| 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 |
| 18.6.115...448.3 |
$x^{18} - 3 x^{17} - 120 x^{16} + 20 x^{15} + 6198 x^{14} + 20970 x^{13} - 178442 x^{12} - 665868 x^{11} - 647649 x^{10} + 9439297 x^{9} + 106641522 x^{8} - 165400536 x^{7} - 2012219134 x^{6} + 2401149960 x^{5} + 14014572888 x^{4} - 21798805792 x^{3} - 7493040096 x^{2} + 52913142528 x - 91792099456$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{30}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$280.507839131$ |
$461.510683112854$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 3]$ |
$2$ |
$11$ |
$2131338973787866.8$ |
| 18.0.312...096.1 |
$x^{18} - 3 x^{17} + 33 x^{16} - 388 x^{15} + 3138 x^{14} + 13218 x^{13} + 53812 x^{12} - 1464732 x^{11} + 5349033 x^{10} - 8306493 x^{9} + 255408471 x^{8} - 450926892 x^{7} - 2241288864 x^{6} - 4931594442 x^{5} + 43187005062 x^{4} + 351848838744 x^{3} + 1835309384631 x^{2} + 4396464030753 x + 7107138128187$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$336.872230229$ |
$461.510683112854$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 6]$ |
$2$ |
$8$ |
$142607524896722.38$ |
| 18.0.396...664.1 |
$x^{18} - 3 x^{17} + 186 x^{16} - 796 x^{15} + 20886 x^{14} - 43086 x^{13} + 1499866 x^{12} - 4087764 x^{11} + 87804711 x^{10} - 169457551 x^{9} + 3935286084 x^{8} - 1528031184 x^{7} + 87470587978 x^{6} + 226709260608 x^{5} + 1850764572768 x^{4} + 12656412331040 x^{3} + 48056367294720 x^{2} + 195986267080704 x + 353454875222016$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{30}\cdot 7^{15}\cdot 17^{13}$ |
$4$ |
$387.966901177$ |
$638.3096819753366$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 6, 6, 90]$ |
$2$ |
$8$ |
$396536534938351.06$ |
| 18.0.473...008.1 |
$x^{18} - 6 x^{17} + 84 x^{16} - 80 x^{15} + 4023 x^{14} - 35010 x^{13} + 336714 x^{12} + 231660 x^{11} + 6155667 x^{10} - 9055570 x^{9} + 472100244 x^{8} - 1268938632 x^{7} + 1311904097 x^{6} - 7064712702 x^{5} + 114946205706 x^{4} - 1253137889748 x^{3} + 6335184914100 x^{2} - 19101117693096 x + 30583236418596$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 3^{30}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$445.278438922$ |
$732.6025438679068$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 6, 6, 12]$ |
$2$ |
$8$ |
$747332298252077.8$ |
| 18.6.107...928.1 |
$x^{18} - 3 x^{17} - 246 x^{16} + 3125 x^{15} + 3255 x^{14} - 418908 x^{13} + 4166569 x^{12} - 12647061 x^{11} - 70918137 x^{10} - 1340270736 x^{9} + 31045362147 x^{8} + 83058323355 x^{7} - 5748857811507 x^{6} + 51725839257288 x^{5} - 149747563691901 x^{4} - 407848752529227 x^{3} + 3785064471133812 x^{2} - 8647499919271113 x + 6085081282980519$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{33}\cdot 7^{15}\cdot 17^{13}$ |
$4$ |
$465.923789009$ |
$638.3096819753366$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 6, 6, 6]$ |
$2$ |
$11$ |
$1261712695498095.0$ |
| 18.6.127...216.1 |
$x^{18} - 6 x^{17} - 87 x^{16} + 826 x^{15} - 3753 x^{14} - 972 x^{13} + 204393 x^{12} - 1520964 x^{11} + 11658492 x^{10} - 51881516 x^{9} - 352803192 x^{8} + 4612889568 x^{7} - 9608361812 x^{6} - 44908575264 x^{5} + 256235575932 x^{4} - 772567331760 x^{3} - 64695851892 x^{2} + 4666625012448 x - 4082274578508$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{33}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$534.751332645$ |
$732.6025438679068$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 3, 18]$ |
$2$ |
$11$ |
$37304242818863384$ |
| 18.6.225...000.1 |
$x^{18} - 3 x^{17} - 273 x^{16} + 428 x^{15} + 30066 x^{14} - 19830 x^{13} - 1673048 x^{12} + 3261132 x^{11} + 37624689 x^{10} - 294267301 x^{9} + 55093017 x^{8} + 8501629836 x^{7} - 21742907816 x^{6} - 60195651810 x^{5} + 313772452266 x^{4} - 376731071584 x^{3} - 106545208833 x^{2} + 1406213648721 x - 525845024439$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{30}\cdot 5^{9}\cdot 7^{12}\cdot 17^{13}$ |
$5$ |
$627.234596519$ |
$1031.9692597827059$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 6, 12]$ |
$2$ |
$11$ |
$132971467933922380$ |
| 18.0.242...096.1 |
$x^{18} - 6 x^{17} + 237 x^{16} - 896 x^{15} + 28503 x^{14} - 127218 x^{13} + 2544555 x^{12} - 8429568 x^{11} + 155383248 x^{10} - 475665960 x^{9} + 7557303396 x^{8} - 26162306688 x^{7} + 232899383856 x^{6} - 1038222554208 x^{5} + 6045973402320 x^{4} - 34008769056256 x^{3} + 141085549266816 x^{2} - 513307676719488 x + 1004539113344704$ |
$18$ |
[0,9] |
$-\,2^{33}\cdot 3^{30}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$629.718807356$ |
$1036.056453367024$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 3, 3, 12]$ |
$2$ |
$8$ |
$23739621985693384$ |
| 18.6.242...096.1 |
$x^{18} - 6 x^{17} - 375 x^{16} + 2368 x^{15} + 55431 x^{14} - 341010 x^{13} - 4247625 x^{12} + 18225072 x^{11} + 196851960 x^{10} - 28919560 x^{9} - 6546800460 x^{8} - 21584096256 x^{7} + 115261502192 x^{6} + 462960621216 x^{5} - 651006518256 x^{4} - 487285125888 x^{3} + 7129891302912 x^{2} - 13932663541632 x + 6790409053632$ |
$18$ |
[6,6] |
$2^{33}\cdot 3^{30}\cdot 7^{12}\cdot 17^{13}$ |
$4$ |
$629.718807356$ |
$1036.056453367024$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
$[3, 6]$ |
$2$ |
$11$ |
$7037583519854197000$ |
| 18.6.160...000.1 |
$x^{18} - 3 x^{17} - 840 x^{16} - 39148 x^{15} + 372102 x^{14} + 34410474 x^{13} + 438897946 x^{12} - 6292646688 x^{11} - 565840514061 x^{10} - 2002216086899 x^{9} + 61678996944750 x^{8} + 4303504696552764 x^{7} + 26352158241463094 x^{6} - 1056477032125368300 x^{5} - 5760620986430140224 x^{4} - 290620036033694106616 x^{3} + 5882949351624155941488 x^{2} + 425577526429058792736 x - 24688926265565708628544$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{30}\cdot 5^{12}\cdot 17^{13}\cdot 31^{12}$ |
$5$ |
$2211.90994578$ |
$3639.1855330031426$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
not computed |
$2$ |
$11$ |
|
| 21.9.136...489.1 |
$x^{21} - 7 x^{20} + 7 x^{19} + 55 x^{18} - 132 x^{17} - 112 x^{16} + 589 x^{15} - 188 x^{14} - 1078 x^{13} + 1042 x^{12} + 579 x^{11} - 1297 x^{10} + 411 x^{9} + 431 x^{8} - 127 x^{7} - 455 x^{6} - 126 x^{5} + 888 x^{4} - 460 x^{3} - 146 x^{2} + 127 x - 1$ |
$21$ |
[9,6] |
$17^{10}\cdot 19^{2}\cdot 61^{2}\cdot 131^{6}$ |
$4$ |
$30.3864653$ |
$30172.450876657273$ |
|
|
? |
$C_3^7.A_7$ (as 21T132) |
trivial |
$2$ |
$14$ |
$39718417.9458$ |
