| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 18.10.684...177.1 |
$x^{18} - 4 x^{17} - x^{16} + 12 x^{15} + 15 x^{14} - 21 x^{13} - 62 x^{12} - 3 x^{11} + 117 x^{10} + 86 x^{9} - 121 x^{8} - 128 x^{7} + 57 x^{6} + 70 x^{5} - 6 x^{4} - 9 x^{3} - x^{2} - 2 x + 1$ |
$18$ |
[10,4] |
$73\cdot 9685993193^{2}$ |
$2$ |
$16.3338856158$ |
$840879.0062125466$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$13$ |
$14292.7475309$ |
| 18.10.834...161.1 |
$x^{18} - 9 x^{17} + 34 x^{16} - 68 x^{15} + 60 x^{14} + 56 x^{13} - 254 x^{12} + 354 x^{11} - 193 x^{10} - 135 x^{9} + 327 x^{8} - 218 x^{7} - 12 x^{6} + 114 x^{5} - 63 x^{4} - 6 x^{3} + 14 x^{2} - 2 x - 1$ |
$18$ |
[10,4] |
$89\cdot 9685993193^{2}$ |
$2$ |
$16.5147125194$ |
$928468.3054240462$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$13$ |
$16166.3861004$ |
| 18.10.106...197.1 |
$x^{18} - 6 x^{17} + 7 x^{16} + 21 x^{15} - 49 x^{14} - 5 x^{13} + 87 x^{12} - 97 x^{11} + 63 x^{10} + 116 x^{9} - 329 x^{8} + 93 x^{7} + 293 x^{6} - 176 x^{5} - 84 x^{4} + 59 x^{3} + 12 x^{2} - 6 x - 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 37$ |
$2$ |
$16.7414158995$ |
$83.32411881951172$ |
|
|
? |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$13$ |
$18497.6611092$ |
| 18.10.113...129.1 |
$x^{18} - 5 x^{17} + 7 x^{16} + 12 x^{15} - 49 x^{14} + 22 x^{13} + 97 x^{12} - 132 x^{11} - 48 x^{10} + 256 x^{9} - 151 x^{8} - 165 x^{7} + 222 x^{6} - 41 x^{5} - 73 x^{4} + 59 x^{3} - 7 x^{2} - 5 x + 1$ |
$18$ |
[10,4] |
$11^{2}\cdot 9685993193^{2}$ |
$2$ |
$16.7989397169$ |
$326413.73304902477$ |
|
|
? |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$13$ |
$19199.1457844$ |
| 18.10.119...029.1 |
$x^{18} - 9 x^{17} + 27 x^{16} - 12 x^{15} - 93 x^{14} + 147 x^{13} + 82 x^{12} - 297 x^{11} + 15 x^{10} + 288 x^{9} - 36 x^{8} - 171 x^{7} - 17 x^{6} + 66 x^{5} + 34 x^{4} - 14 x^{3} - 13 x^{2} + 2 x + 1$ |
$18$ |
[10,4] |
$109^{2}\cdot 541^{2}\cdot 12041^{2}\cdot 23669$ |
$4$ |
$16.8455910233$ |
$4099520.991494128$ |
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$13$ |
$19444.9360928$ |
| 18.10.158...081.1 |
$x^{18} - 5 x^{17} + 37 x^{15} - 50 x^{14} - 54 x^{13} + 130 x^{12} - 18 x^{11} - 35 x^{10} - 49 x^{9} - 4 x^{8} + 97 x^{7} - 76 x^{6} + 43 x^{5} - 15 x^{4} + 2 x^{3} + 2 x^{2} - 4 x - 1$ |
$18$ |
[10,4] |
$13^{2}\cdot 9685993193^{2}$ |
$2$ |
$17.1136661997$ |
$354849.1390844847$ |
|
|
? |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$13$ |
$22900.369309$ |
| 18.10.172...784.1 |
$x^{18} + 2 x^{16} - 16 x^{14} - 26 x^{12} + 73 x^{10} + 57 x^{8} - 132 x^{6} + 33 x^{4} + 8 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{6}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$17.1966729307$ |
$475.2592197863912$ |
|
|
? |
$A_4^3.S_4$ (as 18T711) |
trivial |
$2$ |
$13$ |
$25666.1336978$ |
| 18.10.196...456.1 |
$x^{18} - 9 x^{16} - 8 x^{15} + 24 x^{14} + 41 x^{13} - 21 x^{12} - 91 x^{11} - 14 x^{10} + 151 x^{9} + 112 x^{8} - 119 x^{7} - 161 x^{6} + 5 x^{5} + 79 x^{4} + 27 x^{3} - 10 x^{2} - 7 x - 1$ |
$18$ |
[10,4] |
$2^{6}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$17.3181161646$ |
$75.34971632639669$ |
|
|
? |
$C_2^4:(A_4\times S_4)$ (as 18T463) |
trivial |
$2$ |
$13$ |
$27389.85224$ |
| 18.10.297...113.1 |
$x^{18} - 7 x^{17} + 16 x^{16} - 6 x^{15} - 41 x^{14} + 97 x^{13} - 93 x^{12} - 6 x^{11} + 141 x^{10} - 205 x^{9} + 141 x^{8} - 6 x^{7} - 93 x^{6} + 97 x^{5} - 41 x^{4} - 6 x^{3} + 16 x^{2} - 7 x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 53^{6}\cdot 97$ |
$3$ |
$17.7228484583$ |
$262.3750263924331$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$13$ |
$32865.549989$ |
| 18.10.434...129.1 |
$x^{18} - 3 x^{17} - 3 x^{16} + 14 x^{15} - 11 x^{14} + 25 x^{13} - 28 x^{12} - 75 x^{11} + 161 x^{10} - 138 x^{9} + 34 x^{8} + 178 x^{7} - 246 x^{6} + 16 x^{5} + 216 x^{4} - 196 x^{3} + 51 x^{2} + 6 x - 1$ |
$18$ |
[10,4] |
$23^{2}\cdot 5569^{3}\cdot 21817^{2}$ |
$3$ |
$18.1003775061$ |
$456661.4457254442$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$13$ |
$40229.7394727$ |
| 18.10.539...576.1 |
$x^{18} + 3 x^{16} - 4 x^{14} - 11 x^{12} + 4 x^{10} - 4 x^{8} + 33 x^{6} - 32 x^{4} + 10 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 453771377^{2}$ |
$2$ |
$18.3189587332$ |
|
|
|
? |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$13$ |
$45411.702991$ |
| 18.10.544...984.1 |
$x^{18} - 8 x^{16} + 22 x^{14} - 26 x^{12} + 20 x^{10} - 20 x^{8} + 6 x^{6} + 2 x^{4} + 5 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 109^{2}\cdot 4181741^{2}$ |
$3$ |
$18.3280839544$ |
|
|
|
? |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$13$ |
$44619.8002677$ |
| 18.10.554...001.1 |
$x^{18} - 6 x^{17} + 13 x^{16} - 12 x^{15} - 8 x^{14} + 56 x^{13} - 92 x^{12} + 64 x^{11} - 25 x^{10} + 24 x^{9} + 81 x^{8} - 221 x^{7} + 116 x^{6} - 31 x^{5} + 102 x^{4} - 54 x^{3} - 14 x^{2} + 6 x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 13^{4}\cdot 41\cdot 43^{4}$ |
$4$ |
$18.3456774602$ |
$1590.0050131901644$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$13$ |
$48685.4371082$ |
| 18.10.573...376.1 |
$x^{18} - 8 x^{16} + 19 x^{14} - 4 x^{12} - 27 x^{10} + x^{8} + 27 x^{6} - 9 x^{4} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
✓ |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$13$ |
$46344.8590159$ |
| 18.10.573...376.2 |
$x^{18} - 7 x^{16} + 21 x^{14} - 41 x^{12} + 49 x^{10} - 28 x^{8} + 12 x^{6} - 14 x^{4} + 7 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$18.3814306573$ |
|
|
|
? |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$13$ |
$46475.4634993$ |
| 18.10.638...904.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 10 x^{15} - 44 x^{14} + 60 x^{13} - 44 x^{12} - 10 x^{11} + 78 x^{10} - 116 x^{9} + 78 x^{8} - 10 x^{7} - 44 x^{6} + 60 x^{5} - 44 x^{4} + 10 x^{3} + 9 x^{2} - 6 x + 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 101^{6}\cdot 479^{2}$ |
$3$ |
$18.4906499645$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$2$ |
$13$ |
$53450.3306034$ |
| 18.10.669...569.1 |
$x^{18} - 4 x^{17} + 8 x^{15} - 3 x^{14} + 6 x^{13} + 14 x^{12} - 18 x^{11} - 59 x^{10} - 26 x^{9} + 69 x^{8} + 92 x^{7} + 23 x^{6} - 67 x^{5} - 69 x^{4} - x^{3} + 23 x^{2} + 9 x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 97^{2}\cdot 22679^{2}$ |
$3$ |
$18.5399824833$ |
$5427.458494884186$ |
|
|
? |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$13$ |
$52945.8391576$ |
| 18.10.669...569.2 |
$x^{18} - 6 x^{16} - 4 x^{15} - 12 x^{14} - 10 x^{13} + 111 x^{12} + 194 x^{11} - 28 x^{10} - 377 x^{9} - 412 x^{8} - 17 x^{7} + 333 x^{6} + 281 x^{5} + 54 x^{4} - 53 x^{3} - 28 x^{2} + x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 97^{2}\cdot 22679^{2}$ |
$3$ |
$18.5399824833$ |
$5427.458494884186$ |
|
|
? |
$S_4^3.A_4$ (as 18T838) |
trivial |
$2$ |
$13$ |
$49344.1641862$ |
| 18.10.669...569.3 |
$x^{18} - 3 x^{17} + 3 x^{16} - 18 x^{14} + 37 x^{13} - 27 x^{12} - 12 x^{11} + 107 x^{10} - 158 x^{9} - 7 x^{8} + 207 x^{7} - 134 x^{6} - 64 x^{5} + 90 x^{4} - 10 x^{3} - 16 x^{2} + 2 x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 97^{2}\cdot 22679^{2}$ |
$3$ |
$18.5399824833$ |
$5427.458494884186$ |
|
|
? |
$S_4^3.A_4$ (as 18T838) |
trivial |
$2$ |
$13$ |
$49273.3749081$ |
| 18.10.855...992.1 |
$x^{18} - 4 x^{17} + 3 x^{16} + 14 x^{15} - 46 x^{14} + 41 x^{13} + 72 x^{12} - 216 x^{11} + 76 x^{10} + 273 x^{9} - 151 x^{8} - 170 x^{7} + 53 x^{6} + 93 x^{5} - 79 x^{4} + 45 x^{3} - 7 x + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 37^{9}\cdot 401^{2}$ |
$3$ |
$18.794284184$ |
$193.35691669702553$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$13$ |
$57675.2080079$ |
| 18.10.946...001.1 |
$x^{18} - 3 x^{17} - 4 x^{16} + 32 x^{15} - 38 x^{14} - 92 x^{13} + 269 x^{12} - 37 x^{11} - 577 x^{10} + 459 x^{9} + 400 x^{8} - 596 x^{7} + 54 x^{6} + 295 x^{5} - 75 x^{4} - 92 x^{3} - 6 x^{2} + 10 x + 1$ |
$18$ |
[10,4] |
$83\cdot 1523\cdot 865377817^{2}$ |
$3$ |
$18.8997027136$ |
$10459041.278680995$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$13$ |
$72171.5666031$ |
| 18.10.100...536.1 |
$x^{18} - 8 x^{16} - 3 x^{15} + 6 x^{14} - 14 x^{13} + 28 x^{12} + 68 x^{11} - 70 x^{10} - 101 x^{9} + 62 x^{8} + 66 x^{7} - 8 x^{6} - 2 x^{5} - 10 x^{4} - 19 x^{3} - 2 x^{2} + 4 x + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 101^{7}\cdot 479^{2}$ |
$3$ |
$18.9653137963$ |
$349.15246089026516$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T773) |
trivial |
$2$ |
$13$ |
$68769.6627504$ |
| 18.10.140...525.1 |
$x^{18} - x^{17} - 9 x^{16} + 15 x^{15} + 17 x^{14} - 71 x^{13} + 30 x^{12} + 89 x^{11} - 142 x^{10} + 61 x^{9} + 128 x^{8} - 265 x^{7} + 227 x^{6} - 66 x^{5} - 73 x^{4} + 95 x^{3} - 47 x^{2} + 11 x - 1$ |
$18$ |
[10,4] |
$5^{2}\cdot 257^{6}\cdot 269^{3}$ |
$3$ |
$19.3167068163$ |
$587.9328192914561$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$13$ |
$79194.0173874$ |
| 18.10.148...501.1 |
$x^{18} - 9 x^{17} + 27 x^{16} - 12 x^{15} - 93 x^{14} + 147 x^{13} + 83 x^{12} - 303 x^{11} + 24 x^{10} + 298 x^{9} - 69 x^{8} - 165 x^{7} + 18 x^{6} + 48 x^{5} + 21 x^{4} - 4 x^{3} - 12 x^{2} + 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 19\cdot 2053^{2}\cdot 6551$ |
$4$ |
$19.3759874781$ |
|
|
|
✓ |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$13$ |
$89012.8750016$ |
| 18.10.173...289.1 |
$x^{18} - 4 x^{17} + x^{16} + x^{15} + 23 x^{14} + 6 x^{13} - 75 x^{12} - 10 x^{11} + 39 x^{10} + 124 x^{9} - 36 x^{8} - 145 x^{7} + 75 x^{6} + 12 x^{5} - 43 x^{4} + 15 x^{3} + 12 x^{2} - 2 x - 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 3540067^{2}$ |
$2$ |
$19.5463934184$ |
$6885.007761348169$ |
|
|
? |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$13$ |
$102716.730544$ |
| 18.10.180...616.1 |
$x^{18} + x^{16} - 15 x^{14} + 56 x^{10} - 23 x^{8} - 57 x^{6} + 45 x^{4} - 6 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$19.5868680452$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$2$ |
$13$ |
$100975.232776$ |
| 18.10.180...616.2 |
$x^{18} - 6 x^{17} + 10 x^{16} + 16 x^{15} - 91 x^{14} + 116 x^{13} + 83 x^{12} - 398 x^{11} + 415 x^{10} + 52 x^{9} - 624 x^{8} + 604 x^{7} - 28 x^{6} - 292 x^{5} + 151 x^{4} + 14 x^{3} - 33 x^{2} + 10 x - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$19.5868680452$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$2$ |
$13$ |
$95937.0104383$ |
| 18.10.180...616.3 |
$x^{18} + 6 x^{16} - 13 x^{14} - 51 x^{12} + 47 x^{10} + 104 x^{8} - 64 x^{6} - 49 x^{4} + 19 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$19.5868680452$ |
|
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$13$ |
$96923.4694537$ |
| 18.10.237...529.1 |
$x^{18} - 2 x^{17} - 11 x^{16} + 9 x^{15} + 47 x^{14} + 14 x^{13} - 85 x^{12} - 98 x^{11} + 48 x^{10} + 147 x^{9} + 48 x^{8} - 98 x^{7} - 85 x^{6} + 14 x^{5} + 47 x^{4} + 9 x^{3} - 11 x^{2} - 2 x + 1$ |
$18$ |
[10,4] |
$7^{14}\cdot 769^{4}$ |
$2$ |
$19.8891141337$ |
$424.81442954934494$ |
|
|
? |
$A_4\wr C_3$ (as 18T473) |
trivial |
$2$ |
$13$ |
$117123.22288$ |
| 18.10.250...216.1 |
$x^{18} - 8 x^{17} + 23 x^{16} - 36 x^{15} + 57 x^{14} - 80 x^{13} + 30 x^{12} + 44 x^{11} - 70 x^{10} + 136 x^{9} - 139 x^{8} + 18 x^{7} + 83 x^{6} - 106 x^{5} + 35 x^{4} + 24 x^{3} - 12 x^{2} - 2 x + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 37^{6}\cdot 89\cdot 16361^{2}$ |
$4$ |
$19.9489990873$ |
$11651.650561453322$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$13$ |
$124290.128335$ |
| 18.10.256...128.1 |
$x^{18} - 17 x^{14} - 15 x^{12} + 71 x^{10} + 62 x^{8} - 120 x^{6} - 79 x^{4} + 135 x^{2} - 37$ |
$18$ |
[10,4] |
$2^{24}\cdot 37^{7}\cdot 401^{2}$ |
$3$ |
$19.9741274742$ |
|
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T773) |
trivial |
$2$ |
$13$ |
$108132.523536$ |
| 18.10.266...517.1 |
$x^{18} - 3 x^{17} - 2 x^{16} + 9 x^{15} - 10 x^{14} - 14 x^{13} + 20 x^{12} + 46 x^{11} + 21 x^{10} - 78 x^{9} - 32 x^{8} + 42 x^{7} - 33 x^{6} + 4 x^{5} + 53 x^{4} - 3 x^{3} - 19 x^{2} - 2 x + 1$ |
$18$ |
[10,4] |
$7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 197$ |
$4$ |
$20.0172768869$ |
$3485.2960841717536$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$13$ |
$107647.512463$ |
| 18.10.269...336.1 |
$x^{18} - 7 x^{17} + 26 x^{16} - 66 x^{15} + 111 x^{14} - 111 x^{13} + 19 x^{12} + 138 x^{11} - 198 x^{10} + 159 x^{9} - 188 x^{8} + 15 x^{7} + 326 x^{6} - 200 x^{5} - 118 x^{4} + 78 x^{3} + 22 x^{2} - 5 x - 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 7^{12}\cdot 41^{6}$ |
$3$ |
$20.0299551122$ |
$228.52316699092057$ |
|
|
? |
$A_4^3:A_4$ (as 18T646) |
trivial |
$2$ |
$13$ |
$127022.904615$ |
| 18.10.272...168.1 |
$x^{18} - 3 x^{17} - 2 x^{16} + 10 x^{15} + 3 x^{14} - 35 x^{13} + 24 x^{12} + 147 x^{11} - 120 x^{10} - 425 x^{9} + 194 x^{8} + 737 x^{7} - 254 x^{6} - 625 x^{5} + 287 x^{4} + 154 x^{3} - 114 x^{2} + 21 x - 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 37^{6}\cdot 97\cdot 16361^{2}$ |
$4$ |
$20.0446221078$ |
$12164.053322730662$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$13$ |
$125704.731147$ |
| 18.10.289...217.1 |
$x^{18} - 3 x^{17} + 12 x^{15} - 15 x^{14} - 15 x^{13} + 21 x^{12} + 33 x^{11} - 18 x^{10} - 114 x^{9} + 90 x^{8} + 171 x^{7} - 109 x^{6} - 105 x^{5} + 15 x^{4} + 24 x^{3} + 15 x^{2} - 3 x - 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 73^{2}\cdot 577^{3}$ |
$3$ |
$20.1091408094$ |
$887.9960002144848$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$13$ |
$112014.227164$ |
| 18.10.289...217.2 |
$x^{18} - 6 x^{16} - 3 x^{15} + 9 x^{14} + 21 x^{13} - x^{12} - 21 x^{11} + 27 x^{10} - 60 x^{9} - 162 x^{8} - 3 x^{7} + 183 x^{6} + 162 x^{5} - 48 x^{4} - 92 x^{3} + 12 x^{2} + 9 x - 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 73^{2}\cdot 577^{3}$ |
$3$ |
$20.1091408094$ |
$887.9960002144848$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$13$ |
$113389.185023$ |
| 18.10.289...217.3 |
$x^{18} - 3 x^{17} - 9 x^{16} + 26 x^{15} + 18 x^{14} - 57 x^{13} + 9 x^{12} - 75 x^{10} + 123 x^{9} + 105 x^{8} - 129 x^{7} - 34 x^{6} + 51 x^{5} - 33 x^{4} - 20 x^{3} + 18 x^{2} + 9 x + 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 73^{2}\cdot 577^{3}$ |
$3$ |
$20.1091408094$ |
$887.9960002144848$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$13$ |
$118052.07998$ |
| 18.10.289...217.4 |
$x^{18} - 3 x^{17} + 20 x^{15} - 30 x^{14} - 66 x^{13} + 79 x^{12} + 147 x^{11} + 3 x^{10} - 107 x^{9} - 180 x^{8} - 210 x^{7} + 12 x^{6} + 273 x^{5} + 231 x^{4} + 48 x^{3} - 24 x^{2} - 12 x - 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 73^{2}\cdot 577^{3}$ |
$3$ |
$20.1091408094$ |
$887.9960002144848$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$13$ |
$122151.104699$ |
| 18.10.306...096.1 |
$x^{18} - 2 x^{17} - 7 x^{16} + 23 x^{15} - 19 x^{14} - 17 x^{13} + 101 x^{12} - 207 x^{11} + 139 x^{10} + 202 x^{9} - 406 x^{8} + 149 x^{7} + 137 x^{6} - 109 x^{5} - 9 x^{4} + 32 x^{3} - 7 x^{2} - 3 x + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 37^{6}\cdot 109\cdot 16361^{2}$ |
$4$ |
$20.17492954$ |
$12894.535349762082$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$13$ |
$118538.305491$ |
| 18.10.334...808.1 |
$x^{18} - 13 x^{16} - 10 x^{15} + 58 x^{14} + 89 x^{13} - 98 x^{12} - 286 x^{11} - 20 x^{10} + 429 x^{9} + 229 x^{8} - 282 x^{7} - 227 x^{6} + 53 x^{5} + 71 x^{4} + 5 x^{3} - 2 x^{2} + 3 x + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 13^{2}\cdot 37^{9}\cdot 61^{2}$ |
$4$ |
$20.2735121216$ |
$271.90933608453196$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$13$ |
$113965.764707$ |
| 18.10.385...928.1 |
$x^{18} - x^{17} - 13 x^{16} + 4 x^{15} + 70 x^{14} + 21 x^{13} - 184 x^{12} - 139 x^{11} + 233 x^{10} + 255 x^{9} - 148 x^{8} - 188 x^{7} + 84 x^{6} + 61 x^{5} - 48 x^{4} - 5 x^{3} + 4 x^{2} + 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 37^{6}\cdot 137\cdot 16361^{2}$ |
$4$ |
$20.4328225716$ |
$14456.15285607937$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$13$ |
$144162.848433$ |
| 18.10.394...289.1 |
$x^{18} - 7 x^{17} + 13 x^{16} + 14 x^{15} - 64 x^{14} + 25 x^{13} + 62 x^{12} - 6 x^{11} - 16 x^{10} - 110 x^{9} + 40 x^{8} + 67 x^{7} + 43 x^{6} - 53 x^{5} - 20 x^{4} + 14 x^{3} - 4 x^{2} - x + 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 37^{2}$ |
$2$ |
$20.4604180731$ |
$83.32411881951172$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$2$ |
$13$ |
$135813.9354$ |
| 18.10.394...289.2 |
$x^{18} - 8 x^{17} + 21 x^{16} + 7 x^{15} - 171 x^{14} + 414 x^{13} - 353 x^{12} - 237 x^{11} + 757 x^{10} - 490 x^{9} - 127 x^{8} + 306 x^{7} - 159 x^{6} + 12 x^{5} + 57 x^{4} - 27 x^{3} - 9 x^{2} + 4 x + 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 37^{2}$ |
$2$ |
$20.4604180731$ |
$83.32411881951172$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$2$ |
$13$ |
$139723.055343$ |
| 18.10.402...125.1 |
$x^{18} - x^{17} - 10 x^{16} + 9 x^{15} + 32 x^{14} - 12 x^{13} - 34 x^{12} - 81 x^{11} - 41 x^{10} + 173 x^{9} + 109 x^{8} - 111 x^{7} - 63 x^{6} + 22 x^{5} - 2 x^{4} + 9 x^{2} - 1$ |
$18$ |
[10,4] |
$5^{9}\cdot 453771377^{2}$ |
$2$ |
$20.4812185022$ |
$47632.519196448135$ |
|
|
? |
$C_2\times S_9$ (as 18T913) |
trivial |
$2$ |
$13$ |
$123426.783044$ |
| 18.10.425...000.1 |
$x^{18} - 2 x^{17} - 7 x^{16} + 10 x^{15} + 18 x^{14} - 12 x^{13} - 10 x^{12} + 14 x^{11} - 52 x^{10} - 28 x^{9} + 52 x^{8} + 14 x^{7} + 10 x^{6} - 12 x^{5} - 18 x^{4} + 10 x^{3} + 7 x^{2} - 2 x - 1$ |
$18$ |
[10,4] |
$2^{20}\cdot 5^{5}\cdot 37^{9}$ |
$3$ |
$20.5464582276$ |
|
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$13$ |
$291134.035196$ |
| 18.10.427...125.1 |
$x^{18} - 2 x^{17} - x^{16} + 10 x^{15} - 22 x^{14} - 16 x^{13} + 27 x^{12} - 47 x^{11} - 41 x^{10} + 83 x^{9} + 135 x^{8} + 65 x^{7} - 52 x^{6} - 66 x^{5} - 20 x^{4} + 7 x^{3} + 10 x^{2} + x - 1$ |
$18$ |
[10,4] |
$5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ |
$4$ |
$20.5510642367$ |
$516.0140075482474$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$2$ |
$13$ |
$139386.821518$ |
| 18.10.442...816.1 |
$x^{18} - 9 x^{16} + 29 x^{14} - 36 x^{12} + 33 x^{8} - 17 x^{6} - 5 x^{4} + 6 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{30}\cdot 37^{6}\cdot 401^{2}$ |
$3$ |
$20.5915401536$ |
|
|
|
✓ |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$13$ |
$148455.524422$ |
| 18.10.442...816.2 |
$x^{18} - 3 x^{16} + 5 x^{14} - 18 x^{12} + 54 x^{10} - 97 x^{8} + 103 x^{6} - 57 x^{4} + 14 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{30}\cdot 37^{6}\cdot 401^{2}$ |
$3$ |
$20.5915401536$ |
|
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$13$ |
$154144.671884$ |
| 18.10.655...000.1 |
$x^{18} - 7 x^{17} + 12 x^{16} + 13 x^{15} - 22 x^{14} - 136 x^{13} + 316 x^{12} - 145 x^{11} - 39 x^{10} - 229 x^{9} + 332 x^{8} + 77 x^{7} - 618 x^{6} + 931 x^{5} - 367 x^{4} - 349 x^{3} + 245 x^{2} - 15 x - 1$ |
$18$ |
[10,4] |
$2^{12}\cdot 5^{3}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3}$ |
$5$ |
$21.0439746714$ |
$608.0077592018499$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$13$ |
$181540.688576$ |
| 18.10.770...157.1 |
$x^{18} - 3 x^{17} - 6 x^{16} + 29 x^{15} - 45 x^{14} + 21 x^{13} + 110 x^{12} - 246 x^{11} + 186 x^{10} + 44 x^{9} - 144 x^{8} + 27 x^{7} - 62 x^{6} + 123 x^{5} - 243 x^{4} + 214 x^{3} - 84 x^{2} + 15 x - 1$ |
$18$ |
[10,4] |
$3^{24}\cdot 7^{12}\cdot 197$ |
$3$ |
$21.2339461775$ |
|
|
|
|
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$13$ |
$248683.747013$ |
