## Results (1-50 of at least 1000)

Next   To download results, determine the number of results.
Label Polynomial Discriminant Galois group Class group
16.0.10749542400000000.1 $x^{16} - 2 x^{15} + x^{14} + 6 x^{13} - 15 x^{12} + 13 x^{11} + 15 x^{10} - 45 x^{9} + 42 x^{8} + 14 x^{7} - 65 x^{6} + 50 x^{5} + 3 x^{4} - 29 x^{3} + 21 x^{2} - 7 x + 1$ $2^{22}\cdot 3^{8}\cdot 5^{8}$ $D_8:C_4$ (as 16T114) trivial
16.0.12370583534765625.1 $x^{16} - 7 x^{15} + 24 x^{14} - 50 x^{13} + 65 x^{12} - 40 x^{11} - 28 x^{10} + 94 x^{9} - 94 x^{8} + 16 x^{7} + 82 x^{6} - 128 x^{5} + 108 x^{4} - 59 x^{3} + 22 x^{2} - 6 x + 1$ $3^{8}\cdot 5^{8}\cdot 13^{6}$ $D_8:C_2$ (as 16T44) trivial
16.2.19666546293359375.1 $x^{16} - 3 x^{15} + 5 x^{14} - 4 x^{13} - x^{12} + 6 x^{11} - 6 x^{10} - 8 x^{9} + 20 x^{8} - 19 x^{7} + 11 x^{6} + 4 x^{5} - 14 x^{4} + 4 x^{3} + 5 x^{2} - x - 1$ $-\,5^{8}\cdot 31^{2}\cdot 71\cdot 859^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.0.22028181368750000.1 $x^{16} - 3 x^{15} + 3 x^{14} - 2 x^{13} + 2 x^{12} + 5 x^{11} - 19 x^{10} + 28 x^{9} - 27 x^{8} + 12 x^{7} + 19 x^{6} - 58 x^{5} + 78 x^{4} - 62 x^{3} + 32 x^{2} - 9 x + 1$ $2^{4}\cdot 5^{8}\cdot 59^{3}\cdot 131^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.0.26987918400000000.1 $x^{16} - x^{15} + x^{14} - 5 x^{13} + 4 x^{12} + 5 x^{11} - 4 x^{10} - 9 x^{8} + 12 x^{7} + 2 x^{6} - 9 x^{5} + 8 x^{4} - 7 x^{3} + x^{2} + x + 1$ $2^{12}\cdot 3^{2}\cdot 5^{8}\cdot 37^{4}$ $(C_2^3\times C_4):S_4$ (as 16T1046) trivial
16.0.29862086714453125.1 $x^{16} - 3 x^{15} + 3 x^{14} + x^{13} - 4 x^{12} + 2 x^{11} + 5 x^{10} - 9 x^{9} + 3 x^{8} + 9 x^{7} - 9 x^{6} - 4 x^{5} + 9 x^{4} - x^{3} - 4 x^{2} + x + 1$ $5^{8}\cdot 11^{4}\cdot 151^{2}\cdot 229$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.0.31269954097265625.1 $x^{16} - 4 x^{15} + 5 x^{14} + 5 x^{13} - 24 x^{12} + 31 x^{11} - 4 x^{10} - 44 x^{9} + 69 x^{8} - 44 x^{7} - 4 x^{6} + 31 x^{5} - 24 x^{4} + 5 x^{3} + 5 x^{2} - 4 x + 1$ $3^{8}\cdot 5^{8}\cdot 7^{2}\cdot 499^{2}$ $S_4^2:C_2^2$ (as 16T1494) trivial
16.0.31673320900000000.1 $x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} + 14 x^{12} - 10 x^{11} + 20 x^{10} - 34 x^{9} + 20 x^{8} - 12 x^{7} + 20 x^{6} - 10 x^{5} - x^{4} - 4 x^{3} + 8 x^{2} - 4 x + 1$ $2^{8}\cdot 5^{8}\cdot 13^{2}\cdot 37^{4}$ $(C_2^3\times C_4):S_4$ (as 16T1046) trivial
16.2.36286162879296875.1 $x^{16} - 2 x^{15} + x^{14} + 3 x^{13} - 11 x^{12} + 16 x^{11} - 17 x^{10} + 16 x^{9} - 13 x^{8} + 16 x^{7} - 17 x^{6} + 16 x^{5} - 11 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$ $-\,5^{8}\cdot 31^{2}\cdot 131\cdot 859^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.2.45287535480859375.1 $x^{16} - 3 x^{15} + 6 x^{14} - 11 x^{13} + 14 x^{12} - 16 x^{11} + 13 x^{10} - 8 x^{9} + 7 x^{8} - 8 x^{7} + 13 x^{6} - 16 x^{5} + 14 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ $-\,5^{8}\cdot 11^{4}\cdot 151\cdot 229^{2}$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.2.67969704100000000.1 $x^{16} - 3 x^{14} + x^{12} + 3 x^{10} + 2 x^{8} - x^{6} - 9 x^{4} - 4 x^{2} - 1$ $-\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{2}$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.2.80157081600000000.1 $x^{16} - 2 x^{15} + x^{14} - 3 x^{12} - 2 x^{11} + 19 x^{10} - 4 x^{9} - 37 x^{8} + 28 x^{7} + 19 x^{6} - 30 x^{5} + 6 x^{4} + 10 x^{3} - 6 x^{2} + 1$ $-\,2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151$ $C_2\wr D_4.C_2$ (as 16T1577) trivial
16.2.86899140707421875.1 $x^{16} - 5 x^{15} + 10 x^{14} - 9 x^{13} - 2 x^{12} + 17 x^{11} - 21 x^{10} + 11 x^{9} + x^{8} - 7 x^{7} + 2 x^{6} + 5 x^{5} - 12 x^{4} + 14 x^{3} - 9 x^{2} + 4 x - 1$ $-\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131$ $C_2^7.C_2\wr D_4$ (as 16T1778) trivial
16.2.115558273191796875.1 $x^{16} + 2 x^{14} - 5 x^{13} - x^{12} - 10 x^{11} + 3 x^{10} - 4 x^{9} + 9 x^{8} - 4 x^{7} + 8 x^{6} - x^{5} + 7 x^{4} + 4 x^{2} - x + 1$ $-\,3^{4}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 691$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.0.122444006400000000.1 $x^{16} - 2 x^{15} + 9 x^{14} - 10 x^{13} + 32 x^{12} - 21 x^{11} + 64 x^{10} - 17 x^{9} + 81 x^{8} + x^{7} + 52 x^{6} + 9 x^{5} + 8 x^{4} + 5 x^{3} - 3 x^{2} + x + 1$ $2^{16}\cdot 3^{14}\cdot 5^{8}$ $(C_4\times C_8):D_4$ (as 16T513) trivial
16.0.152812774400000000.1 $x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} + 6 x^{11} - 4 x^{10} - 4 x^{9} + 15 x^{8} - 4 x^{7} - 4 x^{6} + 6 x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$ $2^{16}\cdot 5^{8}\cdot 11\cdot 13^{4}\cdot 19$ $C_2^7.C_2\wr D_4$ (as 16T1778) trivial
16.0.156383420761328125.1 $x^{16} - 3 x^{15} + 4 x^{14} + x^{13} - 5 x^{12} + 12 x^{10} - 5 x^{9} - 8 x^{8} + 10 x^{7} + 11 x^{6} - 8 x^{5} - x^{4} + 7 x^{3} + x^{2} - 2 x + 1$ $5^{8}\cdot 19\cdot 29^{4}\cdot 31^{3}$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.2.173942237590234375.1 $x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 3 x^{11} + 2 x^{10} + x^{8} + 2 x^{6} - 3 x^{5} + 2 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$ $-\,5^{8}\cdot 31\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.0.178853944618750000.1 $x^{16} - 4 x^{15} + 11 x^{14} - 19 x^{13} + 24 x^{12} - 21 x^{11} + 11 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{6} - 9 x^{5} + 9 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$ $2^{4}\cdot 5^{8}\cdot 19\cdot 197^{4}$ $C_2\wr C_2^3.S_4$ (as 16T1846) trivial
16.0.180355734956640625.1 $x^{16} - 5 x^{15} + 14 x^{14} - 28 x^{13} + 46 x^{12} - 63 x^{11} + 73 x^{10} - 72 x^{9} + 57 x^{8} - 34 x^{7} + 23 x^{6} - 21 x^{5} + 8 x^{4} + 8 x^{3} - 7 x^{2} + 1$ $5^{8}\cdot 59^{3}\cdot 131^{3}$ $Q_8^2.A_4^2.D_4$ (as 16T1871) trivial
16.0.180355734956640625.2 $x^{16} - 5 x^{15} + 7 x^{14} + 2 x^{13} - 10 x^{12} + 2 x^{11} + 7 x^{10} - 8 x^{9} + 3 x^{8} + 10 x^{7} - 16 x^{6} + 8 x^{5} + 5 x^{4} - 7 x^{3} + 3 x^{2} - 2 x + 1$ $5^{8}\cdot 59^{3}\cdot 131^{3}$ $Q_8^2.A_4^2.D_4$ (as 16T1871) trivial
16.4.188981478400000000.1 $x^{16} - 2 x^{15} + 3 x^{14} - 7 x^{12} + 10 x^{11} + 4 x^{10} - 22 x^{9} + 17 x^{8} + 20 x^{7} - 36 x^{6} + 28 x^{4} - 8 x^{3} - 10 x^{2} + 2 x + 1$ $2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}$ $C_2^7.C_2\wr D_4$ (as 16T1772) trivial
16.0.189837888276953125.1 $x^{16} - 2 x^{15} + 3 x^{14} - 8 x^{13} + 9 x^{12} - 5 x^{11} + 12 x^{10} - 7 x^{9} - 2 x^{8} - 11 x^{7} + 7 x^{6} + 5 x^{5} + 6 x^{4} - 7 x^{3} - x^{2} + 1$ $5^{8}\cdot 11^{4}\cdot 29^{3}\cdot 1361$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.2.195238297600000000.1 $x^{16} - 4 x^{15} + 6 x^{14} - 6 x^{13} + 10 x^{12} - 26 x^{11} + 52 x^{10} - 54 x^{9} - 12 x^{8} + 82 x^{7} - 54 x^{6} - 24 x^{5} + 49 x^{4} - 32 x^{3} + 16 x^{2} - 6 x + 1$ $-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ $C_4^4:D_4$ (as 16T1477) trivial
16.2.195238297600000000.2 $x^{16} - 6 x^{15} + 14 x^{14} - 14 x^{13} + 2 x^{12} - 4 x^{11} + 40 x^{10} - 78 x^{9} + 79 x^{8} - 52 x^{7} + 36 x^{6} - 34 x^{5} + 26 x^{4} - 18 x^{3} + 10 x^{2} - 4 x + 1$ $-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ $D_8\wr C_2$ (as 16T972) trivial
16.2.195238297600000000.3 $x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 51 x^{12} - 46 x^{11} + 18 x^{10} - 4 x^{9} + 44 x^{8} - 118 x^{7} + 160 x^{6} - 138 x^{5} + 72 x^{4} - 16 x^{3} - 4 x^{2} + 4 x - 1$ $-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ $D_8\wr C_2$ (as 16T972) trivial
16.4.232292068597265625.1 $x^{16} - x^{15} + 5 x^{14} - x^{13} + x^{11} - 19 x^{10} - 13 x^{9} - 20 x^{8} - 11 x^{7} + 17 x^{6} + 35 x^{5} + 46 x^{4} + 36 x^{3} + 22 x^{2} + 4 x - 1$ $3^{6}\cdot 5^{8}\cdot 13^{8}$ $D_8:C_2$ (as 16T44) trivial
16.4.232322192503515625.1 $x^{16} - 3 x^{15} + 2 x^{14} + 7 x^{13} - 15 x^{12} + 12 x^{11} - 6 x^{10} + 16 x^{9} - 24 x^{8} - 5 x^{7} + 67 x^{6} - 114 x^{5} + 110 x^{4} - 70 x^{3} + 30 x^{2} - 8 x + 1$ $5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 131^{2}$ $C_2^7.C_2\wr D_4$ (as 16T1772) trivial
16.0.243112369495703125.1 $x^{16} - 2 x^{15} + 5 x^{14} - x^{13} + 11 x^{11} + x^{10} - x^{9} + 23 x^{8} - 8 x^{7} + 14 x^{6} + 2 x^{5} + 10 x^{4} - 3 x^{3} + 5 x^{2} + x + 1$ $5^{8}\cdot 11^{4}\cdot 349^{3}$ $D_8\wr C_2$ (as 16T972) trivial
16.4.243112369495703125.1 $x^{16} - x^{15} - 3 x^{14} + x^{13} + x^{12} - 3 x^{10} + 2 x^{9} - 4 x^{8} + 11 x^{7} + 13 x^{6} - 25 x^{5} - 4 x^{4} + 13 x^{3} - 2 x^{2} - 2 x + 1$ $5^{8}\cdot 11^{4}\cdot 349^{3}$ $C_4\wr D_4$ (as 16T1432) trivial
16.0.256572640900000000.1 $x^{16} - 3 x^{15} + 14 x^{14} - 27 x^{13} + 67 x^{12} - 89 x^{11} + 151 x^{10} - 144 x^{9} + 188 x^{8} - 132 x^{7} + 139 x^{6} - 68 x^{5} + 57 x^{4} - 16 x^{3} + 11 x^{2} - x + 1$ $2^{8}\cdot 5^{8}\cdot 37^{6}$ $Q_8.(C_2\times S_4)$ (as 16T739) trivial
16.0.311829406284765625.1 $x^{16} + 2 x^{14} - 3 x^{13} + 3 x^{12} - x^{11} + 6 x^{10} + 13 x^{9} + 8 x^{8} + 19 x^{7} + 4 x^{5} + 12 x^{4} - 17 x^{3} + 12 x^{2} - x + 1$ $5^{8}\cdot 61^{2}\cdot 97^{2}\cdot 151^{2}$ $C_2^6.S_4^2:C_2^2$ (as 16T1884) trivial
16.2.398383834480859375.1 $x^{16} - 3 x^{15} + 6 x^{14} - 4 x^{13} - x^{12} + 9 x^{11} - 15 x^{10} + 16 x^{9} - 17 x^{8} + 16 x^{7} - 15 x^{6} + 9 x^{5} - x^{4} - 4 x^{3} + 6 x^{2} - 3 x + 1$ $-\,5^{8}\cdot 71\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.2.472848769600000000.1 $x^{16} - 4 x^{14} + 9 x^{12} - 14 x^{10} + 17 x^{8} - 13 x^{6} + 4 x^{4} + 2 x^{2} - 1$ $-\,2^{12}\cdot 5^{8}\cdot 17191^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.4.499382553081640625.1 $x^{16} - 3 x^{15} + x^{14} + 9 x^{13} - 21 x^{12} + 24 x^{11} - 12 x^{10} - 8 x^{9} + 17 x^{8} - 8 x^{7} - 12 x^{6} + 24 x^{5} - 21 x^{4} + 9 x^{3} + x^{2} - 3 x + 1$ $5^{8}\cdot 89\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.4.499382553081640625.2 $x^{16} - 2 x^{15} + 4 x^{14} - 5 x^{13} - 2 x^{12} - x^{11} - 8 x^{10} + 3 x^{9} + 6 x^{8} + 10 x^{7} + 4 x^{6} - x^{5} - 16 x^{4} - 24 x^{3} - 18 x^{2} - 9 x - 1$ $5^{8}\cdot 89\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.6.505241847543359375.1 $x^{16} - x^{15} - 3 x^{14} + 10 x^{13} - 13 x^{12} + 6 x^{11} + 12 x^{10} - 33 x^{9} + 41 x^{8} - 33 x^{7} + 12 x^{6} + 6 x^{5} - 13 x^{4} + 10 x^{3} - 3 x^{2} - x + 1$ $-\,5^{8}\cdot 71^{3}\cdot 1901^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.0.513114342400000000.1 $x^{16} - 4 x^{13} + 7 x^{12} - 8 x^{11} + 8 x^{10} - 20 x^{9} + 49 x^{8} - 36 x^{7} - 28 x^{6} + 44 x^{5} + 5 x^{4} - 20 x^{3} - 2 x^{2} + 4 x + 1$ $2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2}$ $C_2^7.C_2\wr D_4$ (as 16T1772) trivial
16.4.513114342400000000.2 $x^{16} - 4 x^{15} + 6 x^{14} - 12 x^{13} + 25 x^{12} - 10 x^{11} - 15 x^{10} - 36 x^{9} + 83 x^{8} + 2 x^{7} - 81 x^{6} + 32 x^{5} + 20 x^{4} - 12 x^{3} + 3 x^{2} - 1$ $2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2}$ $C_2^7.C_2\wr D_4$ (as 16T1772) trivial
16.6.561298201600000000.1 $x^{16} - 8 x^{15} + 28 x^{14} - 56 x^{13} + 61 x^{12} - 2 x^{11} - 107 x^{10} + 172 x^{9} - 129 x^{8} + 34 x^{7} + 21 x^{6} - 20 x^{5} + 8 x^{4} - 6 x^{3} + 3 x^{2} - 1$ $-\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 31$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.0.590315622400000000.1 $x^{16} - 2 x^{15} + 3 x^{14} - 7 x^{13} + 12 x^{12} - 11 x^{11} + 14 x^{10} - 9 x^{9} + 5 x^{8} - 3 x^{7} + x^{6} - 8 x^{5} + 27 x^{4} - 14 x^{3} + 2 x^{2} - x + 1$ $2^{18}\cdot 5^{8}\cdot 7^{8}$ $D_8:C_2$ (as 16T44) trivial
16.4.611603351526953125.1 $x^{16} - x^{15} + x^{13} - 12 x^{12} - 2 x^{11} - 14 x^{10} - 25 x^{9} - 5 x^{8} - 25 x^{7} - 14 x^{6} - 2 x^{5} - 12 x^{4} + x^{3} - x + 1$ $5^{8}\cdot 109\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.2.638966001996484375.1 $x^{16} - x^{13} + 2 x^{12} - 6 x^{11} + 4 x^{10} - x^{9} + x^{8} - x^{7} + 4 x^{6} - 6 x^{5} + 2 x^{4} - x^{3} + 1$ $-\,5^{8}\cdot 29^{2}\cdot 31\cdot 89^{4}$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.2.641424792100000000.1 $x^{16} - 2 x^{14} - 8 x^{12} + 16 x^{10} + 11 x^{8} - 18 x^{6} + 3 x^{4} - x^{2} - 1$ $-\,2^{8}\cdot 5^{8}\cdot 283^{4}$ $C_{2440}.D_6$ (as 16T1759) trivial
16.4.683032622823828125.1 $x^{16} - x^{15} - 2 x^{14} - 4 x^{13} - 5 x^{12} - x^{11} + 6 x^{10} + 13 x^{9} + 15 x^{8} + 13 x^{7} + 6 x^{6} - x^{5} - 5 x^{4} - 4 x^{3} - 2 x^{2} - x + 1$ $5^{8}\cdot 29\cdot 31^{2}\cdot 89^{4}$ $C_4^4.C_2\wr D_4$ (as 16T1823) trivial
16.0.748709478400000000.1 $x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} - 3 x^{12} + 6 x^{11} - 8 x^{10} - 10 x^{9} + 48 x^{8} - 90 x^{7} + 122 x^{6} - 114 x^{5} + 83 x^{4} - 44 x^{3} + 17 x^{2} - 4 x + 1$ $2^{26}\cdot 5^{8}\cdot 13^{4}$ $C_2^2.C_2\wr C_2^3$ (as 16T1701) trivial
16.4.771024486400000000.1 $x^{16} - 2 x^{15} - x^{14} - 6 x^{11} + 24 x^{10} + 20 x^{9} - 24 x^{8} - 38 x^{7} + 5 x^{6} + 20 x^{5} - 18 x^{4} + 6 x^{3} - 4 x^{2} + 1$ $2^{24}\cdot 5^{8}\cdot 7^{6}$ $D_8:C_2$ (as 16T44) trivial
16.6.847267028262109375.1 $x^{16} - 7 x^{15} + 19 x^{14} - 27 x^{13} + 19 x^{12} + 6 x^{11} - 38 x^{10} + 66 x^{9} - 77 x^{8} + 66 x^{7} - 38 x^{6} + 6 x^{5} + 19 x^{4} - 27 x^{3} + 19 x^{2} - 7 x + 1$ $-\,5^{8}\cdot 151\cdot 119851^{2}$ $C_2^6.S_4^2:D_4$ (as 16T1905) trivial
16.4.882697830400000000.1 $x^{16} - 2 x^{15} + x^{14} + 4 x^{13} - 5 x^{12} + 2 x^{11} + 3 x^{10} + x^{8} + 3 x^{6} - 2 x^{5} - 5 x^{4} - 4 x^{3} + x^{2} + 2 x + 1$ $2^{24}\cdot 5^{8}\cdot 367^{2}$ $S_4^2:C_2^2$ (as 16T1494) trivial
16.4.887213286400000000.2 $x^{16} - 2 x^{15} - 3 x^{14} + 8 x^{12} + 4 x^{11} - x^{10} + 10 x^{9} + 15 x^{8} + 10 x^{7} - x^{6} + 4 x^{5} + 8 x^{4} - 3 x^{2} - 2 x + 1$ $2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4}$ $C_2^7.C_2\wr D_4$ (as 16T1772) trivial
Next   To download results, determine the number of results.