| 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 |
| 18.0.199...128.1 |
$x^{18} - 6 x^{17} + 24 x^{16} - 68 x^{15} + 159 x^{14} - 300 x^{13} + 479 x^{12} - 630 x^{11} + 702 x^{10} - 636 x^{9} + 480 x^{8} - 270 x^{7} + 114 x^{6} - 12 x^{5} - 12 x^{4} + 14 x^{3} - 3 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{27}$ |
$2$ |
$10.3923048454$ |
$14.696938456699069$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$269.804731118$ |
| 18.0.965...875.1 |
$x^{18} - 9 x^{17} + 36 x^{16} - 78 x^{15} + 84 x^{14} - 111 x^{12} + 90 x^{11} + 72 x^{10} - 156 x^{9} + 45 x^{8} + 81 x^{7} - 57 x^{6} - 27 x^{5} + 36 x^{4} - 9 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 5^{6}$ |
$2$ |
$11.3422399052$ |
$14.831798946842026$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$868.676171318$ |
| 18.0.135...707.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 14 x^{15} - 42 x^{14} - 21 x^{13} + 131 x^{12} - 51 x^{11} - 162 x^{10} + 126 x^{9} + 108 x^{8} - 138 x^{7} - 18 x^{6} + 84 x^{5} - 33 x^{4} - 11 x^{3} + 15 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 11^{6}$ |
$2$ |
$11.5561395357$ |
$17.233687939614086$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$835.1622079049273$ |
| 18.0.141...912.1 |
$x^{18} - 7 x^{17} + 29 x^{16} - 86 x^{15} + 204 x^{14} - 403 x^{13} + 684 x^{12} - 1007 x^{11} + 1301 x^{10} - 1479 x^{9} + 1488 x^{8} - 1316 x^{7} + 1016 x^{6} - 673 x^{5} + 378 x^{4} - 171 x^{3} + 58 x^{2} - 10 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$11.5871185062$ |
$13.915398818088354$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$720.4866908744744$ |
| 18.0.566...000.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 54 x^{15} + 116 x^{14} - 226 x^{13} + 412 x^{12} - 686 x^{11} + 997 x^{10} - 1220 x^{9} + 1225 x^{8} - 994 x^{7} + 652 x^{6} - 356 x^{5} + 169 x^{4} - 70 x^{3} + 25 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 5^{6}\cdot 7^{12}$ |
$3$ |
$12.5146494914$ |
$16.364912636128995$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$476.20211267413316$ |
| 18.0.714...752.2 |
$x^{18} - 11 x^{15} + 48 x^{12} - 49 x^{9} + 48 x^{6} - 11 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$12.6762068204$ |
$17.926863604818365$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$6$ |
$8$ |
$773.953655619971$ |
| 18.6.110...000.1 |
$x^{18} - 5 x^{17} + 5 x^{16} + 10 x^{15} - 19 x^{14} + 7 x^{13} - 18 x^{12} + 34 x^{11} + 21 x^{10} - 70 x^{9} + 22 x^{8} + 14 x^{7} + 11 x^{6} - 7 x^{5} - 20 x^{4} + 13 x^{3} - x^{2} + 4 x - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 5^{9}\cdot 7^{12}$ |
$3$ |
$12.988839767$ |
$16.364912636128995$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$742.586512103$ |
| 18.0.161...368.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 417 x^{14} - 903 x^{13} + 1635 x^{12} - 2517 x^{11} + 3336 x^{10} - 3832 x^{9} + 3861 x^{8} - 3447 x^{7} + 2793 x^{6} - 2067 x^{5} + 1401 x^{4} - 819 x^{3} + 381 x^{2} - 120 x + 19$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{31}$ |
$2$ |
$13.2659642695$ |
$18.760906587882975$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$4471.846205846836$ |
| 18.0.169...264.1 |
$x^{18} + 6 x^{16} + 15 x^{14} + 11 x^{12} - 21 x^{10} - 48 x^{8} - 8 x^{6} + 45 x^{4} + 27 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$13.2987995223$ |
$15.971019805809386$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$734.9033962749014$ |
| 18.6.209...672.1 |
$x^{18} - 5 x^{17} + 9 x^{16} - 6 x^{15} - 5 x^{14} + 16 x^{13} - 14 x^{12} + 13 x^{11} - 33 x^{10} + 54 x^{9} - 59 x^{8} + 34 x^{7} - 12 x^{6} + 35 x^{5} - 39 x^{4} + 8 x^{3} - 3 x^{2} + 6 x - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 13^{15}$ |
$2$ |
$13.4577603621$ |
$16.955715564708598$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$1074.07507043$ |
| 18.0.303...344.2 |
$x^{18} + 9 x^{16} + 36 x^{14} + 97 x^{12} + 171 x^{10} + 189 x^{8} + 131 x^{6} + 54 x^{4} + 12 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{30}\cdot 3^{24}$ |
$2$ |
$13.7365709106$ |
$17.3069948436889$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$1054.6053574204213$ |
| 18.0.303...000.1 |
$x^{18} - 7 x^{17} + 26 x^{16} - 71 x^{15} + 151 x^{14} - 255 x^{13} + 343 x^{12} - 341 x^{11} + 206 x^{10} - 4 x^{9} - 127 x^{8} + 82 x^{7} + 55 x^{6} - 93 x^{5} + 34 x^{4} + 19 x^{3} - 10 x^{2} - 2 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 5^{6}\cdot 7^{15}$ |
$3$ |
$13.7380480777$ |
$22.634106993721137$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$4023.807873190627$ |
| 18.0.303...000.2 |
$x^{18} - 3 x^{17} + 7 x^{16} - 12 x^{15} + 20 x^{14} - 29 x^{13} + 39 x^{12} - 59 x^{11} + 96 x^{10} - 151 x^{9} + 210 x^{8} - 264 x^{7} + 290 x^{6} - 272 x^{5} + 216 x^{4} - 144 x^{3} + 80 x^{2} - 32 x + 8$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 5^{6}\cdot 7^{15}$ |
$3$ |
$13.7380480777$ |
$17.964702626096855$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$4077.3155873667893$ |
| 18.6.382...624.1 |
$x^{18} - 4 x^{17} + 5 x^{16} - x^{15} - 7 x^{14} + 19 x^{13} - 23 x^{12} + 27 x^{11} - 15 x^{10} - 40 x^{9} + 42 x^{8} + 3 x^{7} + 15 x^{6} - 23 x^{5} - 11 x^{4} + 20 x^{3} - 7 x^{2} - x + 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$13.9153988181$ |
$13.915398818088354$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$1508.2719973364074$ |
| 18.6.402...125.1 |
$x^{18} + 6 x^{16} - 6 x^{15} + 9 x^{14} - 21 x^{13} - 3 x^{12} + 9 x^{11} - 36 x^{10} + 91 x^{9} - 90 x^{8} + 48 x^{7} + 6 x^{6} - 72 x^{5} + 126 x^{4} - 87 x^{3} + 18 x^{2} + 3 x - 1$ |
$18$ |
[6,6] |
$3^{30}\cdot 5^{9}$ |
$2$ |
$13.953626481725104$ |
$14.831798946842026$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$1606.1684586798003$ |
| 18.0.488...000.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 15 x^{15} + 21 x^{14} - 33 x^{13} + 73 x^{12} - 123 x^{11} + 216 x^{10} - 257 x^{9} + 72 x^{8} + 171 x^{7} - 164 x^{6} - 12 x^{5} + 72 x^{4} - 19 x^{3} - 9 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 5^{6}$ |
$3$ |
$14.1045276747$ |
$23.2379000772445$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$5780.39296417851$ |
| 18.0.907...368.1 |
$x^{18} - 6 x^{17} + 17 x^{16} - 36 x^{15} + 76 x^{14} - 140 x^{13} + 228 x^{12} - 348 x^{11} + 465 x^{10} - 542 x^{9} + 551 x^{8} - 488 x^{7} + 373 x^{6} - 234 x^{5} + 127 x^{4} - 52 x^{3} + 17 x^{2} - 2 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$14.5988545136$ |
$24.794421938893013$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$7362.5561247660435$ |
| 18.6.102...536.1 |
$x^{18} - 8 x^{15} - 12 x^{14} - 12 x^{13} - 6 x^{12} + 24 x^{11} + 18 x^{10} + 42 x^{9} - 6 x^{8} - 55 x^{6} - 6 x^{4} + 2 x^{3} + 30 x^{2} - 12 x + 1$ |
$18$ |
[6,6] |
$2^{27}\cdot 3^{27}$ |
$2$ |
$14.6969384567$ |
$14.696938456699069$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$2758.583279525211$ |
| 18.0.115...000.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 50 x^{15} + 93 x^{14} - 144 x^{13} + 186 x^{12} - 210 x^{11} + 201 x^{10} - 118 x^{9} + 51 x^{8} + 30 x^{7} - 24 x^{6} + 18 x^{5} + 12 x^{4} - 18 x^{3} + 15 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 5^{6}$ |
$3$ |
$14.797272446$ |
$19.349808478363364$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$2329.0641692193603$ |
| 18.6.135...112.1 |
$x^{18} - 6 x^{17} + 19 x^{16} - 36 x^{15} + 31 x^{14} + 32 x^{13} - 161 x^{12} + 318 x^{11} - 419 x^{10} + 376 x^{9} - 234 x^{8} + 78 x^{7} + 45 x^{6} - 60 x^{5} + 23 x^{4} - 4 x^{3} - 5 x^{2} + 2 x + 1$ |
$18$ |
[6,6] |
$2^{27}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$14.9273977519$ |
$17.926863604818365$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$3212.235626644976$ |
| 18.0.183...127.2 |
$x^{18} - 6 x^{15} + 15 x^{12} - 20 x^{9} + 22 x^{6} - 6 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{18}\cdot 7^{15}$ |
$2$ |
$15.1834205544$ |
$18.234330849744854$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$13130.466313286553$ |
| 18.0.187...208.2 |
$x^{18} - x^{17} + 3 x^{16} + 4 x^{15} - 2 x^{14} + 13 x^{13} + 2 x^{12} + 6 x^{11} + 10 x^{10} - 9 x^{9} + 19 x^{8} - 25 x^{7} + 15 x^{6} - 19 x^{5} + 15 x^{4} - 6 x^{3} + 6 x^{2} - 2 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 13^{12}$ |
$3$ |
$15.2011411853$ |
$19.15223776179792$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$6$ |
$8$ |
$3298.275436928206$ |
| 18.6.225...000.1 |
$x^{18} - 6 x^{17} + 15 x^{16} - 12 x^{15} - 39 x^{14} + 153 x^{13} - 265 x^{12} + 243 x^{11} + 9 x^{10} - 417 x^{9} + 768 x^{8} - 906 x^{7} + 751 x^{6} - 372 x^{5} + 66 x^{4} + 19 x^{3} - 9 x^{2} + 3 x - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{24}\cdot 5^{9}$ |
$3$ |
$15.357953167$ |
$19.349808478363364$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$4306.402696834701$ |
| 18.6.242...752.2 |
$x^{18} - 3 x^{14} + 20 x^{12} - 6 x^{10} - 60 x^{8} + 73 x^{6} - 42 x^{4} + 24 x^{2} - 8$ |
$18$ |
[6,6] |
$2^{33}\cdot 3^{24}$ |
$2$ |
$15.4187795211$ |
$17.3069948436889$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$4673.069947566155$ |
| 18.0.298...123.1 |
$x^{18} + 3 x^{16} - 3 x^{15} + 18 x^{14} + 24 x^{13} + 39 x^{12} + 63 x^{11} + 66 x^{10} + 92 x^{9} + 108 x^{8} + 21 x^{7} - 75 x^{6} - 36 x^{5} + 33 x^{4} + 30 x^{3} + 9 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 13^{6}$ |
$2$ |
$15.596360976469079$ |
$23.91555719607668$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$20791.745081119407$ |
| 18.0.345...184.2 |
$x^{18} - 9 x^{16} + 33 x^{14} - 24 x^{12} - 36 x^{10} + 75 x^{8} - 21 x^{6} - 9 x^{4} + 6 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{30}$ |
$2$ |
$15.7244483653$ |
$16.714067630295588$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$4263.6438614820845$ |
| 18.0.453...827.2 |
$x^{18} - 5 x^{15} - 5 x^{12} + 28 x^{9} + 41 x^{6} + 12 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 29^{6}$ |
$2$ |
$15.964226517109864$ |
$27.982137159266443$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$28239.40988160851$ |
| 18.6.457...128.2 |
$x^{18} - 6 x^{16} + 7 x^{14} + 11 x^{12} - 17 x^{10} - 8 x^{8} + 16 x^{6} - 75 x^{4} + 99 x^{2} - 27$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$15.9710198058$ |
$15.971019805809386$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$6043.138262341402$ |
| 18.6.542...000.1 |
$x^{18} - 5 x^{17} + 9 x^{16} - 6 x^{15} - 19 x^{14} + 71 x^{13} - 117 x^{12} + 135 x^{11} - 70 x^{10} - 84 x^{9} + 177 x^{8} - 123 x^{7} - 51 x^{6} + 135 x^{5} - 33 x^{4} - 25 x^{3} + 11 x^{2} - 8 x + 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 5^{9}\cdot 7^{14}$ |
$3$ |
$16.1239016894$ |
$17.964702626096855$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$6358.139706194206$ |
| 18.0.613...767.1 |
$x^{18} - 3 x^{17} - 2 x^{16} + 12 x^{15} + 11 x^{14} - 55 x^{13} + 101 x^{11} - 8 x^{10} - 107 x^{9} - 8 x^{8} + 101 x^{7} - 55 x^{5} + 11 x^{4} + 12 x^{3} - 2 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{6}\cdot 7^{15}\cdot 11^{6}$ |
$3$ |
$16.23378089165583$ |
$29.074036854473896$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$27994.834823771416$ |
| 18.0.676...147.1 |
$x^{18} - 3 x^{15} + 5 x^{12} - 10 x^{9} + 13 x^{6} - 4 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 31^{6}$ |
$2$ |
$16.323092687567275$ |
$28.930952282978865$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$26589.00333277405$ |
| 18.6.818...288.1 |
$x^{18} - 3 x^{16} - 15 x^{12} - 9 x^{10} - 27 x^{8} + 27 x^{6} + 54 x^{4} - 27$ |
$18$ |
[6,6] |
$2^{30}\cdot 3^{27}$ |
$2$ |
$16.496755644$ |
$20.784609690826528$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$9339.268130221928$ |
| 18.6.103...552.1 |
$x^{18} - 9 x^{16} + 33 x^{14} - 60 x^{12} + 72 x^{10} - 81 x^{8} + 75 x^{6} - 45 x^{4} + 18 x^{2} - 3$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{31}$ |
$2$ |
$16.7140676303$ |
$16.714067630295588$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$12773.243864843542$ |
| 18.0.108...896.3 |
$x^{18} + 8 x^{16} + 18 x^{14} + 27 x^{12} + 45 x^{10} + 7 x^{8} + x^{6} - 8 x^{4} + 13 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{30}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$16.7554374565$ |
$25.352413640746768$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$8510.538851231004$ |
| 18.0.110...971.1 |
$x^{18} - 7 x^{17} + 24 x^{16} - 63 x^{15} + 140 x^{14} - 266 x^{13} + 466 x^{12} - 738 x^{11} + 1061 x^{10} - 1410 x^{9} + 1756 x^{8} - 1965 x^{7} + 1884 x^{6} - 1470 x^{5} + 891 x^{4} - 390 x^{3} + 112 x^{2} - 16 x + 1$ |
$18$ |
[0,9] |
$-\,3^{6}\cdot 19^{15}$ |
$2$ |
$16.7752275153$ |
$20.14599065465418$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$8$ |
$3951.8941267233818$ |
| 18.0.134...008.1 |
$x^{18} + 10 x^{16} - 2 x^{15} + 46 x^{14} - 8 x^{13} + 75 x^{12} + 34 x^{11} - 7 x^{10} + 80 x^{9} + 8 x^{8} - 34 x^{7} + 209 x^{6} - 32 x^{5} - 42 x^{4} + 30 x^{3} + 11 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 13^{15}$ |
$2$ |
$16.9557155647$ |
$16.955715564708598$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$2$ |
$8$ |
$1553.7588045761104$ |
| 18.6.134...008.1 |
$x^{18} - x^{17} + x^{16} + 3 x^{15} - 24 x^{14} - 16 x^{13} - 67 x^{12} - 74 x^{11} - 48 x^{10} - 49 x^{9} + 261 x^{8} + 283 x^{7} + 457 x^{6} + 225 x^{5} + 125 x^{4} + 16 x^{3} - 3 x^{2} + 4 x - 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 13^{15}$ |
$2$ |
$16.9557155647$ |
$23.97900291135148$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$11167.782400474298$ |
| 18.0.149...843.1 |
$x^{18} - 24 x^{15} + 177 x^{12} - 380 x^{9} + 141 x^{6} + 264 x^{3} + 64$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 17^{6}$ |
$2$ |
$17.055264854246897$ |
$27.348485954407977$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$39643.37265517847$ |
| 18.0.174...000.1 |
$x^{18} + x^{16} - 6 x^{15} - 4 x^{14} - 5 x^{13} - 6 x^{12} + 16 x^{11} + 22 x^{10} + 43 x^{9} + 41 x^{8} - 34 x^{7} + 121 x^{6} - 49 x^{5} + 17 x^{4} + 15 x^{3} - 4 x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 7^{12}$ |
$4$ |
$17.2042595524$ |
$28.344860147201352$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$6$ |
$8$ |
$13584.372345087919$ |
| 18.0.175...696.1 |
$x^{18} - 8 x^{15} + 21 x^{14} - 28 x^{13} + 32 x^{12} - 70 x^{11} + 182 x^{10} - 290 x^{9} + 280 x^{8} - 140 x^{7} + x^{6} + 42 x^{5} - 14 x^{4} - 4 x^{3} + 8$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 7^{12}\cdot 13^{6}$ |
$3$ |
$17.2085048979$ |
$26.38762874017197$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$4$ |
$8$ |
$13709.522062672431$ |
| 18.6.179...017.1 |
$x^{18} - 10 x^{15} - 12 x^{14} + 3 x^{13} + 12 x^{12} + 75 x^{11} + 18 x^{10} + 48 x^{9} - 69 x^{8} + 54 x^{7} - 145 x^{6} + 189 x^{5} - 195 x^{4} + 169 x^{3} - 114 x^{2} + 48 x - 8$ |
$18$ |
[6,6] |
$3^{27}\cdot 11^{9}$ |
$2$ |
$17.2336879396$ |
$17.233687939614086$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$16013.863210903846$ |
| 18.6.194...000.1 |
$x^{18} - 6 x^{17} + 11 x^{16} + 6 x^{15} - 60 x^{14} + 122 x^{13} - 141 x^{12} + 74 x^{11} + 54 x^{10} - 122 x^{9} + 71 x^{8} + 36 x^{7} - 70 x^{6} + 16 x^{5} + 33 x^{4} - 10 x^{3} - 11 x^{2} - 4 x + 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 5^{6}\cdot 7^{15}$ |
$3$ |
$17.3088559575$ |
$22.634106993721137$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$13385.82469770262$ |
| 18.6.206...125.1 |
$x^{18} - x^{17} - 9 x^{16} + 6 x^{15} + 20 x^{14} + 44 x^{13} - 84 x^{12} - 111 x^{11} + 29 x^{10} + 115 x^{9} + 121 x^{8} + 109 x^{7} + 56 x^{6} + 11 x^{5} - 25 x^{4} - 29 x^{3} - 11 x^{2} - 4 x + 1$ |
$18$ |
[6,6] |
$5^{15}\cdot 7^{14}$ |
$2$ |
$17.3689465692$ |
$19.351889266884974$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$11855.869329585865$ |
| 18.6.244...936.1 |
$x^{18} + 2 x^{16} - 5 x^{15} - 3 x^{14} + 22 x^{13} - 23 x^{12} + 45 x^{11} + 117 x^{10} - 54 x^{9} - 54 x^{8} - 21 x^{7} + 15 x^{6} + 39 x^{5} - 63 x^{4} + 17 x^{3} + 15 x^{2} - 8 x + 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{9}\cdot 7^{15}$ |
$3$ |
$17.5323038886$ |
$24.794421938893013$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$14420.859848954282$ |
| 18.6.276...472.1 |
$x^{18} - 6 x^{16} + 6 x^{14} - 6 x^{13} - 24 x^{12} - 6 x^{11} + 99 x^{10} + 160 x^{9} + 39 x^{8} - 210 x^{7} - 372 x^{6} - 246 x^{5} + 9 x^{4} + 96 x^{3} + 24 x^{2} - 12 x - 1$ |
$18$ |
[6,6] |
$2^{27}\cdot 3^{30}$ |
$2$ |
$17.6500965206$ |
$18.760906587882975$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$19815.232273990656$ |
| 18.0.290...000.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 54 x^{15} + 125 x^{14} - 252 x^{13} + 448 x^{12} - 670 x^{11} + 911 x^{10} - 1066 x^{9} + 1111 x^{8} - 902 x^{7} + 664 x^{6} - 328 x^{5} + 126 x^{4} - 76 x^{3} + 39 x^{2} - 10 x + 1$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 5^{6}\cdot 7^{12}$ |
$3$ |
$17.69838703901548$ |
$23.143481397064466$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$8$ |
$4763.165700235525$ |
| 18.6.312...000.1 |
$x^{18} - 6 x^{17} + 15 x^{16} - 26 x^{15} + 45 x^{14} - 54 x^{13} - 48 x^{12} + 390 x^{11} - 912 x^{10} + 1260 x^{9} - 1077 x^{8} + 420 x^{7} + 251 x^{6} - 534 x^{5} + 435 x^{4} - 214 x^{3} + 66 x^{2} - 12 x + 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{27}\cdot 5^{6}$ |
$3$ |
$17.7705913162$ |
$23.2379000772445$ |
|
|
|
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$20924.91599744446$ |
| 18.0.344...208.1 |
$x^{18} - x^{17} + 2 x^{15} - 3 x^{14} + x^{13} + 4 x^{12} + 7 x^{11} - 10 x^{10} + 7 x^{9} + 10 x^{8} - 27 x^{7} + 24 x^{6} + 13 x^{5} + 7 x^{4} + 4 x^{3} + 2 x^{2} + x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 7^{15}\cdot 11^{6}$ |
$3$ |
$17.8675878262$ |
$26.645960087356595$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$46255.83388015169$ |
| 18.0.379...000.2 |
$x^{18} + x^{16} - 16 x^{15} + 8 x^{14} - 53 x^{13} + 110 x^{12} - 62 x^{11} + 188 x^{10} - 65 x^{9} + 109 x^{8} - 70 x^{7} + 57 x^{6} - 71 x^{5} + 49 x^{4} - 31 x^{3} + 16 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 5^{9}\cdot 7^{15}$ |
$3$ |
$17.9647026261$ |
$22.634106993721137$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
$[2]$ |
$2$ |
$8$ |
$3652.277942285766$ |
| 18.6.496...429.2 |
$x^{18} - 9 x^{17} + 30 x^{16} - 29 x^{15} - 105 x^{14} + 462 x^{13} - 867 x^{12} + 819 x^{11} - 114 x^{10} - 585 x^{9} + 579 x^{8} - 126 x^{7} - 139 x^{6} + 105 x^{5} - 43 x^{3} + 30 x^{2} - 9 x + 1$ |
$18$ |
[6,6] |
$3^{21}\cdot 7^{15}$ |
$2$ |
$18.2343308497$ |
$18.234330849744854$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$11$ |
$27487.41219391865$ |
