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 |
18.0.111...168.1 |
$x^{18} - 4 x^{17} + 14 x^{16} - 31 x^{15} + 64 x^{14} - 100 x^{13} + 146 x^{12} - 176 x^{11} + 202 x^{10} - 205 x^{9} + 202 x^{8} - 176 x^{7} + 146 x^{6} - 100 x^{5} + 64 x^{4} - 31 x^{3} + 14 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$10.0611120208$ |
$10.061112020813587$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$64.801283476$ |
18.0.252...912.1 |
$x^{18} - 9 x^{17} + 36 x^{16} - 81 x^{15} + 105 x^{14} - 63 x^{13} - 21 x^{12} + 72 x^{11} - 63 x^{10} + 27 x^{9} - 6 x^{6} - 9 x^{5} + 18 x^{4} - 9 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{31}$ |
$2$ |
$10.5292028184$ |
$10.529202818387967$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$404.056392969$ |
18.0.405...267.1 |
$x^{18} - 3 x^{15} + 15 x^{12} + 20 x^{9} + 33 x^{6} + 6 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{39}$ |
$1$ |
$10.8084325966$ |
$10.808432596584025$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$529.942929585$ |
18.0.610...264.1 |
$x^{18} + 5 x^{16} + 12 x^{14} + 29 x^{12} + 55 x^{10} + 57 x^{8} + 39 x^{6} + 22 x^{4} + 8 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 13^{12}$ |
$2$ |
$11.0575496274$ |
$11.057549627357744$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$4$ |
$8$ |
$132.794513852$ |
18.0.379...168.1 |
$x^{18} + 6 x^{16} - 4 x^{15} + 15 x^{14} - 12 x^{13} + 38 x^{12} - 54 x^{11} + 84 x^{10} - 84 x^{9} + 84 x^{8} - 54 x^{7} + 38 x^{6} - 12 x^{5} + 15 x^{4} - 4 x^{3} + 6 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 3^{24}$ |
$2$ |
$12.2378934159$ |
$12.237893415933033$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$182.9899199$ |
18.0.435...963.1 |
$x^{18} - x^{17} + 4 x^{16} - x^{15} + 12 x^{14} - 9 x^{13} + 12 x^{12} - 18 x^{11} + 26 x^{10} - 12 x^{9} - 4 x^{8} - 5 x^{7} + 31 x^{6} - 17 x^{5} - 3 x^{4} + 5 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 19^{12}$ |
$2$ |
$12.3328380342$ |
$12.332838034173273$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$527.323608131$ |
18.0.144...803.2 |
$x^{18} - 9 x^{17} + 36 x^{16} - 80 x^{15} + 114 x^{14} - 132 x^{13} + 151 x^{12} - 138 x^{11} + 99 x^{10} - 73 x^{9} + 30 x^{8} - 6 x^{7} + 25 x^{6} + 30 x^{5} + 48 x^{4} + 36 x^{3} + 21 x^{2} + 21 x + 7$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 7^{12}$ |
$2$ |
$13.1837863724$ |
$13.183786372359444$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$1570.26677096$ |
18.0.485...104.1 |
$x^{18} + 3 x^{16} - 3 x^{14} - 12 x^{12} - 12 x^{10} + 3 x^{8} + 63 x^{6} + 3 x^{4} + 6 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{32}$ |
$2$ |
$14.1008586649$ |
$14.100858664870902$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$4$ |
$8$ |
$1555.42165689$ |
18.0.665...371.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} - 12 x^{14} + 30 x^{13} - 19 x^{12} + 9 x^{11} + 30 x^{10} + 22 x^{9} + 93 x^{8} - 15 x^{7} + 95 x^{6} + 24 x^{5} + 99 x^{4} + 15 x^{3} + 21 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 11^{9}$ |
$2$ |
$14.3502020363$ |
$14.350202036282921$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$550.447518763$ |
18.0.115...375.1 |
$x^{18} - 5 x^{17} + 16 x^{16} - 34 x^{15} + 63 x^{14} - 91 x^{13} + 92 x^{12} - 7 x^{11} - 128 x^{10} + 193 x^{9} - 128 x^{8} - 7 x^{7} + 92 x^{6} - 91 x^{5} + 63 x^{4} - 34 x^{3} + 16 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,5^{12}\cdot 7^{15}$ |
$2$ |
$14.7988636759$ |
$14.798863675926578$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$14$ |
$8$ |
$13425.8394152$ |
18.0.120...375.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 51 x^{15} + 87 x^{14} - 102 x^{13} + 48 x^{12} + 90 x^{11} - 234 x^{10} + 298 x^{9} - 156 x^{8} - 120 x^{7} + 354 x^{6} - 384 x^{5} + 273 x^{4} - 132 x^{3} + 45 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 5^{9}$ |
$2$ |
$14.8317989468$ |
$14.831798946842026$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$1012.11392421$ |
18.0.187...208.1 |
$x^{18} - 6 x^{17} + 22 x^{16} - 59 x^{15} + 110 x^{14} - 126 x^{13} + 64 x^{12} + 20 x^{11} - 28 x^{10} + 5 x^{9} - 28 x^{8} + 20 x^{7} + 64 x^{6} - 126 x^{5} + 110 x^{4} - 59 x^{3} + 22 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 13^{12}$ |
$3$ |
$15.2011411853$ |
$15.201141185311545$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$3594.02576505$ |
18.0.446...579.1 |
$x^{18} - 4 x^{17} + 7 x^{16} - 11 x^{15} + 37 x^{14} - 22 x^{13} + 71 x^{12} + 33 x^{11} + 204 x^{10} + 118 x^{9} + 305 x^{8} + 169 x^{7} + 216 x^{6} + 59 x^{5} + 84 x^{4} + 8 x^{3} + 12 x^{2} + x + 1$ |
$18$ |
[0,9] |
$-\,7^{12}\cdot 19^{9}$ |
$2$ |
$15.9505437935$ |
$15.950543793511486$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$1060.85049787$ |
18.0.708...000.1 |
$x^{18} - 6 x^{17} + 28 x^{16} - 102 x^{15} + 296 x^{14} - 696 x^{13} + 1429 x^{12} - 2684 x^{11} + 4639 x^{10} - 7178 x^{9} + 9523 x^{8} - 10268 x^{7} + 8521 x^{6} - 5202 x^{5} + 2254 x^{4} - 672 x^{3} + 133 x^{2} - 16 x + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 5^{9}\cdot 7^{12}$ |
$3$ |
$16.3649126361$ |
$16.364912636128995$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$1403.6050065$ |
18.0.165...632.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 150 x^{15} + 369 x^{14} - 711 x^{13} + 1119 x^{12} - 1449 x^{11} + 1458 x^{10} - 944 x^{9} + 135 x^{8} + 261 x^{7} + 69 x^{6} - 459 x^{5} + 279 x^{4} + 87 x^{3} - 99 x^{2} - 36 x + 37$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{39}$ |
$2$ |
$17.1573172739$ |
$17.15731727394486$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$47261.4483684$ |
18.0.165...632.2 |
$x^{18} - 12 x^{15} + 132 x^{12} - 160 x^{9} + 240 x^{6} + 96 x^{3} + 64$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{39}$ |
$2$ |
$17.1573172739$ |
$17.15731727394486$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$67625.9042436$ |
18.0.234...951.1 |
$x^{18} - 6 x^{17} + 19 x^{16} - 34 x^{15} + 42 x^{14} - 34 x^{13} + 20 x^{12} + 20 x^{11} - 97 x^{10} + 148 x^{9} - 131 x^{8} - 30 x^{7} + 251 x^{6} - 76 x^{5} - 53 x^{4} + 8 x^{3} + 11 x^{2} + 4 x + 1$ |
$18$ |
[0,9] |
$-\,31^{15}$ |
$1$ |
$17.4904672465$ |
$17.490467246468523$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$2615.01137266$ |
18.0.249...063.1 |
$x^{18} - 3 x^{17} + 7 x^{16} - 8 x^{15} + 35 x^{14} - 28 x^{13} + 110 x^{12} - 162 x^{11} + 286 x^{10} - 260 x^{9} + 262 x^{8} - 100 x^{7} + 124 x^{6} - 126 x^{5} + 105 x^{4} - 43 x^{3} + 21 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,7^{12}\cdot 23^{9}$ |
$2$ |
$17.5494136776$ |
$17.5494136775664$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$2564.16185262$ |
18.0.365...024.1 |
$x^{18} + 2 x^{16} - 6 x^{14} - 30 x^{12} - 19 x^{10} + 292 x^{8} + 337 x^{6} + 66 x^{4} + 540 x^{2} + 216$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$17.9268636048$ |
$17.926863604818365$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$2614.29263124$ |
18.0.379...000.1 |
$x^{18} - 6 x^{17} + 26 x^{16} - 79 x^{15} + 210 x^{14} - 448 x^{13} + 876 x^{12} - 1414 x^{11} + 2146 x^{10} - 2653 x^{9} + 3166 x^{8} - 2968 x^{7} + 2738 x^{6} - 1960 x^{5} + 1344 x^{4} - 753 x^{3} + 318 x^{2} - 34 x + 71$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 5^{9}\cdot 7^{15}$ |
$3$ |
$17.9647026261$ |
$17.964702626096855$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$4110.54115806$ |
18.0.621...704.1 |
$x^{18} - x^{17} - 11 x^{16} + 29 x^{15} + 13 x^{14} - 181 x^{13} + 260 x^{12} + 223 x^{11} - 970 x^{10} + 567 x^{9} + 1007 x^{8} - 1329 x^{7} + 46 x^{6} + 692 x^{5} - 526 x^{4} + 5 x^{3} + 348 x^{2} - 173 x + 83$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 19^{15}$ |
$2$ |
$18.4635269464$ |
$18.463526946433323$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$6329.31955748$ |
18.0.665...875.1 |
$x^{18} - 9 x^{17} + 43 x^{16} - 140 x^{15} + 353 x^{14} - 735 x^{13} + 1291 x^{12} - 1909 x^{11} + 2255 x^{10} - 1903 x^{9} + 935 x^{8} - 61 x^{7} - 215 x^{6} + 87 x^{5} + 35 x^{4} - 38 x^{3} + 13 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$18.532726798$ |
$18.532726798013343$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$21968.4785291$ |
18.0.747...487.1 |
$x^{18} - 6 x^{17} + 12 x^{16} + 3 x^{15} - 42 x^{14} + 33 x^{13} + 96 x^{12} - 225 x^{11} + 168 x^{10} + 85 x^{9} - 264 x^{8} + 381 x^{7} - 150 x^{6} - 153 x^{5} + 327 x^{4} - 243 x^{3} + 114 x^{2} - 36 x + 8$ |
$18$ |
[0,9] |
$-\,3^{32}\cdot 7^{9}$ |
$2$ |
$18.6536826499$ |
$18.65368264985934$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$12481.7713737$ |
18.0.829...416.1 |
$x^{18} + 6 x^{16} - 12 x^{15} + 21 x^{14} - 72 x^{13} + 144 x^{12} - 282 x^{11} + 462 x^{10} - 620 x^{9} + 864 x^{8} - 1122 x^{7} + 1206 x^{6} - 948 x^{5} + 549 x^{4} - 228 x^{3} + 66 x^{2} - 12 x + 1$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 3^{31}$ |
$2$ |
$18.7609065879$ |
$18.760906587882975$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$5165.75638936$ |
18.0.129...923.1 |
$x^{18} - 3 x^{17} + 5 x^{16} + 3 x^{14} - 47 x^{13} + 109 x^{12} - 65 x^{11} - 52 x^{10} + 192 x^{9} + 188 x^{8} + 192 x^{7} + 210 x^{6} + 135 x^{5} + 72 x^{4} + 41 x^{3} + 10 x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 37^{12}$ |
$2$ |
$19.2321768277$ |
$19.232176827720277$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$25740.6797756$ |
18.0.133...536.1 |
$x^{18} - x^{17} + 8 x^{16} - 13 x^{15} + 21 x^{14} - 27 x^{13} + 19 x^{12} + 22 x^{11} + 61 x^{10} + 85 x^{9} + 160 x^{8} - 26 x^{7} + 166 x^{6} - 87 x^{5} + 56 x^{4} - 34 x^{3} + 11 x^{2} - 2 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 7^{12}\cdot 11^{9}$ |
$3$ |
$19.2655627658$ |
$19.26556276580016$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$6989.09727608$ |
18.0.144...000.1 |
$x^{18} - 3 x^{16} - 6 x^{14} + 33 x^{10} + 273 x^{8} - 19 x^{6} + 225 x^{4} + 675 x^{2} + 125$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 5^{9}$ |
$3$ |
$19.3498084784$ |
$19.349808478363364$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$2$ |
$8$ |
$4680.41018868$ |
18.0.150...875.2 |
$x^{18} - 9 x^{17} + 39 x^{16} - 102 x^{15} + 207 x^{14} - 399 x^{13} + 723 x^{12} - 1089 x^{11} + 1371 x^{10} - 1465 x^{9} + 1314 x^{8} - 699 x^{7} + 231 x^{6} + 342 x^{5} - 336 x^{4} + 336 x^{3} - 144 x^{2} - 96 x + 64$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 5^{12}$ |
$2$ |
$19.3949574193$ |
$19.394957419257203$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$111472.114435$ |
18.0.243...643.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 150 x^{15} + 369 x^{14} - 711 x^{13} + 1114 x^{12} - 1473 x^{11} + 1956 x^{10} - 3127 x^{9} + 5337 x^{8} - 7785 x^{7} + 8797 x^{6} - 7140 x^{5} + 3858 x^{4} - 1187 x^{3} + 264 x^{2} - 15 x + 25$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 13^{12}$ |
$2$ |
$19.9191299718$ |
$19.919129971779828$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$61890.554687$ |
18.0.297...208.1 |
$x^{18} - 4 x^{16} + 45 x^{14} + 176 x^{12} + 362 x^{10} + 500 x^{8} + 369 x^{6} + 218 x^{4} + 72 x^{2} + 8$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 19^{12}$ |
$2$ |
$20.1394401761$ |
$20.13944017607579$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$8$ |
$19772.5679745$ |
18.0.365...871.1 |
$x^{18} - 3 x^{17} + 17 x^{16} - 30 x^{15} + 79 x^{14} - 126 x^{13} + 174 x^{12} - 66 x^{11} + 224 x^{10} - 138 x^{9} + 476 x^{8} - 384 x^{7} + 454 x^{6} - 294 x^{5} + 193 x^{4} - 93 x^{3} + 33 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,7^{12}\cdot 31^{9}$ |
$2$ |
$20.374151925$ |
$20.37415192496631$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$7064.88214687$ |
18.0.508...703.2 |
$x^{18} + 3 x^{16} - 3 x^{15} + 45 x^{14} - 60 x^{13} + 254 x^{12} - 198 x^{11} + 450 x^{10} - 400 x^{9} + 468 x^{8} - 534 x^{7} + 956 x^{6} - 774 x^{5} + 405 x^{4} - 138 x^{3} + 45 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 23^{9}$ |
$2$ |
$20.7503578613$ |
$20.75035786129348$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$8598.44783956$ |
18.0.593...088.3 |
$x^{18} - 3 x^{17} - 18 x^{16} + 47 x^{15} + 135 x^{14} - 273 x^{13} - 435 x^{12} + 858 x^{11} + 651 x^{10} - 1545 x^{9} - 168 x^{8} + 1170 x^{7} - 106 x^{6} - 441 x^{5} + 60 x^{4} + 82 x^{3} - 9 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$20.9279563564$ |
$20.927956356407396$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$6$ |
$8$ |
$20971.2187411$ |
18.0.593...088.5 |
$x^{18} - 9 x^{17} + 45 x^{16} - 140 x^{15} + 294 x^{14} - 426 x^{13} + 498 x^{12} - 792 x^{11} + 1791 x^{10} - 3423 x^{9} + 4887 x^{8} - 5184 x^{7} + 4514 x^{6} - 5658 x^{5} + 9858 x^{4} - 11200 x^{3} + 6153 x^{2} - 1209 x + 169$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$20.9279563564$ |
$20.927956356407396$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$6$ |
$8$ |
$51834.4889774$ |
18.0.134...583.2 |
$x^{18} - 3 x^{16} - 7 x^{15} + 9 x^{14} + 42 x^{13} - 6 x^{12} - 126 x^{11} - 108 x^{10} + 140 x^{9} + 450 x^{8} + 588 x^{7} + 498 x^{6} + 378 x^{5} + 525 x^{4} + 980 x^{3} + 1323 x^{2} + 1029 x + 343$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{15}$ |
$2$ |
$21.8982817704$ |
$21.898281770364438$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$14$ |
$8$ |
$725499.841066$ |
18.0.172...464.1 |
$x^{18} + 16 x^{16} + 102 x^{14} + 475 x^{12} + 1129 x^{10} + 1067 x^{8} + 477 x^{6} + 136 x^{4} + 29 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 37^{12}$ |
$2$ |
$22.2074049372$ |
$22.20740493717357$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 2]$ |
$4$ |
$8$ |
$18639.792218$ |
18.0.272...616.1 |
$x^{18} + 9 x^{16} - 4 x^{15} + 18 x^{14} - 9 x^{13} - 16 x^{12} + 36 x^{11} + 162 x^{10} + 231 x^{9} + 711 x^{8} + 342 x^{7} + 767 x^{6} + 297 x^{5} + 165 x^{4} + 77 x^{3} + 18 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{24}\cdot 11^{9}$ |
$3$ |
$22.7795258084$ |
$22.779525808351707$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$14940.9232602$ |
18.0.272...616.2 |
$x^{18} - 9 x^{17} + 57 x^{16} - 243 x^{15} + 840 x^{14} - 2298 x^{13} + 5309 x^{12} - 10128 x^{11} + 16527 x^{10} - 22468 x^{9} + 26112 x^{8} - 25056 x^{7} + 20355 x^{6} - 13275 x^{5} + 7182 x^{4} - 2916 x^{3} + 918 x^{2} - 162 x + 27$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{24}\cdot 11^{9}$ |
$3$ |
$22.7795258084$ |
$22.779525808351707$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$17836.0340898$ |
18.0.272...616.3 |
$x^{18} - 9 x^{17} + 39 x^{16} - 98 x^{15} + 153 x^{14} - 129 x^{13} - 29 x^{12} + 459 x^{11} - 918 x^{10} + 304 x^{9} + 1575 x^{8} - 825 x^{7} - 1475 x^{6} + 441 x^{5} + 2301 x^{4} + 1963 x^{3} + 891 x^{2} + 216 x + 27$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{24}\cdot 11^{9}$ |
$3$ |
$22.7795258084$ |
$22.779525808351707$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$110286.485801$ |
18.0.362...000.1 |
$x^{18} - 2 x^{17} + 5 x^{16} - 32 x^{15} - 10 x^{14} + 28 x^{13} + 172 x^{12} + 416 x^{11} + 5 x^{10} - 514 x^{9} - 735 x^{8} - 824 x^{7} + 1081 x^{6} + 1802 x^{5} + 1721 x^{4} + 1940 x^{3} + 1463 x^{2} - 294 x + 1561$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 5^{9}\cdot 7^{12}$ |
$3$ |
$23.1434813971$ |
$23.143481397064466$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[6]$ |
$2$ |
$8$ |
$19821.7051984$ |
18.0.655...231.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 6 x^{15} - 27 x^{14} - 12 x^{13} + 465 x^{12} - 1398 x^{11} + 2649 x^{10} - 3110 x^{9} + 2157 x^{8} + 1350 x^{7} - 4305 x^{6} + 5526 x^{5} - 3480 x^{4} - 120 x^{3} + 6528 x^{2} - 7680 x + 4096$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 13^{9}$ |
$2$ |
$23.9155571961$ |
$23.91555719607668$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[4]$ |
$2$ |
$8$ |
$29831.8168774$ |
18.0.687...096.1 |
$x^{18} + 2 x^{16} + 6 x^{14} - 110 x^{12} - 203 x^{10} + 1084 x^{8} - 883 x^{6} + 2522 x^{4} + 1352 x^{2} + 104$ |
$18$ |
[0,9] |
$-\,2^{27}\cdot 13^{15}$ |
$2$ |
$23.9790029114$ |
$23.97900291135148$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[6]$ |
$2$ |
$8$ |
$26737.5967738$ |
18.0.746...751.1 |
$x^{18} + 15 x^{16} - 9 x^{15} + 81 x^{14} - 36 x^{13} + 64 x^{12} - 162 x^{11} + 780 x^{10} - 918 x^{9} + 1782 x^{8} - 1674 x^{7} + 1792 x^{6} - 1188 x^{5} + 669 x^{4} - 252 x^{3} + 63 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 31^{9}$ |
$2$ |
$24.0903172796$ |
$24.090317279593503$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$2$ |
$8$ |
$42855.4917555$ |
18.0.762...000.1 |
$x^{18} - 9 x^{15} + 46 x^{12} - 171 x^{9} + 388 x^{6} - 171 x^{3} + 27$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{27}\cdot 5^{12}$ |
$3$ |
$24.118403063$ |
$24.11840306298509$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$2586019.54261$ |
18.0.854...347.2 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 411 x^{14} - 861 x^{13} + 1359 x^{12} - 1407 x^{11} + 264 x^{10} + 2354 x^{9} - 5535 x^{8} + 7515 x^{7} - 4059 x^{6} - 4305 x^{5} + 16131 x^{4} - 20937 x^{3} + 14379 x^{2} - 5190 x + 811$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 7^{12}$ |
$2$ |
$24.2721094002$ |
$24.27210940016998$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$6$ |
$8$ |
$102362.355108$ |
18.0.854...347.3 |
$x^{18} - 9 x^{17} + 63 x^{16} - 300 x^{15} + 1194 x^{14} - 3822 x^{13} + 10548 x^{12} - 24600 x^{11} + 50088 x^{10} - 87574 x^{9} + 133758 x^{8} - 175122 x^{7} + 198099 x^{6} - 188391 x^{5} + 150321 x^{4} - 95718 x^{3} + 47184 x^{2} - 15720 x + 2512$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 7^{12}$ |
$2$ |
$24.2721094002$ |
$24.27210940016998$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$6$ |
$8$ |
$980950.022268$ |
18.0.854...347.4 |
$x^{18} - 9 x^{17} + 39 x^{16} - 102 x^{15} + 117 x^{14} + 243 x^{13} - 1317 x^{12} + 2565 x^{11} - 2241 x^{10} - 1527 x^{9} + 8532 x^{8} - 13725 x^{7} + 11169 x^{6} - 5184 x^{5} + 6561 x^{4} - 14814 x^{3} + 18306 x^{2} - 11799 x + 3249$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 7^{12}$ |
$2$ |
$24.2721094002$ |
$24.27210940016998$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$18$ |
$8$ |
$636348.279995$ |
18.18.122...648.1 |
$x^{18} - 30 x^{16} - 37 x^{15} + 204 x^{14} + 294 x^{13} - 604 x^{12} - 858 x^{11} + 984 x^{10} + 1201 x^{9} - 984 x^{8} - 858 x^{7} + 604 x^{6} + 294 x^{5} - 204 x^{4} - 37 x^{3} + 30 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 13^{9}$ |
$3$ |
$24.7639553837$ |
$24.76395538367976$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$3530519.19402$ |
18.18.148...000.1 |
$x^{18} - 3 x^{17} - 24 x^{16} + 57 x^{15} + 237 x^{14} - 381 x^{13} - 1143 x^{12} + 1122 x^{11} + 2523 x^{10} - 1987 x^{9} - 2604 x^{8} + 2118 x^{7} + 1038 x^{6} - 1077 x^{5} - 12 x^{4} + 162 x^{3} - 21 x^{2} - 6 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{32}\cdot 5^{9}$ |
$3$ |
$25.0257573825$ |
$25.025757382495627$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$4070482.18025$ |
18.0.154...167.1 |
$x^{18} - 2 x^{17} - 13 x^{15} + 83 x^{14} - 101 x^{13} + 27 x^{12} - 399 x^{11} + 1430 x^{10} - 743 x^{9} - 2237 x^{8} + 4368 x^{7} - 3469 x^{6} + 3460 x^{5} + 1340 x^{4} - 4333 x^{3} + 6206 x^{2} - 3917 x + 13411$ |
$18$ |
[0,9] |
$-\,7^{12}\cdot 47^{9}$ |
$2$ |
$25.0869360252$ |
$25.086936025192795$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[5]$ |
$2$ |
$8$ |
$29368.4164899$ |