| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 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 |
trivial |
$14$ |
$8$ |
$725499.841066$ |
| 18.0.102...064.2 |
$x^{18} - 8 x^{15} + 117 x^{14} + 96 x^{13} + 32 x^{12} + 90 x^{11} + 2742 x^{10} + 982 x^{9} + 144 x^{8} - 816 x^{7} + 1321 x^{6} + 594 x^{5} + 258 x^{4} - 196 x^{3} + 144 x^{2} + 48 x + 8$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$31.6657925274$ |
$31.66579252742446$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$4$ |
$8$ |
$2945235.79497$ |
| 18.18.106...000.1 |
$x^{18} - 42 x^{16} - 35 x^{15} + 612 x^{14} + 870 x^{13} - 3614 x^{12} - 6570 x^{11} + 9132 x^{10} + 20685 x^{9} - 9144 x^{8} - 29310 x^{7} + 3176 x^{6} + 19710 x^{5} - 570 x^{4} - 6175 x^{3} + 450 x^{2} + 750 x - 125$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 19^{6}$ |
$4$ |
$40.9811875517$ |
$109.35426842962869$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
trivial |
$2$ |
$17$ |
$441529173.991$ |
| 18.18.524...768.2 |
$x^{18} - 48 x^{16} - 50 x^{15} + 810 x^{14} + 1422 x^{13} - 5781 x^{12} - 13950 x^{11} + 15537 x^{10} + 57258 x^{9} + 1863 x^{8} - 87300 x^{7} - 47013 x^{6} + 19944 x^{5} + 7146 x^{4} - 2466 x^{3} + 81 x^{2} + 18 x - 1$ |
$18$ |
[18,0] |
$2^{27}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$44.7821932556$ |
$44.78219325557628$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$1214573038.11$ |
| 18.0.172...984.1 |
$x^{18} - 24 x^{16} + 162 x^{14} - 46 x^{12} - 2943 x^{10} + 10998 x^{8} + 17569 x^{6} - 8856 x^{4} + 179856 x^{2} + 64$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 13^{12}$ |
$3$ |
$47.8432385961$ |
$47.84323859612865$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 6]$ |
$[2, 6]$ |
$4$ |
$8$ |
$8546548.81393$ |
| 18.0.172...984.5 |
$x^{18} + 27 x^{16} - 18 x^{15} + 306 x^{14} + 24 x^{13} + 1697 x^{12} + 1476 x^{11} + 6207 x^{10} + 11018 x^{9} + 25533 x^{8} + 42540 x^{7} + 67437 x^{6} + 115110 x^{5} + 166650 x^{4} + 270166 x^{3} + 274332 x^{2} + 152754 x + 53689$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 13^{12}$ |
$3$ |
$47.8432385961$ |
$47.84323859612865$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$4$ |
$8$ |
$27957948.204$ |
| 18.0.172...984.8 |
$x^{18} - 6 x^{15} + 126 x^{14} - 258 x^{13} + 18 x^{12} + 2070 x^{11} - 4011 x^{10} + 916 x^{9} + 18594 x^{8} - 35502 x^{7} + 26845 x^{6} + 71712 x^{5} - 151512 x^{4} + 195788 x^{3} + 66564 x^{2} - 242520 x + 441800$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 13^{12}$ |
$3$ |
$47.8432385961$ |
$47.84323859612865$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$4$ |
$8$ |
$1165904638.12$ |
| 18.0.428...819.2 |
$x^{18} - 9 x^{16} - 36 x^{15} - 9 x^{14} + 156 x^{13} + 1299 x^{12} + 216 x^{11} - 1308 x^{10} - 18780 x^{9} + 1719 x^{8} - 81948 x^{7} + 307069 x^{6} - 359964 x^{5} + 1502067 x^{4} - 1116292 x^{3} + 1247409 x^{2} - 627810 x + 240931$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 19^{15}$ |
$2$ |
$50.325682546$ |
$50.32568254601266$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$8$ |
$46149925.512$ |
| 18.18.445...000.1 |
$x^{18} - 42 x^{16} - 6 x^{15} + 621 x^{14} + 174 x^{13} - 4243 x^{12} - 1224 x^{11} + 14907 x^{10} + 2716 x^{9} - 27504 x^{8} - 90 x^{7} + 24358 x^{6} - 4302 x^{5} - 7317 x^{4} + 1174 x^{3} + 657 x^{2} + 42 x - 1$ |
$18$ |
[18,0] |
$2^{33}\cdot 3^{24}\cdot 5^{6}\cdot 7^{6}$ |
$4$ |
$50.4358502357$ |
$126.16348990930013$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$3927677460.06$ |
| 18.18.312...000.1 |
$x^{18} - 6 x^{17} - 33 x^{16} + 238 x^{15} + 321 x^{14} - 3486 x^{13} - 348 x^{12} + 24174 x^{11} - 10032 x^{10} - 84748 x^{9} + 53295 x^{8} + 147828 x^{7} - 98537 x^{6} - 121926 x^{5} + 66267 x^{4} + 46138 x^{3} - 11130 x^{2} - 7596 x - 659$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 7^{12}$ |
$4$ |
$56.1994457182$ |
$56.199445718153555$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$17$ |
$5939462204.29$ |
| 18.0.163...504.2 |
$x^{18} + 39 x^{16} - 6 x^{15} + 690 x^{14} - 456 x^{13} + 6449 x^{12} - 8292 x^{11} + 38547 x^{10} - 72674 x^{9} + 174777 x^{8} - 342684 x^{7} + 626373 x^{6} - 1080342 x^{5} + 1829010 x^{4} - 2676934 x^{3} + 3155688 x^{2} - 2877978 x + 1315333$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 19^{12}$ |
$3$ |
$61.6160805828$ |
$61.61608058284378$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[7, 7]$ |
$[7, 7]$ |
$4$ |
$8$ |
$16492221.647$ |
| 18.18.176...000.1 |
$x^{18} - 3 x^{17} - 57 x^{16} + 114 x^{15} + 1281 x^{14} - 1467 x^{13} - 14285 x^{12} + 6657 x^{11} + 82890 x^{10} + 2168 x^{9} - 247929 x^{8} - 86271 x^{7} + 358513 x^{6} + 187347 x^{5} - 215109 x^{4} - 108905 x^{3} + 56235 x^{2} + 16050 x - 5725$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 23^{8}$ |
$4$ |
$61.8793453523$ |
$124.20866564536522$ |
|
|
|
$C_3^2:S_3$ (as 18T24) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$100698193013$ |
| 18.0.265...127.1 |
$x^{18} - 6 x^{17} + 9 x^{16} - 2 x^{15} + 108 x^{14} - 300 x^{13} - 154 x^{12} - 372 x^{11} + 4437 x^{10} + 3068 x^{9} + 4563 x^{8} - 42312 x^{7} - 15229 x^{6} + 31704 x^{5} + 282339 x^{4} + 338450 x^{3} + 501699 x^{2} + 330378 x + 288787$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{9}\cdot 13^{12}$ |
$3$ |
$63.2906556206$ |
$63.2906556206417$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$8$ |
$953883029.041$ |
| 18.0.327...375.1 |
$x^{18} - 15 x^{16} - 5 x^{15} + 225 x^{14} + 150 x^{13} - 3350 x^{12} + 4500 x^{11} + 49500 x^{10} - 50750 x^{9} - 765000 x^{8} + 513750 x^{7} + 11728750 x^{6} - 3881250 x^{5} + 1284375 x^{4} - 425000 x^{3} + 140625 x^{2} - 46875 x + 15625$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 5^{12}\cdot 7^{15}$ |
$3$ |
$64.0309643329$ |
$64.03096433292906$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3, 9]$ |
$[3, 9]$ |
$14$ |
$8$ |
$482421316.708$ |
| 18.0.327...375.4 |
$x^{18} + 15 x^{16} - 70 x^{15} + 225 x^{14} - 2100 x^{13} + 5475 x^{12} - 31500 x^{11} + 145125 x^{10} - 285250 x^{9} + 2491875 x^{8} - 2940000 x^{7} + 17585625 x^{6} - 86231250 x^{5} + 165112500 x^{4} - 199675000 x^{3} + 330750000 x^{2} - 514500000 x + 343000000$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 5^{12}\cdot 7^{15}$ |
$3$ |
$64.0309643329$ |
$64.03096433292906$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3, 9]$ |
$[3, 9]$ |
$14$ |
$8$ |
$294941269.205$ |
| 18.18.122...125.2 |
$x^{18} - 9 x^{17} - 39 x^{16} + 468 x^{15} + 486 x^{14} - 9408 x^{13} - 2183 x^{12} + 94620 x^{11} + 4764 x^{10} - 506977 x^{9} - 46575 x^{8} + 1420686 x^{7} + 267385 x^{6} - 1902468 x^{5} - 447462 x^{4} + 1054870 x^{3} + 206514 x^{2} - 194931 x - 14641$ |
$18$ |
[18,0] |
$3^{24}\cdot 5^{9}\cdot 19^{12}$ |
$3$ |
$68.8888723452$ |
$68.88887234517178$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$17$ |
$180167785608$ |
| 18.0.126...499.2 |
$x^{18} + 42 x^{16} + 693 x^{14} + 6430 x^{12} + 39774 x^{10} + 162540 x^{8} + 449921 x^{6} + 786828 x^{4} + 727776 x^{2} + 438976$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 19^{9}$ |
$3$ |
$69.0139947971$ |
$69.01399479708432$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[2, 2, 2, 6]$ |
$[2, 2, 2, 6]$ |
$2$ |
$8$ |
$43937127.0651$ |
| 18.0.126...499.3 |
$x^{18} - 6 x^{17} - 24 x^{16} + 184 x^{15} + 279 x^{14} - 2850 x^{13} + 262 x^{12} + 16494 x^{11} + 2925 x^{10} - 94040 x^{9} + 73407 x^{8} + 46704 x^{7} + 266424 x^{6} - 773052 x^{5} + 255156 x^{4} + 815050 x^{3} - 318036 x^{2} - 678846 x + 509627$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 19^{9}$ |
$3$ |
$69.0139947971$ |
$69.01399479708432$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$2$ |
$8$ |
$283548193.676$ |
| 18.0.126...499.4 |
$x^{18} - 6 x^{17} + 30 x^{16} - 38 x^{15} + 165 x^{14} + 429 x^{13} + 1274 x^{12} + 8496 x^{11} + 11622 x^{10} + 98135 x^{9} + 150246 x^{8} + 394203 x^{7} + 1552856 x^{6} + 751800 x^{5} + 4641678 x^{4} + 3243023 x^{3} - 1461639 x^{2} - 809535 x + 2125873$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 19^{9}$ |
$3$ |
$69.0139947971$ |
$69.01399479708432$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$2$ |
$8$ |
$158404418.075$ |
| 18.18.316...853.1 |
$x^{18} - 78 x^{16} - 44 x^{15} + 2115 x^{14} + 1047 x^{13} - 28676 x^{12} - 8091 x^{11} + 216093 x^{10} + 19593 x^{9} - 930249 x^{8} + 20574 x^{7} + 2238465 x^{6} - 72945 x^{5} - 2767386 x^{4} - 215822 x^{3} + 1369629 x^{2} + 438756 x + 7687$ |
$18$ |
[18,0] |
$3^{24}\cdot 7^{15}\cdot 11^{9}$ |
$3$ |
$72.6283841858$ |
$72.62838418577843$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$[2]$ |
$2$ |
$17$ |
$84541091828.4$ |
| 18.0.378...848.2 |
$x^{18} - 6 x^{17} + 9 x^{16} - 2 x^{15} + 108 x^{14} - 300 x^{13} - 19 x^{12} - 912 x^{11} + 11727 x^{10} - 2782 x^{9} + 75573 x^{8} - 103062 x^{7} + 281591 x^{6} + 9834 x^{5} + 1115154 x^{4} - 1142590 x^{3} + 3167544 x^{2} - 1490232 x + 3898777$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 13^{15}$ |
$3$ |
$73.3631204624$ |
$73.36312046236682$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$3164585546.01$ |
| 18.0.142...459.1 |
$x^{18} - 42 x^{16} - 50 x^{15} + 1008 x^{14} + 2625 x^{13} - 10583 x^{12} - 42084 x^{11} + 70308 x^{10} + 573628 x^{9} + 1226484 x^{8} + 2956863 x^{7} + 10723798 x^{6} + 22937040 x^{5} + 24830904 x^{4} + 29539579 x^{3} + 69119064 x^{2} + 91426965 x + 43051499$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{15}\cdot 13^{9}$ |
$3$ |
$78.9553777676$ |
$78.95537776760732$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$8$ |
$1513625862.7$ |
| 18.0.175...624.2 |
$x^{18} - 3 x^{17} + 81 x^{16} - 181 x^{15} + 2367 x^{14} - 5685 x^{13} + 35832 x^{12} - 108153 x^{11} + 347772 x^{10} - 1091869 x^{9} + 2802105 x^{8} - 6679983 x^{7} + 14059302 x^{6} - 26653494 x^{5} + 40703652 x^{4} - 48227875 x^{3} + 44787282 x^{2} - 25200639 x + 5731627$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{24}\cdot 19^{15}$ |
$3$ |
$79.8870414146$ |
$79.88704141455815$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3, 9]$ |
$[3, 9]$ |
$2$ |
$8$ |
$679111745.705$ |
| 18.0.175...624.3 |
$x^{18} - 3 x^{17} + 45 x^{16} - x^{15} + 531 x^{14} + 1707 x^{13} + 2122 x^{12} + 24027 x^{11} + 9156 x^{10} + 77355 x^{9} + 184407 x^{8} - 259503 x^{7} + 1343298 x^{6} - 2120454 x^{5} + 3239058 x^{4} + 2562941 x^{3} + 15892830 x^{2} + 36946497 x + 38031889$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{24}\cdot 19^{15}$ |
$3$ |
$79.8870414146$ |
$79.88704141455815$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3, 9]$ |
$[3, 9]$ |
$2$ |
$8$ |
$1866897191.25$ |
| 18.0.252...687.1 |
$x^{18} - 6 x^{17} - 3 x^{16} + 106 x^{15} - 96 x^{14} - 1344 x^{13} + 3454 x^{12} + 7356 x^{11} - 38763 x^{10} - 4544 x^{9} + 298227 x^{8} - 521196 x^{7} - 490173 x^{6} + 2548380 x^{5} - 1146549 x^{4} - 7608398 x^{3} + 17453919 x^{2} - 16918818 x + 7338191$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{9}\cdot 19^{12}$ |
$3$ |
$81.5104129924$ |
$81.5104129923602$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$4879834290.6$ |
| 18.18.526...000.1 |
$x^{18} - 6 x^{17} - 45 x^{16} + 286 x^{15} + 729 x^{14} - 5178 x^{13} - 4744 x^{12} + 45366 x^{11} + 3528 x^{10} - 201016 x^{9} + 90423 x^{8} + 417660 x^{7} - 345817 x^{6} - 296670 x^{5} + 359631 x^{4} + 1418 x^{3} - 85146 x^{2} + 15000 x + 2605$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 13^{12}$ |
$4$ |
$84.9106646592$ |
$84.91066465919563$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$1909382935840$ |
| 18.18.567...789.1 |
$x^{18} - 6 x^{17} - 33 x^{16} + 238 x^{15} + 321 x^{14} - 3486 x^{13} - 375 x^{12} + 24282 x^{11} - 10086 x^{10} - 84658 x^{9} + 53835 x^{8} + 142374 x^{7} - 94613 x^{6} - 108156 x^{5} + 63189 x^{4} + 26644 x^{3} - 14775 x^{2} + 234 x + 169$ |
$18$ |
[18,0] |
$3^{24}\cdot 7^{12}\cdot 29^{9}$ |
$3$ |
$85.2627557544$ |
$85.26275575435449$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$1179947670400$ |
| 18.0.583...904.2 |
$x^{18} + 63 x^{16} - 6 x^{15} + 1704 x^{14} - 480 x^{13} + 24166 x^{12} - 12444 x^{11} + 202149 x^{10} - 181200 x^{9} + 1162071 x^{8} - 1477062 x^{7} + 4756826 x^{6} - 6804240 x^{5} + 13639524 x^{4} - 20569240 x^{3} + 28026072 x^{2} - 21757248 x + 15211808$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 31^{12}$ |
$3$ |
$85.3950697993$ |
$85.39506979931413$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 2]$ |
$[2, 2]$ |
$4$ |
$8$ |
$1416953828460$ |
| 18.0.103...951.1 |
$x^{18} + 42 x^{16} + 693 x^{14} + 5980 x^{12} + 30324 x^{10} + 94500 x^{8} + 180956 x^{6} + 203763 x^{4} + 121086 x^{2} + 29791$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 31^{9}$ |
$3$ |
$88.1538355775$ |
$88.15383557748156$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 2, 2, 2, 2, 18]$ |
$[2, 2, 2, 2, 2, 18]$ |
$2$ |
$8$ |
$25375511.7068$ |
| 18.0.103...951.2 |
$x^{18} + 15 x^{16} - 29 x^{15} - 243 x^{14} + 918 x^{13} + 891 x^{12} - 20367 x^{11} + 92040 x^{10} - 168884 x^{9} - 153522 x^{8} + 807390 x^{7} + 3503575 x^{6} - 29660418 x^{5} + 97709343 x^{4} - 187863873 x^{3} + 217549836 x^{2} - 137331936 x + 35826112$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 31^{9}$ |
$3$ |
$88.1538355775$ |
$88.15383557748156$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[5, 45]$ |
$[5, 45]$ |
$2$ |
$8$ |
$140696363.146$ |
| 18.0.103...951.3 |
$x^{18} - 12 x^{16} - 40 x^{15} + 27 x^{14} + 2682 x^{13} - 8481 x^{12} - 46773 x^{11} + 196185 x^{10} + 115920 x^{9} - 372438 x^{8} - 2984337 x^{7} + 3855198 x^{6} + 3280617 x^{5} + 17356086 x^{4} + 2265219 x^{3} + 1361610 x^{2} + 81696600 x + 68921000$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{12}\cdot 31^{9}$ |
$3$ |
$88.1538355775$ |
$88.15383557748156$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[9]$ |
$[9]$ |
$2$ |
$8$ |
$2441590543.81$ |
| 18.18.434...125.1 |
$x^{18} - 78 x^{16} + 2349 x^{14} - 34390 x^{12} + 256788 x^{10} - 979902 x^{8} + 1847701 x^{6} - 1481670 x^{4} + 270225 x^{2} - 8000$ |
$18$ |
[18,0] |
$3^{24}\cdot 5^{9}\cdot 31^{12}$ |
$3$ |
$95.4745905073$ |
$95.47459050730286$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$10945855677300$ |
| 18.0.487...184.1 |
$x^{18} + 12 x^{16} - 162 x^{14} - 1198 x^{12} - 819 x^{10} - 89010 x^{8} + 912457 x^{6} + 3815136 x^{4} + 29640960 x^{2} + 4096$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 37^{12}$ |
$3$ |
$96.0858606848$ |
$96.08586068484361$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[2, 2, 2, 6]$ |
$[2, 2, 2, 6]$ |
$4$ |
$8$ |
$965409693.316$ |
| 18.0.487...184.4 |
$x^{18} - 66 x^{15} + 234 x^{14} + 798 x^{13} + 2178 x^{12} - 13626 x^{11} + 3009 x^{10} + 177356 x^{9} + 708066 x^{8} + 289446 x^{7} - 525395 x^{6} + 7333632 x^{5} + 43019544 x^{4} + 99526876 x^{3} + 125484804 x^{2} + 59729064 x + 14215112$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 37^{12}$ |
$3$ |
$96.0858606848$ |
$96.08586068484361$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$4$ |
$8$ |
$23499349537.7$ |
| 18.0.487...184.5 |
$x^{18} + 75 x^{16} - 18 x^{15} + 2262 x^{14} + 648 x^{13} + 35145 x^{12} + 41748 x^{11} + 320943 x^{10} + 693418 x^{9} + 2156541 x^{8} + 5317092 x^{7} + 11496917 x^{6} + 23263158 x^{5} + 41815602 x^{4} + 60119870 x^{3} + 67983876 x^{2} + 54028266 x + 20963581$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 37^{12}$ |
$3$ |
$96.0858606848$ |
$96.08586068484361$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
$[3]$ |
$[3]$ |
$4$ |
$8$ |
$13300928671.4$ |
| 18.0.583...019.2 |
$x^{18} + 9 x^{16} - 89 x^{15} + 414 x^{14} - 843 x^{13} + 12287 x^{12} - 21249 x^{11} + 28950 x^{10} + 60037 x^{9} + 394146 x^{8} + 1211622 x^{7} + 4130146 x^{6} - 2249577 x^{5} + 25709991 x^{4} + 49727523 x^{3} + 7647219 x^{2} + 20166849 x + 324972701$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 7^{9}\cdot 13^{15}$ |
$3$ |
$97.0502860735$ |
$97.05028607354826$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
$[14]$ |
$[14]$ |
$2$ |
$8$ |
$1404958821.12$ |
| 18.18.780...417.2 |
$x^{18} - 99 x^{16} - 107 x^{15} + 2565 x^{14} + 5592 x^{13} - 15601 x^{12} - 44307 x^{11} + 30192 x^{10} + 130936 x^{9} - 684 x^{8} - 162336 x^{7} - 46879 x^{6} + 73710 x^{5} + 32559 x^{4} - 6419 x^{3} - 5652 x^{2} - 1056 x - 64$ |
$18$ |
[18,0] |
$3^{24}\cdot 13^{12}\cdot 17^{9}$ |
$3$ |
$98.6313631017$ |
$98.63136310173302$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$17$ |
$4821214894440$ |
| 18.0.897...667.2 |
$x^{18} - 3 x^{17} - 21 x^{16} + 140 x^{15} + 414 x^{14} - 774 x^{13} + 3528 x^{12} - 7740 x^{11} - 22944 x^{10} + 269182 x^{9} - 230346 x^{8} - 1126530 x^{7} + 2050863 x^{6} - 2830905 x^{5} + 164733 x^{4} + 4266030 x^{3} - 19535244 x^{2} + 49794000 x + 102509248$ |
$18$ |
[0,9] |
$-\,3^{24}\cdot 43^{15}$ |
$2$ |
$99.399771477$ |
$99.39977147697093$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
trivial |
$2$ |
$8$ |
$275157487154$ |
| 18.10.361...000.1 |
$x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 384 x^{14} - 672 x^{13} + 749 x^{12} - 204 x^{11} - 1008 x^{10} + 2191 x^{9} - 2253 x^{8} + 876 x^{7} + 684 x^{6} - 1107 x^{5} + 414 x^{4} + 269 x^{3} - 180 x^{2} - 24 x + 16$ |
$18$ |
[10,4] |
$2^{12}\cdot 3^{24}\cdot 5^{14}\cdot 13^{6}\cdot 1061117$ |
$5$ |
$122.059265$ |
|
|
|
? |
$C_2^5.S_4^2$ (as 18T623) |
trivial |
trivial |
$2$ |
$13$ |
$5673649067000$ |
| 18.0.182...544.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 28 x^{15} - 18 x^{14} + 84 x^{13} + 1125 x^{12} - 684 x^{11} - 9033 x^{10} + 4406 x^{9} + 37749 x^{8} - 9228 x^{7} - 91515 x^{6} + 116022 x^{5} + 259530 x^{4} - 471756 x^{3} - 406206 x^{2} + 1193652 x + 1108729$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{24}\cdot 89^{12}$ |
$3$ |
$172.498374276$ |
$172.49837427579374$ |
|
|
|
$C_3:S_5$ (as 18T146) |
$[8]$ |
$[8]$ |
$2$ |
$8$ |
$744195720478$ |
| 18.18.989...000.1 |
$x^{18} - 6 x^{17} - 63 x^{16} + 322 x^{15} + 1890 x^{14} - 6870 x^{13} - 32995 x^{12} + 72990 x^{11} + 340410 x^{10} - 421850 x^{9} - 2110887 x^{8} + 1343502 x^{7} + 7913161 x^{6} - 2202504 x^{5} - 17506260 x^{4} + 1440476 x^{3} + 21040944 x^{2} + 15732 x - 10624348$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{24}\cdot 5^{19}\cdot 7^{4}\cdot 1531^{2}\cdot 1115815069^{2}$ |
$6$ |
$1667.12076641$ |
|
|
|
? |
$A_5^3:S_3$ (as 18T935) |
trivial |
$[2]$ |
$2$ |
$17$ |
$1474239817750000000000000$ |
| 18.6.516...000.1 |
$x^{18} - 6 x^{17} - 79635 x^{16} + 726016 x^{15} - 21346492116 x^{14} + 262385243232 x^{13} - 222640923218036 x^{12} + 5287125117175824 x^{11} + 36115874586042869742 x^{10} - 315574620417688738476 x^{9} + 1064246929788629129834742 x^{8} - 10094756489315953842318336 x^{7} + 5555830520763339794029338844 x^{6} - 66983200453112231194458550608 x^{5} - 95464018377851901223533667416996 x^{4} + 244705662148773213221767445905616 x^{3} - 887010722785755909642099142950505815 x^{2} + 1957760134295180518228084208239496514 x - 371023633673372769266300083152445623019$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{24}\cdot 5^{14}\cdot 13^{6}\cdot 1061117^{7}$ |
$5$ |
$12449.6891505$ |
|
|
|
? |
$C_2^7:S_3^2$ (as 18T461) |
not computed |
not computed |
$2$ |
$11$ |
|
| 20.4.289...000.1 |
$x^{20} - 2 x^{19} - 7 x^{18} + 6 x^{17} + 42 x^{16} - 18 x^{15} - 121 x^{14} - 52 x^{13} + 292 x^{12} + 114 x^{11} - 96 x^{10} - 180 x^{9} + 610 x^{8} - 920 x^{7} + 683 x^{6} - 420 x^{5} + 231 x^{4} - 78 x^{3} + 19 x^{2} - 2 x - 1$ |
$20$ |
[4,8] |
$2^{24}\cdot 3^{24}\cdot 5^{14}$ |
$3$ |
$26.4886913864$ |
$40.91986287620002$ |
|
|
? |
$S_6$ (as 20T145) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$2105909.73103$ |
| 20.0.984...656.1 |
$x^{20} - 6 x^{19} + 16 x^{18} - 40 x^{17} + 69 x^{16} + 44 x^{15} - 275 x^{14} - 36 x^{13} + 1240 x^{12} - 2696 x^{11} + 3576 x^{10} - 3812 x^{9} + 5907 x^{8} - 12888 x^{7} + 25347 x^{6} - 36688 x^{5} + 26208 x^{4} + 6056 x^{3} - 16823 x^{2} - 1620 x + 7048$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{24}\cdot 7^{16}$ |
$3$ |
$35.4530769535$ |
$41.045930044873074$ |
|
|
? |
$S_6$ (as 20T145) |
$[4]$ |
$[4]$ |
$4$ |
$9$ |
$78497371.7756$ |
| 28.4.475...624.1 |
$x^{28} - 18 x^{26} + 141 x^{24} - 144 x^{23} - 408 x^{22} + 2880 x^{21} - 546 x^{20} - 28320 x^{19} - 324 x^{18} + 164448 x^{17} + 96294 x^{16} - 562272 x^{15} - 723000 x^{14} + 913152 x^{13} + 2332629 x^{12} + 312864 x^{11} - 3011346 x^{10} - 2835936 x^{9} - 647823 x^{8} + 201840 x^{7} + 2076816 x^{6} + 5139456 x^{5} + 4893776 x^{4} + 2123136 x^{3} + 420096 x^{2} + 31744 x + 576$ |
$28$ |
[4,12] |
$2^{98}\cdot 3^{36}$ |
$2$ |
$46.45651185000656$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
$[2]$ |
$[2]$ |
$2$ |
$15$ |
$14967380498102.287$ |
| 28.4.121...744.2 |
$x^{28} + 6 x^{26} - 32 x^{25} + 150 x^{24} - 384 x^{23} + 920 x^{22} - 1728 x^{21} + 8364 x^{20} - 22384 x^{19} + 31200 x^{18} - 30816 x^{17} + 68908 x^{16} - 85392 x^{15} - 268320 x^{14} + 2154976 x^{13} - 6464163 x^{12} + 8428848 x^{11} + 6064966 x^{10} - 40987584 x^{9} + 61579314 x^{8} - 16839984 x^{7} - 77072616 x^{6} + 126099552 x^{5} - 73961834 x^{4} - 14277120 x^{3} + 49274868 x^{2} - 29147456 x + 5983140$ |
$28$ |
[4,12] |
$2^{106}\cdot 3^{36}$ |
$2$ |
$56.63112227187001$ |
|
|
|
|
$G(2,2)$ (as 28T393) |
trivial |
$[2]$ |
$2$ |
$15$ |
$654344330188521.6$ |
