| 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 |
| 18.0.403...848.1 |
$x^{18} - x^{17} + x^{16} + 6 x^{15} - 6 x^{14} + 5 x^{13} + 14 x^{12} - 18 x^{11} + 14 x^{10} + 13 x^{9} - 27 x^{8} + 21 x^{7} - 3 x^{6} - 13 x^{5} + 23 x^{4} - 18 x^{3} + 10 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 29^{8}$ |
$3$ |
$12.2801015121$ |
$18.65475810617763$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$6$ |
$8$ |
$506.867373576$ |
| 18.0.428...000.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 154 x^{15} + 399 x^{14} - 822 x^{13} + 1393 x^{12} - 1974 x^{11} + 2358 x^{10} - 2374 x^{9} + 2019 x^{8} - 1455 x^{7} + 896 x^{6} - 471 x^{5} + 210 x^{4} - 78 x^{3} + 24 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{21}\cdot 5^{6}$ |
$3$ |
$12.321439841$ |
$22.786176627742247$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$6$ |
$8$ |
$735.644505219$ |
| 18.2.433...096.1 |
$x^{18} - x^{15} - 8 x^{12} + 17 x^{9} - 8 x^{6} - x^{3} + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{6}\cdot 29^{9}$ |
$3$ |
$12.3289497064$ |
$18.65475810617763$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$230.414214587$ |
| 18.2.149...000.1 |
$x^{18} + 4 x^{16} - 6 x^{15} + 10 x^{14} - 20 x^{13} + 25 x^{12} - 40 x^{11} + 40 x^{10} - 40 x^{9} + 44 x^{8} - 20 x^{7} + x^{6} - 4 x^{5} - 10 x^{4} + 14 x^{3} - 4 x + 1$ |
$18$ |
[2,8] |
$2^{26}\cdot 3^{6}\cdot 5^{15}$ |
$3$ |
$15.0084736369$ |
$23.600649568042265$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$2754.9090905251223$ |
| 18.2.166...000.1 |
$x^{18} - 2 x^{17} + 2 x^{16} - 4 x^{13} + 3 x^{12} - 2 x^{11} + 2 x^{10} + 6 x^{8} - 10 x^{7} + 7 x^{6} - 12 x^{5} + 8 x^{4} - 8 x^{3} + 6 x^{2} - 2 x + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 5^{9}\cdot 7^{6}\cdot 11^{6}$ |
$4$ |
$15.1008678731$ |
$31.147057781097917$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$3181.46652648$ |
| 18.0.305...000.1 |
$x^{18} + x^{16} + 8 x^{14} + 18 x^{10} - 22 x^{8} + 20 x^{6} - 12 x^{4} + x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{6}\cdot 5^{12}$ |
$3$ |
$15.6182595264$ |
$22.739048476302873$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$14740.263954526403$ |
| 18.0.485...504.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 36 x^{15} + 63 x^{14} - 102 x^{13} + 126 x^{12} - 96 x^{11} + 39 x^{10} + 14 x^{9} - 66 x^{8} + 108 x^{7} - 99 x^{6} + 54 x^{5} - 6 x^{4} - 24 x^{3} + 36 x^{2} - 24 x + 8$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{24}$ |
$2$ |
$16.0241088715$ |
$20.649049558832502$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$15048.506111538745$ |
| 18.0.688...784.1 |
$x^{18} - 6 x^{15} + 3 x^{14} + 18 x^{13} + 18 x^{12} + 12 x^{11} - 21 x^{10} - 4 x^{9} + 36 x^{8} + 42 x^{7} + 45 x^{6} - 6 x^{5} + 18 x^{4} + 48 x^{3} + 36 x^{2} + 24 x + 8$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{20}\cdot 7^{6}$ |
$3$ |
$16.338320145$ |
$24.01949163173274$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$14270.669184852277$ |
| 18.2.107...000.1 |
$x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 55 x^{14} - 85 x^{13} + 145 x^{12} - 285 x^{11} + 530 x^{10} - 820 x^{9} + 985 x^{8} - 885 x^{7} + 545 x^{6} - 145 x^{5} - 85 x^{4} + 103 x^{3} - 45 x^{2} + 10 x - 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{6}\cdot 5^{15}\cdot 7^{6}$ |
$4$ |
$16.7456277326$ |
$27.814503675501406$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$7575.010436613877$ |
| 18.0.115...064.3 |
$x^{18} - x^{12} + 3 x^{6} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{18}\cdot 11^{6}$ |
$3$ |
$16.8122359839$ |
$30.110026238816843$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$13763.617804942303$ |
| 18.2.145...512.1 |
$x^{18} - 9 x^{16} + 39 x^{14} - 99 x^{12} + 156 x^{10} - 156 x^{8} + 108 x^{6} - 72 x^{4} + 36 x^{2} - 12$ |
$18$ |
[2,8] |
$2^{34}\cdot 3^{25}$ |
$2$ |
$17.0325872916$ |
$20.649049558832502$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$23530.998055402946$ |
| 18.2.206...352.1 |
$x^{18} - 6 x^{17} + 24 x^{16} - 64 x^{15} + 129 x^{14} - 180 x^{13} + 146 x^{12} + 72 x^{11} - 471 x^{10} + 958 x^{9} - 1302 x^{8} + 1392 x^{7} - 1187 x^{6} + 876 x^{5} - 552 x^{4} + 336 x^{3} - 168 x^{2} + 72 x - 12$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{21}\cdot 7^{6}$ |
$3$ |
$17.3665734737$ |
$24.01949163173274$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$54188.49745843781$ |
| 18.2.244...000.1 |
$x^{18} + 11 x^{14} + 16 x^{12} + 27 x^{10} + 54 x^{8} + 125 x^{6} + 124 x^{4} + 44 x^{2} - 2$ |
$18$ |
[2,8] |
$2^{37}\cdot 3^{6}\cdot 5^{12}$ |
$3$ |
$17.530903579$ |
$22.739048476302873$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$22555.101398872506$ |
| 18.0.388...032.1 |
$x^{18} - 9 x^{14} + 30 x^{12} + 3 x^{10} - 12 x^{8} + 9 x^{6} + 6 x^{4} + 12 x^{2} + 8$ |
$18$ |
[0,9] |
$-\,2^{37}\cdot 3^{24}$ |
$2$ |
$17.9864540662$ |
$20.649049558832502$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$8$ |
$40390.91671831928$ |
| 18.0.403...000.1 |
$x^{18} - 7 x^{17} + 20 x^{16} - 22 x^{15} - 20 x^{14} + 88 x^{13} - 86 x^{12} - 40 x^{11} + 149 x^{10} - 65 x^{9} - 60 x^{8} + 60 x^{7} + 70 x^{6} - 10 x^{4} + 38 x^{3} + 44 x^{2} + 20 x + 4$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{9}\cdot 5^{15}$ |
$3$ |
$18.0242306313$ |
$23.600649568042265$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$41069.839937116616$ |
| 18.0.740...000.1 |
$x^{18} - 6 x^{16} + 15 x^{14} - 9 x^{12} + 3 x^{10} - 12 x^{6} + 9 x^{4} + 3 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{24}\cdot 5^{6}$ |
$3$ |
$18.6433950357$ |
$25.91353963371521$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$37893.31215464969$ |
| 18.0.762...984.1 |
$x^{18} - 20 x^{14} + 39 x^{12} + 40 x^{10} - 112 x^{8} + 55 x^{6} + 12 x^{4} - 8 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 11^{6}\cdot 37^{6}$ |
$3$ |
$18.6740333736$ |
$50.83590180772078$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$36250.2959789$ |
| 18.2.825...000.1 |
$x^{18} - 2 x^{17} - 2 x^{15} + 35 x^{14} - 82 x^{13} + 108 x^{12} - 122 x^{11} + 105 x^{10} - 10 x^{9} - 64 x^{8} + 26 x^{7} + 19 x^{6} - 2 x^{5} - 18 x^{4} + 2 x^{3} + 6 x^{2} - 2$ |
$18$ |
[2,8] |
$2^{34}\cdot 3^{9}\cdot 5^{12}$ |
$3$ |
$18.7565450408$ |
$22.739048476302873$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$47025.46397036979$ |
| 18.2.116...096.1 |
$x^{18} + 3 x^{14} - 24 x^{12} + 3 x^{10} + 66 x^{8} - 27 x^{6} - 36 x^{4} + 36 x^{2} - 6$ |
$18$ |
[2,8] |
$2^{37}\cdot 3^{25}$ |
$2$ |
$19.1184328193$ |
$20.649049558832502$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$77983.91631785831$ |
| 18.0.147...432.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 28 x^{15} + 21 x^{14} - 6 x^{13} + 16 x^{12} - 24 x^{11} - 3 x^{10} + 26 x^{9} + 12 x^{8} + 36 x^{7} - 31 x^{6} + 6 x^{5} + 66 x^{4} + 84 x^{3} + 72 x^{2} + 24 x + 4$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{20}\cdot 7^{9}$ |
$3$ |
$19.3714228137$ |
$24.01949163173274$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$8$ |
$158670.5761863574$ |
| 18.0.191...000.1 |
$x^{18} - 4 x^{17} + 14 x^{15} - 24 x^{13} - 19 x^{12} + 20 x^{11} + 44 x^{10} + 20 x^{9} - 70 x^{8} - 20 x^{7} + 155 x^{6} - 100 x^{5} + 20 x^{4} + 14 x^{3} - 6 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{33}\cdot 3^{6}\cdot 5^{15}$ |
$3$ |
$19.6518638771$ |
$23.600649568042265$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$18590.202593393617$ |
| 18.0.221...000.1 |
$x^{18} - 4 x^{17} + 12 x^{16} - 26 x^{15} + 60 x^{14} - 92 x^{13} + 147 x^{12} - 192 x^{11} + 244 x^{10} - 236 x^{9} + 244 x^{8} - 192 x^{7} + 147 x^{6} - 92 x^{5} + 60 x^{4} - 26 x^{3} + 12 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{15}$ |
$4$ |
$19.8136939369$ |
$31.11577769126579$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$2$ |
$8$ |
$31526.6275023892$ |
| 18.2.222...000.1 |
$x^{18} + 3 x^{16} + 9 x^{14} + 24 x^{12} + 36 x^{10} - 21 x^{8} - 45 x^{6} - 45 x^{4} - 18 x^{2} - 3$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{25}\cdot 5^{6}$ |
$3$ |
$19.816718415$ |
$25.91353963371521$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$38038.42412055933$ |
| 18.0.261...000.1 |
$x^{18} - 3 x^{17} + 6 x^{16} + 11 x^{15} - 39 x^{14} + 69 x^{13} + 13 x^{12} - 114 x^{11} + 225 x^{10} - 219 x^{9} + 174 x^{8} - 72 x^{7} - 24 x^{6} + 45 x^{5} + 36 x^{4} + 18 x^{3} - 9 x^{2} + 9$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{21}\cdot 5^{14}$ |
$3$ |
$19.9973047137$ |
$27.55157706505336$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$6$ |
$8$ |
$87439.9587358$ |
| 18.0.289...000.1 |
$x^{18} + x^{16} - 2 x^{15} + 15 x^{14} - 20 x^{13} + 50 x^{12} - 60 x^{11} + 50 x^{10} - 80 x^{9} + 21 x^{8} - 20 x^{7} + x^{6} + 48 x^{5} + 25 x^{4} + 48 x^{3} + 30 x^{2} + 18 x + 9$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{15}\cdot 7^{6}$ |
$4$ |
$20.1104431817$ |
$27.814503675501406$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$23139.13431049142$ |
| 18.2.310...728.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 38 x^{15} + 72 x^{14} - 132 x^{13} + 219 x^{12} - 300 x^{11} + 318 x^{10} - 306 x^{9} + 444 x^{8} - 828 x^{7} + 1205 x^{6} - 1206 x^{5} + 816 x^{4} - 340 x^{3} + 72 x^{2} - 12 x + 1$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{21}\cdot 11^{6}$ |
$3$ |
$20.1904354922$ |
$30.110026238816843$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$67426.43711447202$ |
| 18.0.351...000.1 |
$x^{18} - 6 x^{15} + 18 x^{12} + 28 x^{9} + 16 x^{6} + 16 x^{3} + 8$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{6}\cdot 5^{12}\cdot 7^{6}$ |
$4$ |
$20.3279271363$ |
$33.76470641024235$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$95838.02769622154$ |
| 18.2.364...000.2 |
$x^{18} - 4 x^{15} + 3 x^{12} + 4 x^{9} - 5 x^{6} + 4 x^{3} + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{18}\cdot 5^{9}\cdot 7^{6}$ |
$4$ |
$20.3700580825$ |
$33.834685952203664$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$70553.37834594054$ |
| 18.0.382...000.1 |
$x^{18} - 4 x^{17} - 2 x^{16} + 18 x^{15} + 10 x^{14} - 44 x^{13} - 44 x^{12} + 48 x^{11} + 108 x^{10} + 40 x^{9} - 92 x^{8} - 152 x^{7} - 46 x^{6} + 144 x^{5} + 240 x^{4} + 188 x^{3} + 88 x^{2} + 24 x + 4$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{6}\cdot 5^{15}$ |
$3$ |
$20.423380843$ |
$29.734955181968793$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$37891.20519244316$ |
| 18.6.435...000.1 |
$x^{18} - 3 x^{17} - 11 x^{15} + 45 x^{14} + 12 x^{13} - 111 x^{12} + 30 x^{11} + 48 x^{10} - 60 x^{9} + 195 x^{8} + 105 x^{7} - 285 x^{6} - 90 x^{5} + 165 x^{4} + 29 x^{3} - 42 x^{2} + 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{20}\cdot 5^{15}$ |
$3$ |
$20.5729416753$ |
$27.55157706505336$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$11$ |
$90961.5357762$ |
| 18.6.439...000.1 |
$x^{18} - 12 x^{15} - 135 x^{12} - 160 x^{9} - 5 x^{6} + 28 x^{3} - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{6}\cdot 5^{15}\cdot 13^{6}$ |
$4$ |
$20.5833726325$ |
$37.904779177166446$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$11$ |
$164778.665218$ |
| 18.2.442...296.1 |
$x^{18} - 3 x^{17} + 3 x^{16} + 2 x^{15} - 12 x^{14} + 30 x^{13} - 60 x^{12} + 114 x^{11} - 189 x^{10} + 229 x^{9} - 189 x^{8} + 114 x^{7} - 60 x^{6} + 30 x^{5} - 12 x^{4} + 2 x^{3} + 3 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$2^{20}\cdot 3^{21}\cdot 7^{9}$ |
$3$ |
$20.5905646725$ |
$24.01949163173274$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$86222.15448461822$ |
| 18.2.457...000.2 |
$x^{18} - 6 x^{17} + 12 x^{16} - 16 x^{15} + 24 x^{14} - 6 x^{13} - 33 x^{12} - 24 x^{11} + 216 x^{10} - 356 x^{9} + 216 x^{8} - 24 x^{7} - 33 x^{6} - 6 x^{5} + 24 x^{4} - 16 x^{3} + 12 x^{2} - 6 x + 1$ |
$18$ |
[2,8] |
$2^{26}\cdot 3^{20}\cdot 5^{9}$ |
$3$ |
$20.6272263596$ |
$28.708783579915032$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$95139.22929671641$ |
| 18.2.467...000.2 |
$x^{18} - 12 x^{16} + 63 x^{14} - 204 x^{12} + 447 x^{10} - 678 x^{8} + 657 x^{6} - 288 x^{4} - 48 x^{2} - 2$ |
$18$ |
[2,8] |
$2^{33}\cdot 3^{20}\cdot 5^{6}$ |
$3$ |
$20.6544223923$ |
$28.708783579915032$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$240132.01327780026$ |
| 18.0.660...000.1 |
$x^{18} + 6 x^{16} + 7 x^{14} - 10 x^{12} - 17 x^{10} + 28 x^{8} + 73 x^{6} + 186 x^{4} + 180 x^{2} + 54$ |
$18$ |
[0,9] |
$-\,2^{37}\cdot 3^{9}\cdot 5^{12}$ |
$3$ |
$21.0535099657$ |
$22.739048476302873$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$61992.719757773724$ |
| 18.0.935...000.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 34 x^{15} + 51 x^{14} - 78 x^{13} + 128 x^{12} - 210 x^{11} + 291 x^{10} - 330 x^{9} + 396 x^{8} - 510 x^{7} + 625 x^{6} - 642 x^{5} + 288 x^{4} + 50 x^{3} + 2$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{20}\cdot 5^{6}$ |
$3$ |
$21.4652990296$ |
$36.17080074921124$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$489834.7260177265$ |
| 18.0.962...736.2 |
$x^{18} - 4 x^{15} + 8 x^{12} - 20 x^{9} + 36 x^{6} - 24 x^{3} + 8$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{18}\cdot 23^{6}$ |
$3$ |
$21.4982872261$ |
$43.53902600734561$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$104030.5216493536$ |
| 18.0.100...000.1 |
$x^{18} - 4 x^{15} + 5 x^{12} - 14 x^{9} + 33 x^{6} - 6 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 7^{9}$ |
$4$ |
$21.5450219036$ |
$33.834685952203664$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$8$ |
$195368.59577386398$ |
| 18.0.137...000.1 |
$x^{18} - 9 x^{17} + 36 x^{16} - 84 x^{15} + 120 x^{14} - 84 x^{13} - 76 x^{12} + 378 x^{11} - 651 x^{10} + 505 x^{9} + 180 x^{8} - 918 x^{7} + 1180 x^{6} - 954 x^{5} + 570 x^{4} - 266 x^{3} + 96 x^{2} - 24 x + 4$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{21}\cdot 5^{9}$ |
$3$ |
$21.9254023029$ |
$28.708783579915032$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$398664.7871956061$ |
| 18.0.140...000.1 |
$x^{18} - 6 x^{16} - 6 x^{15} + 18 x^{14} + 12 x^{13} - 55 x^{12} + 270 x^{10} + 268 x^{9} - 258 x^{8} - 660 x^{7} - 311 x^{6} + 204 x^{5} + 342 x^{4} + 202 x^{3} + 66 x^{2} + 12 x + 1$ |
$18$ |
[0,9] |
$-\,2^{33}\cdot 3^{21}\cdot 5^{6}$ |
$3$ |
$21.9543099199$ |
$28.708783579915032$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$8$ |
$135115.59906768618$ |
| 18.0.141...504.1 |
$x^{18} + 3 x^{12} + 111 x^{6} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{20}\cdot 17^{6}$ |
$3$ |
$21.9612823448$ |
$37.43167419292487$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$4$ |
$8$ |
$217506.82125768872$ |
| 18.0.156...024.1 |
$x^{18} - 2 x^{17} + 2 x^{16} - 2 x^{15} + 20 x^{14} - 24 x^{13} + 10 x^{12} + 116 x^{10} - 104 x^{9} + 64 x^{8} - 168 x^{7} + 644 x^{6} - 600 x^{5} + 304 x^{4} - 104 x^{3} + 64 x^{2} - 32 x + 8$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{8}\cdot 7^{12}$ |
$3$ |
$22.0833420016$ |
$28.457122144779103$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$4$ |
$8$ |
$133785.59033967915$ |
| 18.0.209...872.1 |
$x^{18} - x^{17} + 6 x^{15} - 4 x^{14} - 16 x^{13} + 36 x^{12} + 10 x^{11} - 105 x^{10} + 191 x^{9} + 132 x^{8} - 680 x^{7} + 278 x^{6} + 852 x^{5} - 714 x^{4} - 218 x^{3} + 376 x^{2} - 144 x + 36$ |
$18$ |
[0,9] |
$-\,2^{26}\cdot 3^{8}\cdot 7^{15}$ |
$3$ |
$22.44519395$ |
$31.239014120786564$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$2$ |
$8$ |
$256078.49869658783$ |
| 18.0.264...000.1 |
$x^{18} - 4 x^{17} + 2 x^{16} + 6 x^{15} + 10 x^{14} - 22 x^{13} - 51 x^{12} + 94 x^{11} + 42 x^{10} - 148 x^{9} + 42 x^{8} + 94 x^{7} - 51 x^{6} - 22 x^{5} + 10 x^{4} + 6 x^{3} + 2 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{6}\cdot 5^{6}\cdot 7^{12}$ |
$4$ |
$22.7406273028$ |
$35.712285955785276$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$4$ |
$8$ |
$169260.62829015162$ |
| 18.2.280...000.1 |
$x^{18} + 3 x^{16} - 9 x^{14} - 43 x^{12} - 120 x^{10} - 252 x^{8} - 104 x^{6} - 432 x^{4} - 240 x^{2} - 48$ |
$18$ |
[2,8] |
$2^{34}\cdot 3^{21}\cdot 5^{6}$ |
$3$ |
$22.8162191354$ |
$36.17080074921124$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$427082.8993575692$ |
| 18.2.305...000.1 |
$x^{18} - 6 x^{17} + 7 x^{16} + 36 x^{15} - 150 x^{14} + 284 x^{13} - 354 x^{12} + 348 x^{11} - 346 x^{10} + 400 x^{9} - 498 x^{8} + 548 x^{7} - 456 x^{6} + 312 x^{5} - 180 x^{4} + 76 x^{3} - 21 x^{2} + 2 x + 1$ |
$18$ |
[2,8] |
$2^{37}\cdot 3^{6}\cdot 5^{15}$ |
$3$ |
$22.9244698944$ |
$29.734955181968793$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[2]$ |
$2$ |
$9$ |
$165711.7100392055$ |
| 18.2.309...000.1 |
$x^{18} - 2 x^{15} - 15 x^{12} - 20 x^{9} - 25 x^{6} - 2 x^{3} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 3^{18}\cdot 5^{15}$ |
$3$ |
$22.94173474$ |
$38.96381395016598$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$388319.365113364$ |
| 18.0.319...504.1 |
$x^{18} - 7 x^{17} + 31 x^{16} - 88 x^{15} + 174 x^{14} - 234 x^{13} + 140 x^{12} + 226 x^{11} - 813 x^{10} + 1245 x^{9} - 1067 x^{8} + 242 x^{7} + 856 x^{6} - 1558 x^{5} + 1590 x^{4} - 1116 x^{3} + 549 x^{2} - 171 x + 27$ |
$18$ |
[0,9] |
$-\,2^{20}\cdot 3^{6}\cdot 11^{15}$ |
$3$ |
$22.9797568366$ |
$32.192980946026715$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$2$ |
$8$ |
$170014.48092527897$ |
| 18.0.353...416.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 18 x^{15} - 9 x^{14} + 54 x^{13} - 18 x^{11} + 99 x^{10} + 6 x^{9} - 36 x^{8} + 18 x^{7} + 9 x^{6} - 54 x^{5} + 18 x^{3} + 18$ |
$18$ |
[0,9] |
$-\,2^{34}\cdot 3^{30}$ |
$2$ |
$23.1107641344$ |
$29.78108285348256$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[3]$ |
$4$ |
$8$ |
$233467.89303899015$ |
| 18.0.367...000.1 |
$x^{18} - 5 x^{17} + 6 x^{16} + 3 x^{15} - 5 x^{14} + 25 x^{13} - 25 x^{12} - 10 x^{11} + 85 x^{10} + 55 x^{9} - 4 x^{8} + 50 x^{7} + 186 x^{6} + 123 x^{5} + 170 x^{4} + 248 x^{3} + 225 x^{2} + 78 x + 9$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{6}\cdot 5^{15}\cdot 7^{9}$ |
$4$ |
$23.1606693054$ |
$27.814503675501406$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[6]$ |
$2$ |
$8$ |
$68107.00331887082$ |
