 x10 - x9 + x7 - 3x6 + 2x5 + x4 - 3x3 + 4x2 - 2x + 1 \( -\,7^{2}\cdot 36644303 \) $S_{10}$ (as 10T45) trivial
10.2.1880601821.1 x10 - x8 - 3x7 - 2x6 + 5x5 + 5x4 - x3 - 4x2 - 2x + 1 \( 7^{2}\cdot 787\cdot 48767 \) $S_{10}$ (as 10T45) trivial
10.0.1887157027.1 x10 - x9 + 2x8 + x6 + 4x5 - x4 + 2x3 + 2x2 + 1 \( -\,7\cdot 491\cdot 549071 \) $S_{10}$ (as 10T45) trivial
10.0.1888076939.1 x10 - x9 + 2x8 - 4x7 + 2x6 - 3x5 + 2x4 + x2 + 1 \( -\,7\cdot 269725277 \) $S_{10}$ (as 10T45) trivial
10.0.1896111791.1 x10 - x9 - x7 + x4 - x3 + x2 + 1 \( -\,7^{2}\cdot 1009\cdot 38351 \) $S_{10}$ (as 10T45) trivial
10.0.1937783792.1 x10 - x9 + 2x8 - x7 + 2x6 + x5 - 3x4 + 3x3 + x2 - 2x + 1 \( -\,2^{4}\cdot 7^{2}\cdot 2471663 \) $S_{10}$ (as 10T45) trivial
10.0.1979862311.1 x10 - 2x9 + 4x8 - 7x7 + 11x6 - 14x5 + 15x4 - 12x3 + 8x2 - 4x + 1 \( -\,7\cdot 6067\cdot 46619 \) $S_{10}$ (as 10T45) trivial
10.2.2012250709.1 x10 - x9 + 2x8 - 2x7 + 4x6 - 7x5 + 10x4 - 10x3 + 7x2 - 4x + 1 \( 7^{2}\cdot 229\cdot 389\cdot 461 \) $S_{10}$ (as 10T45) trivial
10.0.2038643719.1 x10 - x9 + x8 + 2x6 - 3x5 + x4 + 2x3 - 2x2 - x + 1 \( -\,7\cdot 1039\cdot 280303 \) $S_{10}$ (as 10T45) trivial
10.0.2103848971.1 x10 - 3x9 + 5x8 - 2x7 - 5x6 + 10x5 - 5x4 - 4x3 + 7x2 - 4x + 1 \( -\,7\cdot 37\cdot 8122969 \) $S_{10}$ (as 10T45) trivial
10.0.2106354859.1 x10 - 2x9 + 3x8 - x7 + x6 + 2x4 + 2x3 - x2 + x + 1 \( -\,7\cdot 17\cdot 17700461 \) $S_{10}$ (as 10T45) trivial
10.0.2113889743.1 x10 - x9 + 2x8 - x7 + x6 + x5 + 2x4 - x3 + 4x2 - x + 1 \( -\,7^{2}\cdot 43140607 \) $S_{10}$ (as 10T45) trivial
10.0.2288851495.1 x10 - 2x9 + 3x8 - 4x7 + 2x6 - 2x5 + 2x4 + 3x2 + x + 1 \( -\,5\cdot 7^{2}\cdot 71\cdot 131581 \) $S_{10}$ (as 10T45) trivial
10.2.2321314093.1 x10 - x9 - x8 + x7 - 2x5 + x4 + 4x3 - 6x2 + 3x - 1 \( 7^{2}\cdot 67\cdot 707071 \) $S_{10}$ (as 10T45) trivial
10.0.2340363151.1 x10 - x9 + 2x8 - 2x7 + 4x6 - 3x5 + 4x4 - 4x3 + 4x2 - 2x + 1 \( -\,7\cdot 334337593 \) $S_{10}$ (as 10T45) trivial
10.0.2343232031.1 x10 - x9 + 2x8 - 2x7 + 2x5 - 2x4 + x3 + 2x2 - 3x + 1 \( -\,7\cdot 334747433 \) $S_{10}$ (as 10T45) trivial
10.0.2343831427.1 x10 + x4 - x3 + x2 - 2x + 1 \( -\,7\cdot 14551\cdot 23011 \) $S_{10}$ (as 10T45) trivial
10.2.2382678361.1 x10 - x8 - x7 - x6 - 2x5 + x4 + x3 + 3x2 - x + 1 \( 7^{2}\cdot 59^{2}\cdot 61\cdot 229 \) $S_{10}$ (as 10T45) trivial
10.0.2433240775.1 x10 - 2x9 + x8 - x7 + 3x6 - 2x5 + 2x4 - 3x3 + x2 + 1 \( -\,5^{2}\cdot 7^{2}\cdot 149\cdot 13331 \) $S_{10}$ (as 10T45) trivial
10.0.2448037907.1 x10 - 3x9 + 4x8 - 4x7 + 3x6 - 2x5 + x4 + 2x2 - 2x + 1 \( -\,7\cdot 1747\cdot 200183 \) $S_{10}$ (as 10T45) trivial
10.0.2481749207.1 x10 - x9 + 3x6 + 2x5 - 4x4 + 3x3 + 2x2 - 2x + 1 \( -\,7^{2}\cdot 5647\cdot 8969 \) $S_{10}$ (as 10T45) trivial
10.2.2520749581.1 x10 - 2x9 + 2x8 + x7 - 5x6 + 9x5 - 12x4 + 13x3 - 9x2 + 4x - 1 \( 7^{2}\cdot 89\cdot 578021 \) $S_{10}$ (as 10T45) trivial
10.0.2539968116.1 x10 - x9 + x7 + 2x6 - x5 + 2x4 + x3 + 2x + 1 \( -\,2^{2}\cdot 7^{2}\cdot 12959021 \) $S_{10}$ (as 10T45) trivial
10.0.2632784896.1 x10 - 2x9 + 4x8 - 4x7 + 5x6 - 2x5 + 2x4 + 2x2 + 1 \( -\,2^{10}\cdot 7^{2}\cdot 137\cdot 383 \) $S_{10}$ (as 10T45) trivial
10.0.2639232512.1 x10 - 2x9 + 5x8 - 7x7 + 11x6 - 11x5 + 12x4 - 8x3 + 6x2 - 3x + 1 \( -\,2^{9}\cdot 7^{2}\cdot 105199 \) $S_{10}$ (as 10T45) trivial
10.0.2659086731.1 x10 - 2x9 + 3x8 - 5x7 + 7x6 - 6x5 + 8x4 - 4x3 + 3x2 - x + 1 \( -\,7\cdot 89\cdot 4268197 \) $S_{10}$ (as 10T45) trivial
10.0.2673672491.1 x10 - x9 - 3x8 + 4x7 + 3x6 - 6x5 + 5x3 - x2 - 2x + 1 \( -\,7\cdot 381953213 \) $S_{10}$ (as 10T45) trivial
10.2.2718826397.1 x10 - 5x9 + 13x8 - 22x7 + 26x6 - 21x5 + 9x4 + 2x3 - 5x2 + 2x + 1 \( 7^{2}\cdot 701\cdot 79153 \) $S_{10}$ (as 10T45) trivial
10.2.2730344813.1 x10 - x9 - x8 + 4x7 - 2x6 - 4x5 + 5x4 - 4x2 + 2x + 1 \( 7\cdot 43\cdot 9070913 \) $S_{10}$ (as 10T45) trivial
10.0.2792932352.1 x10 - 2x9 + 2x8 - 4x7 + 8x6 - 8x5 + 7x4 - 8x3 + 8x2 - 4x + 1 \( -\,2^{10}\cdot 7\cdot 31\cdot 12569 \) $S_{10}$ (as 10T45) trivial
10.0.2851952747.1 x10 - x9 + 3x7 - 3x6 + 2x5 + 2x4 - 4x3 + 4x2 - 2x + 1 \( -\,7\cdot 743\cdot 548347 \) $S_{10}$ (as 10T45) trivial
10.0.2916205859.1 x10 + x8 - 2x7 + x6 - x5 + 4x4 - 4x3 + 2x2 + 1 \( -\,7\cdot 541\cdot 770057 \) $S_{10}$ (as 10T45) trivial
10.0.3076447367.1 x10 - x9 + 2x8 - 2x7 + 2x6 - 2x5 + 3x4 - 3x3 + 2x2 - 2x + 1 \( -\,7\cdot 13177\cdot 33353 \) $S_{10}$ (as 10T45) trivial
10.0.3099649987.1 x10 - 2x9 + 3x8 - 4x7 + 4x6 - 5x5 + 5x4 - 2x3 + 4x2 + 1 \( -\,7^{2}\cdot 19\cdot 3329377 \) $S_{10}$ (as 10T45) trivial
10.2.3113754889.1 x10 - 2x9 + x8 - 2x7 + 3x6 + x5 - 3x4 + 2x2 - x - 1 \( 7\cdot 113\cdot 461\cdot 8539 \) $S_{10}$ (as 10T45) trivial
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