| 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 |
| 18.18.122...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 |
$2$ |
$17$ |
$3530519.19402$ |
| 18.18.133...125.1 |
$x^{18} - 24 x^{16} - 3 x^{15} + 216 x^{14} + 42 x^{13} - 943 x^{12} - 180 x^{11} + 2190 x^{10} + 272 x^{9} - 2772 x^{8} - 54 x^{7} + 1819 x^{6} - 180 x^{5} - 522 x^{4} + 110 x^{3} + 36 x^{2} - 6 x - 1$ |
$18$ |
[18,0] |
$3^{24}\cdot 5^{9}\cdot 17^{6}$ |
$3$ |
$24.8769031616$ |
$39.890652095882146$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$17$ |
$3646318.70374$ |
| 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 |
$2$ |
$17$ |
$4070482.18025$ |
| 18.18.177...000.1 |
$x^{18} - 6 x^{17} - 10 x^{16} + 97 x^{15} + 2 x^{14} - 560 x^{13} + 222 x^{12} + 1460 x^{11} - 630 x^{10} - 1983 x^{9} + 630 x^{8} + 1460 x^{7} - 222 x^{6} - 560 x^{5} - 2 x^{4} + 97 x^{3} + 10 x^{2} - 6 x - 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 5^{9}\cdot 19^{12}$ |
$3$ |
$25.2740049713$ |
$25.274004971349576$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$4327937.33071$ |
| 18.18.211...841.1 |
$x^{18} - 3 x^{17} - 24 x^{16} + 96 x^{15} + 111 x^{14} - 861 x^{13} + 529 x^{12} + 2301 x^{11} - 3117 x^{10} - 1647 x^{9} + 4395 x^{8} - 453 x^{7} - 2235 x^{6} + 573 x^{5} + 474 x^{4} - 100 x^{3} - 45 x^{2} + 3 x + 1$ |
$18$ |
[18,0] |
$3^{24}\cdot 73^{3}\cdot 577^{3}$ |
$3$ |
$25.5218088628$ |
$887.9960002144848$ |
|
|
? |
$S_3\wr C_3$ (as 18T207) |
trivial |
$2$ |
$17$ |
$4705474.71742$ |
| 18.18.233...669.1 |
$x^{18} - 4 x^{17} - 14 x^{16} + 71 x^{15} + 53 x^{14} - 472 x^{13} + 33 x^{12} + 1522 x^{11} - 555 x^{10} - 2661 x^{9} + 1098 x^{8} + 2705 x^{7} - 839 x^{6} - 1574 x^{5} + 194 x^{4} + 435 x^{3} + 27 x^{2} - 22 x + 1$ |
$18$ |
[18,0] |
$3^{9}\cdot 7^{5}\cdot 643^{6}$ |
$3$ |
$25.6673130347$ |
$292.54642426075026$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$17$ |
$5484058.78058$ |
| 18.18.362...741.1 |
$x^{18} - 18 x^{16} - x^{15} + 135 x^{14} + 15 x^{13} - 546 x^{12} - 90 x^{11} + 1287 x^{10} + 276 x^{9} - 1782 x^{8} - 459 x^{7} + 1385 x^{6} + 405 x^{5} - 534 x^{4} - 170 x^{3} + 72 x^{2} + 24 x + 1$ |
$18$ |
[18,0] |
$3^{27}\cdot 7^{15}$ |
$2$ |
$26.2984558329$ |
$26.298455832887633$ |
|
✓ |
✓ |
$C_6 \times C_3$ (as 18T2) |
trivial |
$2$ |
$17$ |
$6228406.91508$ |
| 18.18.364...121.1 |
$x^{18} - 2 x^{17} - 28 x^{16} + 40 x^{15} + 301 x^{14} - 276 x^{13} - 1523 x^{12} + 872 x^{11} + 3837 x^{10} - 1473 x^{9} - 4871 x^{8} + 1489 x^{7} + 3019 x^{6} - 864 x^{5} - 779 x^{4} + 222 x^{3} + 44 x^{2} - 7 x - 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 138041^{3}$ |
$2$ |
$26.3067204321$ |
$1359.5736588385284$ |
|
|
? |
$S_3\wr C_3$ (as 18T207) |
trivial |
$2$ |
$17$ |
$6072713.5102$ |
| 18.18.456...733.1 |
$x^{18} - 8 x^{17} - x^{16} + 141 x^{15} - 219 x^{14} - 798 x^{13} + 2016 x^{12} + 1242 x^{11} - 6472 x^{10} + 2028 x^{9} + 7364 x^{8} - 5183 x^{7} - 2609 x^{6} + 2861 x^{5} - 66 x^{4} - 342 x^{3} + 35 x^{2} + 10 x - 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 53^{9}$ |
$2$ |
$26.6401476874$ |
$26.640147687438905$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$6981069.98989$ |
| 18.18.460...584.1 |
$x^{18} - 7 x^{17} - 6 x^{16} + 144 x^{15} - 189 x^{14} - 975 x^{13} + 2404 x^{12} + 1953 x^{11} - 10054 x^{10} + 3451 x^{9} + 15638 x^{8} - 14529 x^{7} - 5420 x^{6} + 10671 x^{5} - 2089 x^{4} - 1318 x^{3} + 248 x^{2} + 75 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{6}\cdot 16361^{3}$ |
$3$ |
$26.651534093$ |
$1235.0724893715435$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$17$ |
$8288644.28023$ |
| 18.18.708...264.1 |
$x^{18} - 17 x^{16} + 115 x^{14} - 404 x^{12} + 802 x^{10} - 911 x^{8} + 568 x^{6} - 176 x^{4} + 24 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$27.2980167006$ |
$475.2592197863912$ |
|
|
✓ |
$C_3^3:S_4$ (as 18T203) |
trivial |
$2$ |
$17$ |
$9691749.65253$ |
| 18.18.804...776.1 |
$x^{18} - 17 x^{16} + 117 x^{14} - 421 x^{12} + 854 x^{10} - 979 x^{8} + 601 x^{6} - 177 x^{4} + 23 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
$75.34971632639669$ |
|
|
✓ |
$C_3\times S_4$ (as 18T33) |
trivial |
$2$ |
$17$ |
$10297407.3594$ |
| 18.18.102...584.1 |
$x^{18} - 3 x^{17} - 27 x^{16} + 93 x^{15} + 240 x^{14} - 1056 x^{13} - 675 x^{12} + 5580 x^{11} - 1083 x^{10} - 15058 x^{9} + 9870 x^{8} + 20628 x^{7} - 20619 x^{6} - 12441 x^{5} + 18096 x^{4} + 1416 x^{3} - 6102 x^{2} + 654 x + 487$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{31}\cdot 7^{9}$ |
$3$ |
$27.8576521612$ |
$27.857652161214947$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$15149384.4329$ |
| 18.18.104...456.1 |
$x^{18} - 17 x^{16} + 114 x^{14} - 389 x^{12} + 728 x^{10} - 758 x^{8} + 433 x^{6} - 131 x^{4} + 19 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 7^{12}\cdot 169457^{2}$ |
$3$ |
$27.889151509$ |
|
|
|
✓ |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$17$ |
$11298027.0227$ |
| 18.18.107...337.1 |
$x^{18} - x^{17} - 18 x^{16} + 18 x^{15} + 134 x^{14} - 134 x^{13} - 531 x^{12} + 531 x^{11} + 1198 x^{10} - 1198 x^{9} - 1519 x^{8} + 1519 x^{7} + 989 x^{6} - 989 x^{5} - 265 x^{4} + 265 x^{3} + 20 x^{2} - 20 x + 1$ |
$18$ |
[18,0] |
$3^{9}\cdot 19^{17}$ |
$2$ |
$27.9429569456$ |
$27.942956945645935$ |
|
✓ |
✓ |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$10972846.7711$ |
| 18.18.110...000.1 |
$x^{18} - 3 x^{17} - 25 x^{16} + 86 x^{15} + 210 x^{14} - 928 x^{13} - 506 x^{12} + 4615 x^{11} - 1713 x^{10} - 10195 x^{9} + 9755 x^{8} + 7035 x^{7} - 12770 x^{6} + 2985 x^{5} + 2555 x^{4} - 1109 x^{3} - 13 x^{2} + 20 x + 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 5^{15}\cdot 7^{12}$ |
$3$ |
$27.9836069772$ |
$39.574796511339834$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$17$ |
$11944012.4366$ |
| 18.18.111...352.1 |
$x^{18} - 6 x^{17} - 14 x^{16} + 114 x^{15} + 112 x^{14} - 925 x^{13} - 833 x^{12} + 3876 x^{11} + 4484 x^{10} - 7794 x^{9} - 12791 x^{8} + 4448 x^{7} + 15963 x^{6} + 4714 x^{5} - 6240 x^{4} - 4367 x^{3} - 319 x^{2} + 381 x + 79$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{12}\cdot 13^{15}$ |
$3$ |
$27.9932696238$ |
$58.22834729881542$ |
|
|
? |
$C_3^2\times S_3$ (as 18T17) |
trivial |
$2$ |
$17$ |
$11924892.4742$ |
| 18.18.128...008.1 |
$x^{18} - 24 x^{16} + 207 x^{14} - 876 x^{12} + 2046 x^{10} - 2748 x^{8} + 2099 x^{6} - 852 x^{4} + 156 x^{2} - 8$ |
$18$ |
[18,0] |
$2^{15}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$28.2110139716$ |
$63.33158505484892$ |
|
|
? |
$C_6\times A_4$ (as 18T25) |
trivial |
$2$ |
$17$ |
$14433379.8322$ |
| 18.18.142...832.1 |
$x^{18} - 3 x^{17} - 18 x^{16} + 43 x^{15} + 143 x^{14} - 223 x^{13} - 603 x^{12} + 508 x^{11} + 1359 x^{10} - 505 x^{9} - 1624 x^{8} + 146 x^{7} + 1012 x^{6} + 93 x^{5} - 302 x^{4} - 70 x^{3} + 31 x^{2} + 12 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{9}\cdot 16361^{2}$ |
$3$ |
$28.3784466401$ |
$1235.0724893715435$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$17$ |
$13397623.9367$ |
| 18.18.183...125.1 |
$x^{18} - 2 x^{17} - 25 x^{16} + 26 x^{15} + 214 x^{14} - 115 x^{13} - 823 x^{12} + 231 x^{11} + 1560 x^{10} - 284 x^{9} - 1556 x^{8} + 238 x^{7} + 826 x^{6} - 122 x^{5} - 220 x^{4} + 30 x^{3} + 25 x^{2} - 2 x - 1$ |
$18$ |
[18,0] |
$5^{9}\cdot 9685993193^{2}$ |
$2$ |
$28.7777327721$ |
$220068.0939277659$ |
|
|
? |
$C_2\times S_9$ (as 18T913) |
trivial |
$2$ |
$17$ |
$15038258.4518$ |
| 18.18.203...184.1 |
$x^{18} - 6 x^{17} - 18 x^{16} + 178 x^{15} - 126 x^{14} - 1323 x^{13} + 2437 x^{12} + 2646 x^{11} - 8874 x^{10} + 1316 x^{9} + 10665 x^{8} - 6174 x^{7} - 4241 x^{6} + 4158 x^{5} - 84 x^{4} - 765 x^{3} + 243 x^{2} - 27 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{21}\cdot 7^{15}$ |
$3$ |
$28.9451959728$ |
$28.94519597282117$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$21322924.4726$ |
| 18.18.279...217.1 |
$x^{18} - 4 x^{17} - 19 x^{16} + 93 x^{15} + 70 x^{14} - 668 x^{13} + 255 x^{12} + 1811 x^{11} - 1506 x^{10} - 2121 x^{9} + 2524 x^{8} + 876 x^{7} - 1788 x^{6} + 174 x^{5} + 468 x^{4} - 169 x^{3} - 4 x^{2} + 9 x - 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 53^{6}\cdot 97^{3}$ |
$3$ |
$29.4636087549$ |
$262.3750263924331$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$2$ |
$17$ |
$18498419.9543$ |
| 18.18.314...368.1 |
$x^{18} - 9 x^{17} + 12 x^{16} + 102 x^{15} - 283 x^{14} - 341 x^{13} + 1564 x^{12} + 355 x^{11} - 3972 x^{10} - 17 x^{9} + 5382 x^{8} + 199 x^{7} - 3798 x^{6} - 569 x^{5} + 1139 x^{4} + 236 x^{3} - 114 x^{2} - 25 x - 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{6}\cdot 31033^{3}$ |
$3$ |
$29.6522644978$ |
$1700.9807805094924$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$17$ |
$24136096.3741$ |
| 18.18.431...112.1 |
$x^{18} - 5 x^{17} - 17 x^{16} + 116 x^{15} + 28 x^{14} - 898 x^{13} + 729 x^{12} + 2639 x^{11} - 3688 x^{10} - 2725 x^{9} + 6303 x^{8} - 110 x^{7} - 4279 x^{6} + 1433 x^{5} + 961 x^{4} - 464 x^{3} - 59 x^{2} + 35 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$30.1782223225$ |
$104.21525486870038$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$2$ |
$17$ |
$23947078.6456$ |
| 18.18.453...000.1 |
$x^{18} - 30 x^{16} + 349 x^{14} - 2006 x^{12} + 6022 x^{10} - 9096 x^{8} + 6089 x^{6} - 1684 x^{4} + 196 x^{2} - 8$ |
$18$ |
[18,0] |
$2^{27}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$30.2638161317$ |
$30.26381613169108$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$30658656.5617$ |
| 18.18.456...917.1 |
$x^{18} - x^{17} - 17 x^{16} + 16 x^{15} + 120 x^{14} - 105 x^{13} - 455 x^{12} + 364 x^{11} + 1001 x^{10} - 715 x^{9} - 1287 x^{8} + 792 x^{7} + 924 x^{6} - 462 x^{5} - 330 x^{4} + 120 x^{3} + 45 x^{2} - 9 x - 1$ |
$18$ |
[18,0] |
$37^{17}$ |
$1$ |
$30.2746691718$ |
$30.27466917182413$ |
|
✓ |
✓ |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$24199468.4506$ |
| 18.18.512...888.1 |
$x^{18} - 25 x^{16} - 4 x^{15} + 230 x^{14} + 55 x^{13} - 996 x^{12} - 244 x^{11} + 2176 x^{10} + 393 x^{9} - 2413 x^{8} - 90 x^{7} + 1367 x^{6} - 175 x^{5} - 347 x^{4} + 95 x^{3} + 24 x^{2} - 11 x + 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{9}\cdot 31033^{2}$ |
$3$ |
$30.4704631024$ |
$1700.9807805094924$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$17$ |
$26691044.0882$ |
| 18.18.543...376.1 |
$x^{18} - 36 x^{16} - 18 x^{15} + 432 x^{14} + 342 x^{13} - 1995 x^{12} - 1530 x^{11} + 4203 x^{10} + 2810 x^{9} - 4293 x^{8} - 2628 x^{7} + 2097 x^{6} + 1296 x^{5} - 414 x^{4} - 294 x^{3} + 9 x^{2} + 18 x + 1$ |
$18$ |
[18,0] |
$2^{27}\cdot 3^{39}$ |
$2$ |
$30.5708639322$ |
$30.57086393216915$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$46962264.4542$ |
| 18.18.563...125.1 |
$x^{18} - x^{17} - 25 x^{16} + 20 x^{15} + 232 x^{14} - 137 x^{13} - 1018 x^{12} + 403 x^{11} + 2291 x^{10} - 566 x^{9} - 2742 x^{8} + 387 x^{7} + 1711 x^{6} - 131 x^{5} - 505 x^{4} + 30 x^{3} + 55 x^{2} - 5 x - 1$ |
$18$ |
[18,0] |
$5^{9}\cdot 19^{16}$ |
$2$ |
$30.6305552646$ |
$30.630555264593426$ |
|
✓ |
? |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$26179751.3516$ |
| 18.18.708...157.1 |
$x^{18} - x^{17} - 27 x^{16} + 22 x^{15} + 269 x^{14} - 180 x^{13} - 1259 x^{12} + 711 x^{11} + 2914 x^{10} - 1420 x^{9} - 3300 x^{8} + 1287 x^{7} + 1831 x^{6} - 522 x^{5} - 466 x^{4} + 89 x^{3} + 45 x^{2} - 6 x - 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 13^{15}$ |
$2$ |
$31.0230733917$ |
$31.02307339173177$ |
|
✓ |
? |
$C_6 \times C_3$ (as 18T2) |
trivial |
$2$ |
$17$ |
$37124865.5559$ |
| 18.18.737...136.1 |
$x^{18} - 17 x^{16} + 115 x^{14} - 400 x^{12} + 776 x^{10} - 851 x^{8} + 511 x^{6} - 157 x^{4} + 22 x^{2} - 1$ |
$18$ |
[18,0] |
$2^{30}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$31.0922149397$ |
|
|
|
✓ |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$17$ |
$34417835.0423$ |
| 18.18.774...592.1 |
$x^{18} - 18 x^{16} + 135 x^{14} - 546 x^{12} + 1287 x^{10} - 1782 x^{8} + 1386 x^{6} - 540 x^{4} + 81 x^{2} - 3$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{45}$ |
$2$ |
$31.1769145362$ |
$31.176914536239792$ |
|
✓ |
✓ |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$43670324.6529$ |
| 18.18.781...712.1 |
$x^{18} - 30 x^{16} - 18 x^{15} + 342 x^{14} + 384 x^{13} - 1776 x^{12} - 2898 x^{11} + 3831 x^{10} + 9322 x^{9} - 1350 x^{8} - 12804 x^{7} - 5103 x^{6} + 5976 x^{5} + 4440 x^{4} - 276 x^{3} - 828 x^{2} - 168 x - 8$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{31}\cdot 13^{6}$ |
$3$ |
$31.1927219529$ |
$73.34452913237226$ |
|
|
|
$C_3^2\times S_3$ (as 18T17) |
trivial |
$2$ |
$17$ |
$56996133.1215$ |
| 18.18.822...224.1 |
$x^{18} - 3 x^{17} - 30 x^{16} + 79 x^{15} + 385 x^{14} - 819 x^{13} - 2727 x^{12} + 4210 x^{11} + 11347 x^{10} - 11183 x^{9} - 27282 x^{8} + 14876 x^{7} + 35618 x^{6} - 8833 x^{5} - 21852 x^{4} + 2338 x^{3} + 4189 x^{2} - 986 x + 29$ |
$18$ |
[18,0] |
$2^{12}\cdot 7^{12}\cdot 29^{9}$ |
$3$ |
$31.2812685046$ |
$31.281268504572243$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$36105703.1937$ |
| 18.18.965...000.1 |
$x^{18} - 2 x^{17} - 22 x^{16} + 35 x^{15} + 174 x^{14} - 218 x^{13} - 650 x^{12} + 630 x^{11} + 1268 x^{10} - 931 x^{9} - 1322 x^{8} + 732 x^{7} + 728 x^{6} - 302 x^{5} - 200 x^{4} + 59 x^{3} + 24 x^{2} - 4 x - 1$ |
$18$ |
[18,0] |
$2^{12}\cdot 5^{9}\cdot 19^{6}\cdot 37^{6}$ |
$4$ |
$31.5614374187$ |
$153.73577043029613$ |
|
|
? |
$C_3\times S_3^2$ (as 18T46) |
trivial |
$2$ |
$17$ |
$37555765.5049$ |
| 18.18.984...889.1 |
$x^{18} - 9 x^{17} + 18 x^{16} + 60 x^{15} - 243 x^{14} - 63 x^{13} + 1112 x^{12} - 471 x^{11} - 2680 x^{10} + 1773 x^{9} + 3874 x^{8} - 2611 x^{7} - 3495 x^{6} + 1802 x^{5} + 1864 x^{4} - 499 x^{3} - 469 x^{2} + 36 x + 37$ |
$18$ |
[18,0] |
$2836601\cdot 18625670317^{2}$ |
$2$ |
$31.5945618853$ |
$229855596.0747367$ |
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$17$ |
$37477327.1808$ |
| 18.18.111...461.1 |
$x^{18} - 6 x^{17} - 21 x^{16} + 195 x^{15} - 87 x^{14} - 1848 x^{13} + 3708 x^{12} + 3330 x^{11} - 16686 x^{10} + 12758 x^{9} + 9624 x^{8} - 17265 x^{7} + 4149 x^{6} + 4521 x^{5} - 2802 x^{4} + 384 x^{3} + 63 x^{2} - 18 x + 1$ |
$18$ |
[18,0] |
$3^{31}\cdot 23^{9}$ |
$2$ |
$31.8106648154$ |
$31.810664815402767$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$50341250.6584$ |
| 18.18.127...272.1 |
$x^{18} - 22 x^{16} + 195 x^{14} - 905 x^{12} + 2407 x^{10} - 3777 x^{8} + 3444 x^{6} - 1699 x^{4} + 374 x^{2} - 17$ |
$18$ |
[18,0] |
$2^{18}\cdot 17^{3}\cdot 994046201^{2}$ |
$3$ |
$32.0491604229$ |
|
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$17$ |
$43529725.5707$ |
| 18.18.128...629.1 |
$x^{18} - 3 x^{17} - 27 x^{16} + 86 x^{15} + 198 x^{14} - 618 x^{13} - 806 x^{12} + 1917 x^{11} + 2124 x^{10} - 2696 x^{9} - 3204 x^{8} + 1365 x^{7} + 2209 x^{6} + 24 x^{5} - 561 x^{4} - 123 x^{3} + 30 x^{2} + 12 x + 1$ |
$18$ |
[18,0] |
$3^{27}\cdot 7^{12}\cdot 23^{3}$ |
$3$ |
$32.0652931532$ |
$91.18942839776756$ |
|
|
? |
$C_6\times A_4$ (as 18T25) |
trivial |
$2$ |
$17$ |
$41142192.1629$ |
| 18.18.136...328.1 |
$x^{18} - 35 x^{16} + 421 x^{14} - 2148 x^{12} + 5568 x^{10} - 7923 x^{8} + 6263 x^{6} - 2627 x^{4} + 518 x^{2} - 37$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{15}$ |
$2$ |
$32.1752132382$ |
$32.17521323820123$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$2$ |
$17$ |
$46590724.5415$ |
| 18.18.137...281.1 |
$x^{18} - 9 x^{17} + 16 x^{16} + 76 x^{15} - 296 x^{14} + 28 x^{13} + 1181 x^{12} - 1340 x^{11} - 1305 x^{10} + 3126 x^{9} - 756 x^{8} - 2054 x^{7} + 1651 x^{6} - 80 x^{5} - 370 x^{4} + 141 x^{3} - 3 x^{2} - 7 x + 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 71^{2}\cdot 281^{2}\cdot 15791^{2}$ |
$4$ |
$32.1856663352$ |
$64951.00036926973$ |
|
|
? |
$S_4\wr C_3$ (as 18T703) |
trivial |
$2$ |
$17$ |
$52369643.6382$ |
| 18.18.143...216.1 |
$x^{18} - 19 x^{16} + 152 x^{14} - 665 x^{12} + 1729 x^{10} - 2717 x^{8} + 2508 x^{6} - 1254 x^{4} + 285 x^{2} - 19$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{17}$ |
$2$ |
$32.265747429$ |
$32.26574742904561$ |
|
✓ |
✓ |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$39601653.8367$ |
| 18.18.153...328.1 |
$x^{18} - 7 x^{17} - 9 x^{16} + 163 x^{15} - 171 x^{14} - 1289 x^{13} + 2593 x^{12} + 4189 x^{11} - 13056 x^{10} - 3731 x^{9} + 30276 x^{8} - 8192 x^{7} - 32468 x^{6} + 18836 x^{5} + 12672 x^{4} - 11006 x^{3} + 190 x^{2} + 1275 x - 223$ |
$18$ |
[18,0] |
$2^{9}\cdot 7^{16}\cdot 67^{6}$ |
$3$ |
$32.38954569559743$ |
$137.8020245618911$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$2$ |
$17$ |
$63132777.18666566$ |
| 18.18.158...125.1 |
$x^{18} - 2 x^{17} - 28 x^{16} + 48 x^{15} + 282 x^{14} - 420 x^{13} - 1262 x^{12} + 1718 x^{11} + 2548 x^{10} - 3446 x^{9} - 2165 x^{8} + 3163 x^{7} + 695 x^{6} - 1290 x^{5} - 24 x^{4} + 203 x^{3} - 13 x^{2} - 10 x + 1$ |
$18$ |
[18,0] |
$5^{9}\cdot 7^{12}\cdot 3881^{3}$ |
$3$ |
$32.4370215468$ |
$509.7479840194441$ |
|
|
? |
$S_3^2:C_6$ (as 18T93) |
trivial |
$2$ |
$17$ |
$50253035.0963$ |
| 18.18.177...309.1 |
$x^{18} - 42 x^{16} - 14 x^{15} + 567 x^{14} + 378 x^{13} - 3339 x^{12} - 3402 x^{11} + 8505 x^{10} + 12726 x^{9} - 5481 x^{8} - 18417 x^{7} - 8008 x^{6} + 5796 x^{5} + 7770 x^{4} + 3731 x^{3} + 945 x^{2} + 126 x + 7$ |
$18$ |
[18,0] |
$3^{27}\cdot 7^{17}$ |
$2$ |
$32.6460041112$ |
$47.08368540167671$ |
|
|
? |
$C_9:C_6$ (as 18T14) |
trivial |
$2$ |
$17$ |
$59140273.8142$ |
| 18.18.181...389.1 |
$x^{18} - 4 x^{17} - 25 x^{16} + 105 x^{15} + 200 x^{14} - 957 x^{13} - 568 x^{12} + 4008 x^{11} - 85 x^{10} - 8113 x^{9} + 2772 x^{8} + 7493 x^{7} - 3445 x^{6} - 3093 x^{5} + 1357 x^{4} + 499 x^{3} - 146 x^{2} - x + 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 53^{6}\cdot 181^{3}$ |
$3$ |
$32.6916679418$ |
$358.4065315453231$ |
|
|
? |
$A_4\times D_6$ (as 18T60) |
trivial |
$2$ |
$17$ |
$50635216.4715$ |
| 18.18.192...125.1 |
$x^{18} - 27 x^{16} + 270 x^{14} - 1269 x^{12} + 3042 x^{10} - 76 x^{9} - 3888 x^{8} + 261 x^{7} + 2601 x^{6} - 297 x^{5} - 810 x^{4} + 120 x^{3} + 81 x^{2} - 9 x - 1$ |
$18$ |
[18,0] |
$3^{44}\cdot 5^{9}$ |
$2$ |
$32.7930191469$ |
$32.793019146867586$ |
|
✓ |
? |
$C_{18}$ (as 18T1) |
trivial |
$2$ |
$17$ |
$49974435.7673$ |
| 18.18.194...049.1 |
$x^{18} - 9 x^{17} + 18 x^{16} + 60 x^{15} - 245 x^{14} - 49 x^{13} + 1095 x^{12} - 551 x^{11} - 2499 x^{10} + 1935 x^{9} + 3304 x^{8} - 2755 x^{7} - 2633 x^{6} + 1881 x^{5} + 1204 x^{4} - 546 x^{3} - 244 x^{2} + 33 x - 1$ |
$18$ |
[18,0] |
$7^{12}\cdot 1583\cdot 4663\cdot 138041^{2}$ |
$4$ |
$32.815149647$ |
$3693821.517761268$ |
|
|
✓ |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$17$ |
$52675310.6177$ |
| 18.18.263...277.1 |
$x^{18} - 3 x^{17} - 31 x^{16} + 89 x^{15} + 346 x^{14} - 876 x^{13} - 2020 x^{12} + 3762 x^{11} + 7196 x^{10} - 7031 x^{9} - 15065 x^{8} + 2957 x^{7} + 14804 x^{6} + 4714 x^{5} - 3305 x^{4} - 1621 x^{3} + 195 x^{2} + 128 x - 1$ |
$18$ |
[18,0] |
$13^{15}\cdot 61^{6}$ |
$2$ |
$33.373063279$ |
$66.21418599701536$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$2$ |
$17$ |
$66833881.58911677$ |
| 18.18.279...368.1 |
$x^{18} - 21 x^{16} + 177 x^{14} - 780 x^{12} + 1970 x^{10} - 2950 x^{8} + 2615 x^{6} - 1323 x^{4} + 349 x^{2} - 37$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{16}\cdot 37$ |
$3$ |
$33.482831799$ |
|
|
|
? |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$17$ |
$60174129.1209$ |
