| 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 |
Unit signature rank |
Max $p$ |
| 12.0.148231719413132544.2 |
$x^{12} - 13 x^{9} + 45 x^{6} + 25 x^{3} + 128$ |
$12$ |
(0, 6) |
$2^{8}\cdot 3^{15}\cdot 7^{9}$ |
$3$ |
$26.971913747123093$ |
$31.418004901678522$ |
|
|
? |
$S_3\times S_4$ (as 12T83) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$18556.493475900643$ |
$0$ |
$7$ |
| 16.8.368...704.1 |
$x^{16} - 36 x^{14} - 24 x^{13} + 564 x^{12} + 816 x^{11} - 4372 x^{10} - 9672 x^{9} + 14364 x^{8} + 42912 x^{7} - 30240 x^{6} - 83808 x^{5} + 170748 x^{4} + 321408 x^{3} - 128952 x^{2} - 297216 x + 41148$ |
$16$ |
(8, 4) |
$2^{36}\cdot 3^{18}\cdot 7^{12}$ |
$3$ |
$70.45347710739163$ |
$96.90637454417673$ |
|
|
|
$S_4^2$ (as 16T1033) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$5113934341.234144$ |
$5$ |
$7$ |
| 18.4.266...007.1 |
$x^{18} - 5 x^{15} + 3 x^{12} + 7 x^{9} - 13 x^{6} - 8 x^{3} - 1$ |
$18$ |
(4, 7) |
$-\,3^{6}\cdot 7^{9}\cdot 67^{6}$ |
$3$ |
$15.4981920814$ |
$61.01288466109334$ |
|
|
|
$C_2\times C_6^2:D_6$ (as 18T228) |
trivial |
trivial |
$2$ |
$10$ |
$5730.4211423$ |
$4$ |
$67$ |
| 18.2.718...189.1 |
$x^{18} - 2 x^{17} - 7 x^{16} + 13 x^{15} + 23 x^{14} - 59 x^{13} + 7 x^{12} + 64 x^{11} - 58 x^{10} - 6 x^{9} + 69 x^{8} - 49 x^{7} - 20 x^{6} - 12 x^{5} - 2 x^{4} + 6 x^{3} + 2 x^{2} - 3 x + 1$ |
$18$ |
(2, 8) |
$3^{9}\cdot 7^{9}\cdot 67^{6}$ |
$3$ |
$18.612351609$ |
$61.01288466109334$ |
|
|
|
$C_2\times C_6^2:D_6$ (as 18T228) |
trivial |
$[2]$ |
$2$ |
$9$ |
$68054.6206665$ |
$1$ |
$67$ |
| 18.6.108...672.1 |
$x^{18} - 3 x^{17} - 10 x^{16} + 37 x^{15} + 36 x^{14} - 193 x^{13} - 18 x^{12} + 455 x^{11} - 94 x^{10} - 445 x^{9} - 141 x^{8} + 404 x^{7} + 500 x^{6} - 480 x^{5} - 287 x^{4} + 101 x^{3} + 147 x^{2} + 50 x + 4$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6}$ |
$4$ |
$24.6018464137$ |
$172.57049793444716$ |
|
|
|
$C_2\times C_6^2:D_6$ (as 18T228) |
trivial |
$[2]$ |
$2$ |
$11$ |
$788082.245978$ |
$5$ |
$67$ |
| 18.6.108...672.2 |
$x^{18} - x^{16} - 18 x^{14} + 16 x^{12} + 98 x^{10} - 42 x^{8} - 294 x^{6} - 245 x^{4} + 1372 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6}$ |
$4$ |
$24.6018464137$ |
$238.8220174269005$ |
|
|
? |
$C_2^3\wr C_3.S_3^2$ (as 18T734) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1312710.96517$ |
$5$ |
$67$ |
| 18.0.435...688.1 |
$x^{18} - 6 x^{17} + 8 x^{16} - 2 x^{15} + 51 x^{14} - 74 x^{13} - 188 x^{12} + 76 x^{11} + 682 x^{10} + 30 x^{9} - 373 x^{8} - 3434 x^{7} + 5336 x^{6} - 3832 x^{5} + 7421 x^{4} - 11846 x^{3} + 9861 x^{2} - 6026 x + 2818$ |
$18$ |
(0, 9) |
$-\,2^{14}\cdot 3^{6}\cdot 7^{9}\cdot 67^{6}$ |
$4$ |
$26.5714638138$ |
$238.8220174269005$ |
|
|
|
$C_2^3\wr C_3.S_3^2$ (as 18T734) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$308249.375193$ |
$0$ |
$67$ |
| 18.0.294...144.1 |
$x^{18} - 3 x^{17} + 11 x^{16} - 11 x^{15} + 24 x^{14} - 12 x^{13} + 121 x^{12} - 95 x^{11} + 727 x^{10} + 25 x^{9} + 1172 x^{8} + 1386 x^{7} + 3079 x^{6} + 893 x^{5} + 4781 x^{4} + 825 x^{3} + 1247 x^{2} - 1319 x + 982$ |
$18$ |
(0, 9) |
$-\,2^{12}\cdot 3^{9}\cdot 7^{9}\cdot 67^{6}$ |
$4$ |
$29.5452665237$ |
$172.57049793444716$ |
|
|
|
$C_2\times C_6^2:D_6$ (as 18T228) |
$[2, 8]$ |
$[2, 8]$ |
$2$ |
$8$ |
$189663.911394$ |
$0$ |
$67$ |
| 18.6.239...744.1 |
$x^{18} - 14 x^{16} + 14 x^{14} + 343 x^{12} + 1176 x^{10} - 15435 x^{8} - 3087 x^{6} + 120050 x^{4} + 84035 x^{2} - 117649$ |
$18$ |
(6, 6) |
$2^{18}\cdot 3^{6}\cdot 7^{12}\cdot 67^{6}$ |
$4$ |
$42.870713163$ |
$172.57049793444716$ |
|
|
? |
$C_6^2:D_6$ (as 18T154) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$132947544.849$ |
$3$ |
$67$ |
| 18.6.209...104.1 |
$x^{18} - 2838 x^{12} + 1982540 x^{6} - 103161709$ |
$18$ |
(6, 6) |
$2^{18}\cdot 3^{6}\cdot 7^{9}\cdot 67^{9}$ |
$4$ |
$62.4678897678269$ |
$172.57049793444716$ |
|
|
? |
$C_6^2:D_6$ (as 18T152) |
$[3]$ |
$[2, 2, 6]$ |
$2$ |
$11$ |
$1341511454.1418636$ |
$3$ |
$67$ |
| 18.0.527...576.1 |
$x^{18} - 3 x^{17} - 12 x^{16} + 35 x^{15} + 81 x^{14} - 186 x^{13} - 243 x^{12} + 168 x^{11} + 1209 x^{10} - 259 x^{9} + 2328 x^{8} + 537 x^{7} + 3744 x^{6} - 1023 x^{5} + 17733 x^{4} - 11939 x^{3} + 14211 x^{2} - 3756 x + 11663$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 3^{24}\cdot 7^{9}\cdot 67^{6}$ |
$4$ |
$65.75326030143323$ |
$431.0896517689961$ |
✓ |
|
? |
$C_6\times S_4$ (as 18T61) |
$[2, 2, 114]$ |
$[2, 2, 114]$ |
$2$ |
$8$ |
$1817591.191451564$ |
$0$ |
$67$ |
| 18.0.491...736.1 |
$x^{18} - 3 x^{17} - 14 x^{16} + 43 x^{15} + 97 x^{14} - 286 x^{13} - 279 x^{12} + 1069 x^{11} + 913 x^{10} - 2174 x^{9} + 2663 x^{8} - 6131 x^{7} + 10351 x^{6} + 730 x^{5} + 13119 x^{4} - 17749 x^{3} + 12414 x^{2} + 517 x + 24767$ |
$18$ |
(0, 9) |
$-\,2^{19}\cdot 7^{9}\cdot 37^{6}\cdot 67^{6}$ |
$4$ |
$74.42664001476615$ |
$763.5722184344154$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[6, 120]$ |
$[6, 120]$ |
$2$ |
$8$ |
$9611772.980867488$ |
$0$ |
$67$ |
| 18.0.435...576.1 |
$x^{18} - 3 x^{17} - 20 x^{16} + 45 x^{15} + 220 x^{14} - 263 x^{13} - 1363 x^{12} + 621 x^{11} + 6177 x^{10} + 2712 x^{9} - 9313 x^{8} - 12478 x^{7} + 17291 x^{6} + 34451 x^{5} + 7728 x^{4} - 24459 x^{3} + 49471 x^{2} + 33276 x + 83777$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 7^{9}\cdot 13^{12}\cdot 67^{6}$ |
$4$ |
$84.0203565680035$ |
$550.8518678520647$ |
✓ |
|
? |
$C_6\times S_4$ (as 18T61) |
$[2, 6, 126]$ |
$[2, 6, 126]$ |
$2$ |
$8$ |
$4325325.638119452$ |
$0$ |
$67$ |
| 18.0.465...984.1 |
$x^{18} - 3 x^{17} - 20 x^{16} + 63 x^{15} + 175 x^{14} - 590 x^{13} - 643 x^{12} + 2979 x^{11} + 1194 x^{10} - 7929 x^{9} + 7301 x^{8} - 9772 x^{7} + 20564 x^{6} - 9388 x^{5} + 41580 x^{4} - 53376 x^{3} + 7504 x^{2} + 13920 x + 77984$ |
$18$ |
(0, 9) |
$-\,2^{19}\cdot 7^{9}\cdot 67^{6}\cdot 79^{6}$ |
$4$ |
$95.83780733726971$ |
$1252.3752270066932$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[2, 1462]$ |
$[2, 1462]$ |
$2$ |
$8$ |
$84534799.4544512$ |
$0$ |
$79$ |
| 18.0.392...344.1 |
$x^{18} - 3 x^{17} - 32 x^{16} + 67 x^{15} + 511 x^{14} - 514 x^{13} - 4647 x^{12} + 439 x^{11} + 26134 x^{10} + 21559 x^{9} - 62083 x^{8} - 121808 x^{7} + 41368 x^{6} + 274780 x^{5} + 198780 x^{4} - 49984 x^{3} + 263712 x^{2} + 566272 x + 563072$ |
$18$ |
(0, 9) |
$-\,2^{23}\cdot 7^{9}\cdot 67^{6}\cdot 71^{6}$ |
$4$ |
$107.88875364292909$ |
$1187.2716481556513$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[2, 2, 988]$ |
$[2, 2, 988]$ |
$2$ |
$8$ |
$202899159.5803885$ |
$0$ |
$71$ |
| 18.18.744...744.1 |
$x^{18} - 6 x^{17} - 48 x^{16} + 320 x^{15} + 765 x^{14} - 6290 x^{13} - 4011 x^{12} + 56852 x^{11} - 7295 x^{10} - 240614 x^{9} + 108969 x^{8} + 451000 x^{7} - 236236 x^{6} - 341944 x^{5} + 167341 x^{4} + 88132 x^{3} - 25656 x^{2} - 9016 x + 68$ |
$18$ |
(18, 0) |
$2^{23}\cdot 7^{9}\cdot 67^{6}\cdot 79^{6}$ |
$4$ |
$111.79758534822614$ |
$1252.3752270066932$ |
|
|
|
$D_6\times S_4$ (as 18T111) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$43070517344021.266$ |
$15$ |
$79$ |
| 18.0.150...264.1 |
$x^{18} - 3 x^{17} - 26 x^{16} + 83 x^{15} + 283 x^{14} - 1004 x^{13} - 1329 x^{12} + 6473 x^{11} + 2071 x^{10} - 21760 x^{9} + 17081 x^{8} - 1963 x^{7} + 20293 x^{6} - 29248 x^{5} + 109977 x^{4} - 146369 x^{3} + 4104 x^{2} + 29519 x + 216761$ |
$18$ |
(0, 9) |
$-\,2^{19}\cdot 3^{6}\cdot 7^{9}\cdot 47^{6}\cdot 67^{6}$ |
$5$ |
$116.25211854856516$ |
$1490.5920927681134$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[2, 2856]$ |
$[2, 2856]$ |
$2$ |
$8$ |
$74274850.384501$ |
$0$ |
$67$ |
| 18.0.209...544.1 |
$x^{18} - 3 x^{17} - 24 x^{16} + 67 x^{15} + 267 x^{14} - 628 x^{13} - 1587 x^{12} + 2464 x^{11} + 7201 x^{10} - 7319 x^{9} - 4812 x^{8} + 12881 x^{7} + 10102 x^{6} - 16649 x^{5} + 78341 x^{4} + 7021 x^{3} - 53431 x^{2} - 4442 x + 163271$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 7^{9}\cdot 11^{6}\cdot 43^{6}\cdot 67^{6}$ |
$5$ |
$118.40662407155634$ |
$2166.8881532605888$ |
✓ |
|
? |
$D_6\times S_4$ (as 18T111) |
$[5474]$ |
$[5474]$ |
$2$ |
$8$ |
$23259241.65231708$ |
$0$ |
$67$ |
| 18.18.597...912.1 |
$x^{18} - x^{17} - 72 x^{16} + 73 x^{15} + 2162 x^{14} - 2235 x^{13} - 35067 x^{12} + 36930 x^{11} + 332578 x^{10} - 352420 x^{9} - 1864236 x^{8} + 1924168 x^{7} + 5927960 x^{6} - 5543552 x^{5} - 9529568 x^{4} + 6640768 x^{3} + 5651584 x^{2} - 638976 x - 54784$ |
$18$ |
(18, 0) |
$2^{19}\cdot 7^{9}\cdot 23^{3}\cdot 37^{6}\cdot 67^{6}$ |
$5$ |
$125.51136494284751$ |
$3661.963715493595$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$36092995843453.414$ |
$15$ |
$67$ |
| 18.18.125...008.1 |
$x^{18} - 2 x^{17} - 69 x^{16} + 134 x^{15} + 1955 x^{14} - 3708 x^{13} - 29118 x^{12} + 54528 x^{11} + 241096 x^{10} - 454832 x^{9} - 1064328 x^{8} + 2106272 x^{7} + 2063696 x^{6} - 4784128 x^{5} - 491264 x^{4} + 3594752 x^{3} - 1185536 x^{2} - 196608 x + 69632$ |
$18$ |
(18, 0) |
$2^{28}\cdot 7^{9}\cdot 67^{6}\cdot 71^{6}$ |
$4$ |
$130.79634835734768$ |
$1187.2716481556513$ |
|
|
|
$D_6\times S_4$ (as 18T111) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$188619133764619.62$ |
$14$ |
$71$ |
| 18.18.146...176.1 |
$x^{18} - 3 x^{17} - 68 x^{16} + 203 x^{15} + 1888 x^{14} - 5595 x^{13} - 27403 x^{12} + 80294 x^{11} + 220562 x^{10} - 634428 x^{9} - 957532 x^{8} + 2664376 x^{7} + 1974200 x^{6} - 5135136 x^{5} - 1262432 x^{4} + 2851968 x^{3} - 352640 x^{2} - 169472 x + 8704$ |
$18$ |
(18, 0) |
$2^{19}\cdot 7^{9}\cdot 31^{3}\cdot 37^{6}\cdot 67^{6}$ |
$5$ |
$131.91333358596236$ |
$4251.390186246199$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$64034638371440.11$ |
$14$ |
$67$ |
| 18.18.188...736.1 |
$x^{18} - 3 x^{17} - 69 x^{16} + 204 x^{15} + 1959 x^{14} - 5664 x^{13} - 29525 x^{12} + 82398 x^{11} + 254538 x^{10} - 669732 x^{9} - 1264992 x^{8} + 2998608 x^{7} + 3506056 x^{6} - 6826032 x^{5} - 5048064 x^{4} + 6782976 x^{3} + 2993664 x^{2} - 2155008 x - 644608$ |
$18$ |
(18, 0) |
$2^{9}\cdot 3^{24}\cdot 7^{9}\cdot 67^{6}\cdot 71^{3}$ |
$5$ |
$133.80130517740142$ |
$3632.425971472002$ |
|
|
? |
$A_4^2:C_2^2$ (as 18T176) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$32103389288927.953$ |
$13$ |
$71$ |
| 18.0.437...000.1 |
$x^{18} - 3 x^{17} - 32 x^{16} + 109 x^{15} + 406 x^{14} - 1697 x^{13} - 1987 x^{12} + 13753 x^{11} - 1705 x^{10} - 56666 x^{9} + 72107 x^{8} + 27474 x^{7} - 91793 x^{6} - 43573 x^{5} + 407996 x^{4} - 554635 x^{3} + 260709 x^{2} - 172130 x + 488893$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 5^{6}\cdot 7^{9}\cdot 67^{6}\cdot 157^{6}$ |
$5$ |
$140.1884296684039$ |
$2791.520061096599$ |
✓ |
|
? |
$D_6\times S_4$ (as 18T111) |
$[13266]$ |
$[13266]$ |
$2$ |
$8$ |
$39164443.55110223$ |
$0$ |
$157$ |
| 18.0.642...464.1 |
$x^{18} - 3 x^{17} - 30 x^{16} + 83 x^{15} + 405 x^{14} - 954 x^{13} - 2952 x^{12} + 4974 x^{11} + 14646 x^{10} - 17212 x^{9} - 22098 x^{8} + 35466 x^{7} + 29163 x^{6} - 53835 x^{5} + 149808 x^{4} + 72721 x^{3} - 193059 x^{2} - 36312 x + 454292$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 3^{18}\cdot 7^{9}\cdot 31^{6}\cdot 67^{6}$ |
$5$ |
$143.21794507350833$ |
$1998.6108262880957$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[2, 2, 9150]$ |
$[2, 2, 9150]$ |
$2$ |
$8$ |
$259851444.82223874$ |
$0$ |
$67$ |
| 18.18.415...024.1 |
$x^{18} - 75 x^{16} - 2 x^{15} + 2343 x^{14} + 93 x^{13} - 39361 x^{12} - 1482 x^{11} + 382560 x^{10} + 7908 x^{9} - 2147532 x^{8} + 14976 x^{7} + 6494872 x^{6} - 212016 x^{5} - 8648448 x^{4} + 328448 x^{3} + 2290944 x^{2} - 322560 x + 8704$ |
$18$ |
(18, 0) |
$2^{9}\cdot 3^{24}\cdot 7^{9}\cdot 67^{6}\cdot 199^{3}$ |
$5$ |
$158.8764294746941$ |
$6081.267901071334$ |
|
|
? |
$A_4^2:C_2^2$ (as 18T176) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$125306860344573.28$ |
$14$ |
$199$ |
| 18.18.452...048.1 |
$x^{18} - x^{17} - 73 x^{16} + 76 x^{15} + 2229 x^{14} - 2372 x^{13} - 36921 x^{12} + 39170 x^{11} + 360050 x^{10} - 367084 x^{9} - 2100368 x^{8} + 1939664 x^{7} + 7106952 x^{6} - 5326352 x^{5} - 12660928 x^{4} + 5785472 x^{3} + 9115136 x^{2} + 296960 x - 531968$ |
$18$ |
(18, 0) |
$2^{9}\cdot 7^{9}\cdot 13^{12}\cdot 47^{3}\cdot 67^{6}$ |
$5$ |
$159.61271927258736$ |
$3776.450141979516$ |
|
|
? |
$A_4^2:C_2^2$ (as 18T176) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$109706742203558.3$ |
$13$ |
$67$ |
| 18.18.566...328.1 |
$x^{18} - x^{17} - 73 x^{16} + 70 x^{15} + 2208 x^{14} - 2012 x^{13} - 35748 x^{12} + 30248 x^{11} + 334520 x^{10} - 248896 x^{9} - 1830176 x^{8} + 1049792 x^{7} + 5704992 x^{6} - 1725056 x^{5} - 9539968 x^{4} - 406528 x^{3} + 6703616 x^{2} + 2643968 x + 34816$ |
$18$ |
(18, 0) |
$2^{19}\cdot 7^{9}\cdot 23^{3}\cdot 67^{6}\cdot 79^{6}$ |
$5$ |
$161.61866247950843$ |
$6006.180592694623$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$1818605845910672.5$ |
$15$ |
$79$ |
| 18.0.644...016.1 |
$x^{18} - 3 x^{17} - 38 x^{16} + 129 x^{15} + 574 x^{14} - 2361 x^{13} - 3592 x^{12} + 22563 x^{11} + 992 x^{10} - 110821 x^{9} + 122102 x^{8} + 134329 x^{7} - 304797 x^{6} - 44640 x^{5} + 900714 x^{4} - 1350036 x^{3} + 718752 x^{2} - 454992 x + 1115872$ |
$18$ |
(0, 9) |
$-\,2^{9}\cdot 7^{9}\cdot 67^{6}\cdot 1229^{6}$ |
$4$ |
$162.78194988184893$ |
$3492.865530133035$ |
✓ |
|
|
$D_6\times S_4$ (as 18T111) |
$[2, 2, 12996]$ |
$[2, 2, 12996]$ |
$2$ |
$8$ |
$550503498.3345392$ |
$0$ |
$1229$ |
| 18.18.169...936.1 |
$x^{18} - x^{17} - 74 x^{16} + 71 x^{15} + 2278 x^{14} - 2057 x^{13} - 37727 x^{12} + 30994 x^{11} + 363234 x^{10} - 254772 x^{9} - 2053212 x^{8} + 1076264 x^{7} + 6564728 x^{6} - 1801888 x^{5} - 10732384 x^{4} - 331904 x^{3} + 6599296 x^{2} + 2195968 x - 122368$ |
$18$ |
(18, 0) |
$2^{19}\cdot 7^{9}\cdot 37^{6}\cdot 67^{6}\cdot 151^{3}$ |
$5$ |
$171.7478217939456$ |
$9382.932507883292$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$628872186274597.1$ |
$15$ |
$151$ |
| 18.18.173...528.1 |
$x^{18} - 3 x^{17} - 69 x^{16} + 188 x^{15} + 1776 x^{14} - 4350 x^{13} - 21664 x^{12} + 47652 x^{11} + 134430 x^{10} - 263916 x^{9} - 405264 x^{8} + 706758 x^{7} + 436815 x^{6} - 727497 x^{5} + 141639 x^{4} + 61864 x^{3} - 17040 x^{2} - 768 x + 256$ |
$18$ |
(18, 0) |
$2^{9}\cdot 3^{21}\cdot 7^{9}\cdot 31^{6}\cdot 67^{6}$ |
$5$ |
$171.9957228831431$ |
$1998.6108262880957$ |
|
|
|
$D_6\times S_4$ (as 18T111) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$2239342013403661.5$ |
$14$ |
$67$ |
| 18.18.214...464.1 |
$x^{18} - 2 x^{17} - 71 x^{16} + 136 x^{15} + 2065 x^{14} - 3739 x^{13} - 31541 x^{12} + 52706 x^{11} + 269520 x^{10} - 395916 x^{9} - 1273500 x^{8} + 1466992 x^{7} + 3144440 x^{6} - 2034704 x^{5} - 3834112 x^{4} + 286976 x^{3} + 1538560 x^{2} + 541184 x + 55808$ |
$18$ |
(18, 0) |
$2^{9}\cdot 7^{9}\cdot 13^{12}\cdot 67^{6}\cdot 79^{3}$ |
$5$ |
$174.04265595263834$ |
$4896.078496610587$ |
|
|
? |
$A_4^2:C_2^2$ (as 18T176) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$227960177975235.84$ |
$13$ |
$79$ |
| 18.18.103...256.1 |
$x^{18} - x^{17} - 70 x^{16} + 65 x^{15} + 2051 x^{14} - 1790 x^{13} - 32620 x^{12} + 27284 x^{11} + 305204 x^{10} - 251072 x^{9} - 1698656 x^{8} + 1414176 x^{7} + 5381200 x^{6} - 4646336 x^{5} - 8491328 x^{4} + 7678464 x^{3} + 4342272 x^{2} - 4116480 x + 548864$ |
$18$ |
(18, 0) |
$2^{13}\cdot 7^{9}\cdot 67^{6}\cdot 1229^{6}$ |
$4$ |
$189.8898716560008$ |
$4939.657804259628$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$5119256370074194.0$ |
$14$ |
$1229$ |
| 18.18.156...272.1 |
$x^{18} - x^{17} - 72 x^{16} + 69 x^{15} + 2148 x^{14} - 1977 x^{13} - 34339 x^{12} + 30162 x^{11} + 318274 x^{10} - 259700 x^{9} - 1736316 x^{8} + 1224552 x^{7} + 5471288 x^{6} - 2818016 x^{5} - 9561184 x^{4} + 2464128 x^{3} + 8024704 x^{2} + 9728 x - 1818112$ |
$18$ |
(18, 0) |
$2^{19}\cdot 3^{6}\cdot 7^{9}\cdot 47^{9}\cdot 67^{6}$ |
$5$ |
$220.8431089877317$ |
$3902.862737609678$ |
|
|
|
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$17$ |
$8106602749681106.0$ |
$14$ |
$67$ |
| 18.0.164...096.1 |
$x^{18} + 117 x^{16} + 4892 x^{14} + 97513 x^{12} + 1025325 x^{10} + 5957980 x^{8} + 19502000 x^{6} + 35179648 x^{4} + 31962112 x^{2} + 11239424$ |
$18$ |
(0, 9) |
$-\,2^{17}\cdot 7^{9}\cdot 67^{6}\cdot 1229^{6}$ |
$4$ |
$221.51204960810665$ |
$4939.657804259628$ |
✓ |
|
|
$C_2\times S_4^2$ (as 18T266) |
$[2, 2, 2, 2, 31344]$ |
$[2, 2, 2, 2, 31344]$ |
$2$ |
$8$ |
$550503498.3345392$ |
$0$ |
$1229$ |
| 18.18.532...000.1 |
$x^{18} - x^{17} - 71 x^{16} + 66 x^{15} + 2091 x^{14} - 1814 x^{13} - 33065 x^{12} + 26882 x^{11} + 304042 x^{10} - 231380 x^{9} - 1650416 x^{8} + 1155520 x^{7} + 5164904 x^{6} - 3171248 x^{5} - 8814848 x^{4} + 4312832 x^{3} + 7329536 x^{2} - 2179072 x - 2289152$ |
$18$ |
(18, 0) |
$2^{9}\cdot 5^{6}\cdot 7^{9}\cdot 23^{3}\cdot 67^{6}\cdot 157^{6}$ |
$6$ |
$236.41052657200265$ |
$13387.65990696692$ |
|
|
? |
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$3322834171818968.5$ |
$16$ |
$157$ |
| 18.18.749...584.1 |
$x^{18} - 73 x^{16} - 2 x^{15} + 2211 x^{14} + 111 x^{13} - 35993 x^{12} - 2334 x^{11} + 341648 x^{10} + 22748 x^{9} - 1925580 x^{8} - 96672 x^{7} + 6316408 x^{6} + 74608 x^{5} - 11375552 x^{4} + 562816 x^{3} + 9913088 x^{2} - 965120 x - 2848256$ |
$18$ |
(18, 0) |
$2^{9}\cdot 7^{9}\cdot 11^{6}\cdot 43^{6}\cdot 67^{6}\cdot 71^{3}$ |
$6$ |
$240.94563174198714$ |
$18258.524121095248$ |
|
|
? |
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$4244993661224835.5$ |
$16$ |
$71$ |
| 18.0.421...344.1 |
$x^{18} - 3 x^{17} + 97 x^{16} - 252 x^{15} + 3705 x^{14} - 8583 x^{13} + 74494 x^{12} - 152401 x^{11} + 854821 x^{10} - 1463500 x^{9} + 5412147 x^{8} - 7223195 x^{7} + 15914937 x^{6} - 12013190 x^{5} + 6121006 x^{4} - 8546916 x^{3} + 40317820 x^{2} - 46377384 x + 54261112$ |
$18$ |
(0, 9) |
$-\,2^{19}\cdot 3^{9}\cdot 7^{9}\cdot 47^{9}\cdot 67^{6}$ |
$5$ |
$265.21865087932866$ |
$3902.862737609678$ |
✓ |
|
|
$C_2\times S_4^2$ (as 18T266) |
$[2, 2, 2, 2, 574368]$ |
$[2, 2, 2, 2, 574368]$ |
$2$ |
$8$ |
$74274850.384501$ |
$0$ |
$67$ |
| 18.14.203...232.1 |
$x^{18} - 2 x^{17} - 149 x^{16} + 396 x^{15} + 7463 x^{14} - 16914 x^{13} - 187423 x^{12} + 221696 x^{11} + 2710648 x^{10} + 637224 x^{9} - 19959604 x^{8} - 34537200 x^{7} + 24770664 x^{6} + 159286048 x^{5} + 314846192 x^{4} + 529773984 x^{3} + 748672224 x^{2} + 648947488 x + 238335952$ |
$18$ |
(14, 2) |
$2^{12}\cdot 7^{9}\cdot 19^{2}\cdot 71^{9}\cdot 199^{2}\cdot 4337821^{2}$ |
$6$ |
$482.893474189$ |
$1078630818.753979$ |
|
|
|
$C_3^6.C_2^5.S_5$ (as 18T950) |
$[3]$ |
$[2, 6]$ |
$2$ |
$15$ |
$2746506431500000000$ |
$12$ |
$4337821$ |
| 36.0.213...976.1 |
$x^{36} - 12 x^{35} + 81 x^{34} - 380 x^{33} + 1401 x^{32} - 4264 x^{31} + 11152 x^{30} - 25700 x^{29} + 52417 x^{28} - 98968 x^{27} + 167673 x^{26} - 261006 x^{25} + 387102 x^{24} - 498860 x^{23} + 635387 x^{22} + 84728 x^{21} - 1693615 x^{20} + 4919942 x^{19} - 9149200 x^{18} + 7596626 x^{17} - 2947235 x^{16} - 23798720 x^{15} + 89631925 x^{14} - 136657168 x^{13} + 91142993 x^{12} + 35139946 x^{11} + 24486230 x^{10} - 286151236 x^{9} + 175344416 x^{8} + 195622728 x^{7} - 98323744 x^{6} - 298086184 x^{5} + 365041592 x^{4} - 148537280 x^{3} + 9211792 x^{2} + 6957280 x + 3853712$ |
$36$ |
(0, 18) |
$2^{38}\cdot 7^{18}\cdot 31^{6}\cdot 37^{12}\cdot 67^{12}$ |
$5$ |
$131.913333586$ |
$4251.390186246199$ |
✓ |
|
|
$C_2^2\times S_4^2$ (as 36T3379) |
not computed |
not computed |
$2$ |
$17$ |
|
|
$67$ |
| 36.0.173...576.1 |
$x^{36} - 3 x^{34} - 2 x^{33} - 9 x^{32} - 27 x^{31} + 71 x^{30} - 6 x^{29} + 524 x^{27} + 1812 x^{26} - 1104 x^{25} - 2280 x^{24} - 15024 x^{23} - 21696 x^{22} - 3264 x^{21} + 97152 x^{20} + 16896 x^{19} + 301568 x^{18} + 67584 x^{17} + 1554432 x^{16} - 208896 x^{15} - 5554176 x^{14} - 15384576 x^{13} - 9338880 x^{12} - 18087936 x^{11} + 118751232 x^{10} + 137363456 x^{9} - 25165824 x^{7} + 1191182336 x^{6} - 1811939328 x^{5} - 2415919104 x^{4} - 2147483648 x^{3} - 12884901888 x^{2} + 68719476736$ |
$36$ |
(0, 18) |
$2^{18}\cdot 3^{48}\cdot 7^{18}\cdot 67^{12}\cdot 199^{6}$ |
$5$ |
$158.876429475$ |
$6081.267901071334$ |
✓ |
|
? |
$A_4^2:C_2^3$ (as 36T1803) |
not computed |
not computed |
$2$ |
$17$ |
|
|
$199$ |
| 36.0.204...304.1 |
$x^{36} + 13 x^{34} - 26 x^{33} + 94 x^{32} - 262 x^{31} + 731 x^{30} - 1205 x^{29} + 4274 x^{28} - 1133 x^{27} + 6981 x^{26} - 11062 x^{25} - 109813 x^{24} - 65593 x^{23} - 338726 x^{22} - 14803 x^{21} + 1910654 x^{20} + 3560178 x^{19} + 19134908 x^{18} + 11250407 x^{17} + 41426055 x^{16} + 87117071 x^{15} - 47139783 x^{14} + 24379819 x^{13} + 323548427 x^{12} - 115066148 x^{11} + 662418 x^{10} + 484355456 x^{9} - 417892300 x^{8} - 73724176 x^{7} + 692053512 x^{6} - 56244592 x^{5} - 152888384 x^{4} + 87904448 x^{3} + 14238336 x^{2} - 7037952 x + 3195392$ |
$36$ |
(0, 18) |
$2^{18}\cdot 7^{18}\cdot 13^{24}\cdot 47^{6}\cdot 67^{12}$ |
$5$ |
$159.612719273$ |
$3776.450141979516$ |
✓ |
|
|
$A_4^2:C_2^3$ (as 36T1803) |
not computed |
not computed |
$2$ |
$17$ |
|
|
$67$ |
| 36.0.301...784.1 |
$x^{36} - 15 x^{35} + 102 x^{34} - 437 x^{33} + 1473 x^{32} - 4506 x^{31} + 12677 x^{30} - 32463 x^{29} + 81279 x^{28} - 205392 x^{27} + 436041 x^{26} - 922797 x^{25} + 2311886 x^{24} - 4344519 x^{23} + 7934277 x^{22} - 5812916 x^{21} - 10800621 x^{20} - 1082763 x^{19} - 87601572 x^{18} + 283125477 x^{17} + 30203313 x^{16} - 2665629236 x^{15} + 5162377947 x^{14} + 6448161405 x^{13} - 21535096595 x^{12} - 7499756334 x^{11} + 128073851037 x^{10} - 201803107819 x^{9} + 66368918904 x^{8} + 208034846421 x^{7} - 162114898461 x^{6} - 110109059538 x^{5} + 183104592072 x^{4} + 84141618520 x^{3} - 36678744624 x^{2} - 11975800896 x + 3663748864$ |
$36$ |
(0, 18) |
$2^{18}\cdot 3^{42}\cdot 7^{18}\cdot 31^{12}\cdot 67^{12}$ |
$5$ |
$171.995722883$ |
$1998.6108262880957$ |
✓ |
|
|
$C_2^2:D_6^2$ (as 36T807) |
not computed |
not computed |
$6$ |
$17$ |
|
|
$67$ |
| 36.0.243...984.1 |
$x^{36} + 7 x^{34} - 6 x^{33} + 43 x^{32} - 32 x^{31} + 232 x^{30} - 84 x^{29} + 249 x^{28} + 1084 x^{27} - 5077 x^{26} + 3864 x^{25} - 160184 x^{24} + 1428 x^{23} - 392723 x^{22} + 62334 x^{21} + 2265243 x^{20} + 155606 x^{19} + 20361840 x^{18} + 778766 x^{17} + 7129517 x^{16} + 21684224 x^{15} - 124613413 x^{14} + 13773482 x^{13} + 200257783 x^{12} - 65564958 x^{11} + 306548006 x^{10} + 140749772 x^{9} - 298838636 x^{8} + 29250664 x^{7} + 894665816 x^{6} - 609872 x^{5} - 1101504 x^{4} + 1726400 x^{3} + 27136 x^{2} - 5888 x + 512$ |
$36$ |
(0, 18) |
$2^{38}\cdot 3^{12}\cdot 7^{18}\cdot 47^{18}\cdot 67^{12}$ |
$5$ |
$220.843108988$ |
$3902.862737609678$ |
✓ |
|
|
$C_2^2\times S_4^2$ (as 36T3379) |
not computed |
not computed |
$2$ |
$17$ |
|
|
$67$ |
| 36.0.177...336.1 |
$x^{36} - x^{35} + 73 x^{34} - 66 x^{33} + 3105 x^{32} - 2649 x^{31} + 88762 x^{30} - 71975 x^{29} + 1899311 x^{28} - 1478352 x^{27} + 31232683 x^{26} - 23276523 x^{25} + 406458419 x^{24} - 286872742 x^{23} + 4190952558 x^{22} - 2720369448 x^{21} + 34479543144 x^{20} - 19495741960 x^{19} + 223256681352 x^{18} - 98727072288 x^{17} + 1132339328928 x^{16} - 316069561248 x^{15} + 4386525309664 x^{14} - 299570401728 x^{13} + 13075210905536 x^{12} + 1574606120192 x^{11} + 29950092829952 x^{10} + 8845110654976 x^{9} + 51321732841472 x^{8} + 19494359330816 x^{7} + 62930183213056 x^{6} + 25083388919808 x^{5} + 46988599885824 x^{4} + 9038185693184 x^{3} + 14589905272832 x^{2} - 17686593536 x + 3305531244544$ |
$36$ |
(0, 18) |
$2^{38}\cdot 3^{18}\cdot 7^{18}\cdot 47^{18}\cdot 67^{12}$ |
$5$ |
$265.21865087932866$ |
$3902.862737609678$ |
✓ |
|
|
$C_2^2\times S_4^2$ (as 36T3161) |
not computed |
not computed |
$6$ |
$17$ |
|
|
$67$ |
