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 |
18.0.504...712.1 |
$x^{18} - x^{15} + 2 x^{12} - 9 x^{9} + 12 x^{6} - 5 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{21}\cdot 7^{6}$ |
$3$ |
$10.940255742$ |
$20.927956356407396$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
trivial |
$6$ |
$8$ |
$153.95173876$ |
18.0.513...176.1 |
$x^{18} - 6 x^{17} + 16 x^{16} - 20 x^{15} - 2 x^{14} + 51 x^{13} - 87 x^{12} + 64 x^{11} + 16 x^{10} - 108 x^{9} + 181 x^{8} - 232 x^{7} + 253 x^{6} - 224 x^{5} + 154 x^{4} - 79 x^{3} + 29 x^{2} - 7 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{12}\cdot 11^{9}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
trivial |
$2$ |
$8$ |
$51.3669704577$ |
18.0.184...848.2 |
$x^{18} - 3 x^{15} + 6 x^{12} - 11 x^{9} + 12 x^{6} + 3 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{37}$ |
$2$ |
$15.1857382405$ |
$18.611942300804063$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
trivial |
$6$ |
$8$ |
$5055.733475945769$ |
18.0.165...632.4 |
$x^{18} - 6 x^{15} - 3 x^{12} + 34 x^{9} + 285 x^{6} + 12 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{39}$ |
$2$ |
$17.1573172739$ |
$18.611942300804063$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
trivial |
trivial |
$6$ |
$8$ |
$29043.077221801348$ |
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 |
$2$ |
$17$ |
$441529173.991$ |
18.0.450...000.10 |
$x^{18} - 21 x^{15} + 354 x^{12} - 1141 x^{9} + 366 x^{6} - 29841 x^{3} + 117649$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{37}\cdot 5^{12}$ |
$3$ |
$44.40336798307826$ |
$54.421649430145465$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3]$ |
$[3, 3]$ |
$6$ |
$8$ |
$21142523.787012096$ |
18.0.323...003.4 |
$x^{18} - 18 x^{15} + 267 x^{12} - 594 x^{9} - 639 x^{6} - 12312 x^{3} + 46656$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 17^{12}$ |
$2$ |
$49.54748116432225$ |
$71.45983341905817$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 3]$ |
$[3, 3]$ |
$6$ |
$8$ |
$48552007.225683525$ |
18.0.405...000.10 |
$x^{18} + 9 x^{16} - 18 x^{15} + 36 x^{14} + 72 x^{13} + 177 x^{12} + 270 x^{11} - 3240 x^{10} - 4056 x^{9} + 945 x^{8} + 14490 x^{7} + 48987 x^{6} - 4428 x^{5} - 150804 x^{4} - 35748 x^{3} + 170424 x^{2} - 15120 x + 34896$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{39}\cdot 5^{12}$ |
$3$ |
$50.1683000492$ |
$54.421649430145465$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3]$ |
$[3, 3, 3]$ |
$6$ |
$8$ |
$16318156.115223706$ |
18.18.116...000.1 |
$x^{18} - 72 x^{16} - 15 x^{15} + 1692 x^{14} - 120 x^{13} - 16668 x^{12} + 7470 x^{11} + 65196 x^{10} - 39545 x^{9} - 104526 x^{8} + 52290 x^{7} + 84016 x^{6} - 18900 x^{5} - 34320 x^{4} - 2525 x^{3} + 4950 x^{2} + 1500 x + 125$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 61^{6}$ |
$4$ |
$60.45653938$ |
$237.98699696942433$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$13504431477.0$ |
18.0.236...187.6 |
$x^{18} + 9 x^{16} - 36 x^{15} + 36 x^{14} - 117 x^{13} + 519 x^{12} + 54 x^{11} - 783 x^{10} - 2565 x^{9} - 1323 x^{8} + 10323 x^{7} + 3276 x^{6} - 23787 x^{5} - 43209 x^{4} + 7146 x^{3} + 132030 x^{2} + 138402 x + 47523$ |
$18$ |
[0,9] |
$-\,3^{39}\cdot 17^{12}$ |
$2$ |
$71.4598334191$ |
$71.45983341905817$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 9, 9]$ |
$[3, 3, 9, 9]$ |
$6$ |
$8$ |
$34420157.5786797$ |
18.0.132...288.5 |
$x^{18} - 9 x^{17} + 39 x^{16} - 90 x^{15} + 69 x^{14} + 225 x^{13} - 1676 x^{12} + 5337 x^{11} - 8355 x^{10} - 78 x^{9} + 17625 x^{8} - 19323 x^{7} + 283375 x^{6} - 836352 x^{5} + 1123398 x^{4} - 814854 x^{3} + 360072 x^{2} - 109404 x + 19476$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 17^{12}$ |
$3$ |
$78.6517237226$ |
$113.43541474288524$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3]$ |
$[3, 3]$ |
$6$ |
$8$ |
$5411532426.153941$ |
18.0.503...488.13 |
$x^{18} - 9 x^{17} + 39 x^{16} - 90 x^{15} + 69 x^{14} + 225 x^{13} - 1100 x^{12} + 3825 x^{11} - 10119 x^{10} + 12342 x^{9} + 6465 x^{8} - 43155 x^{7} + 160075 x^{6} - 339732 x^{5} + 408726 x^{4} - 315030 x^{3} + 174384 x^{2} - 56916 x + 8796$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 19^{12}$ |
$3$ |
$84.7054520929$ |
$122.1664018837223$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 9]$ |
$[3, 3, 3, 9]$ |
$6$ |
$8$ |
$480855346.25948936$ |
18.0.149...448.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 90 x^{15} + 69 x^{14} + 225 x^{13} - 2756 x^{12} + 14733 x^{11} - 41133 x^{10} + 44796 x^{9} + 31989 x^{8} - 156159 x^{7} + 1476721 x^{6} - 3954150 x^{5} + 5131062 x^{4} - 3847170 x^{3} + 1822716 x^{2} - 520884 x + 66996$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 37^{12}$ |
$3$ |
$132.09208038$ |
$190.5097461690282$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 9]$ |
$[3, 3, 3, 9]$ |
$6$ |
$8$ |
$25473645362.465027$ |
18.0.323...000.3 |
$x^{18} - 9 x^{17} + 39 x^{16} - 18 x^{15} - 579 x^{14} + 2889 x^{13} - 7292 x^{12} - 207 x^{11} + 62061 x^{10} - 66486 x^{9} - 912039 x^{8} + 3557637 x^{7} + 13853359 x^{6} - 59070312 x^{5} + 91169694 x^{4} + 75997794 x^{3} - 287391240 x^{2} + 162804708 x + 385910388$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 5^{12}\cdot 17^{12}$ |
$4$ |
$229.979035306$ |
$331.6871648497297$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 3]$ |
$[3, 3, 3, 3, 3]$ |
$6$ |
$8$ |
$3978163078155.4883$ |
18.0.363...843.1 |
$x^{18} - 111 x^{15} + 15423 x^{12} - 955510 x^{9} + 46926843 x^{6} - 46126884 x^{3} + 174676879$ |
$18$ |
[0,9] |
$-\,3^{37}\cdot 7^{12}\cdot 17^{12}$ |
$3$ |
$231.44468935667894$ |
$283.6632066161777$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 63]$ |
$[3, 3, 63]$ |
$6$ |
$8$ |
$790510130167.0256$ |
18.0.562...368.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 90 x^{15} + 177 x^{14} - 531 x^{13} + 4408 x^{12} - 23931 x^{11} + 73689 x^{10} - 272778 x^{9} + 747021 x^{8} - 1223703 x^{7} + 1661599 x^{6} - 1645560 x^{5} + 2088558 x^{4} + 11847282 x^{3} - 23111064 x^{2} + 9854892 x + 47870076$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 89^{12}$ |
$3$ |
$237.138627451$ |
$342.01308354450924$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[6, 6]$ |
$[6, 6]$ |
$6$ |
$8$ |
$40553438788528.734$ |
18.0.123...000.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 18 x^{15} - 615 x^{14} + 3141 x^{13} + 2680 x^{12} - 55755 x^{11} + 190365 x^{10} - 168870 x^{9} - 379995 x^{8} + 1417041 x^{7} - 4869773 x^{6} - 236412 x^{5} + 20343942 x^{4} - 85483590 x^{3} + 33435936 x^{2} + 35801892 x + 1328391828$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 5^{12}\cdot 19^{12}$ |
$4$ |
$247.680244443$ |
$357.2167261216457$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 9, 9]$ |
$[3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$315019930628.8986$ |
18.0.326...587.3 |
$x^{18} - 21 x^{15} - 7815 x^{12} + 467768 x^{9} + 44713203 x^{6} - 127849638 x^{3} + 174676879$ |
$18$ |
[0,9] |
$-\,3^{39}\cdot 7^{12}\cdot 17^{12}$ |
$3$ |
$261.493376468$ |
$283.6632066161777$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 27, 189]$ |
$[3, 27, 189]$ |
$6$ |
$8$ |
$267000059795.07947$ |
18.0.872...243.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 99 x^{15} - 129 x^{14} + 1845 x^{13} + 4363 x^{12} - 46008 x^{11} + 155823 x^{10} - 946308 x^{9} + 2059689 x^{8} - 1186992 x^{7} + 4368925 x^{6} - 19419525 x^{5} + 104639490 x^{4} + 498275931 x^{3} - 2708142030 x^{2} + 2120234994 x + 21867232251$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 271^{12}$ |
$2$ |
$313.835326301$ |
$452.6288645053164$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 9, 9, 9, 27]$ |
$[3, 9, 9, 9, 27]$ |
$6$ |
$8$ |
$165741048476.84244$ |
18.0.996...000.3 |
$x^{18} + 63 x^{16} - 171 x^{15} + 1593 x^{14} - 3591 x^{13} + 29385 x^{12} + 44631 x^{11} - 127413 x^{10} + 1015740 x^{9} - 2416230 x^{8} + 27041769 x^{7} + 129192813 x^{6} - 190141911 x^{5} - 546767253 x^{4} + 2437342002 x^{3} + 7962223293 x^{2} + 8011432251 x + 2750600349$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{37}\cdot 5^{12}\cdot 19^{12}$ |
$4$ |
$316.1682920120243$ |
$387.502136220015$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 9, 9]$ |
$[3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$2108011631411.0369$ |
18.0.716...483.1 |
$x^{18} - 9 x^{17} + 39 x^{16} + 45 x^{15} - 876 x^{14} + 3330 x^{13} - 20 x^{12} - 18045 x^{11} + 30651 x^{10} + 308622 x^{9} - 801240 x^{8} + 228735 x^{7} + 21624805 x^{6} - 58489497 x^{5} + 67758066 x^{4} + 128113350 x^{3} - 288291726 x^{2} + 129533769 x + 451250391$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 17^{12}\cdot 19^{12}$ |
$3$ |
$352.79626759825146$ |
$508.82026534963563$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 18, 18]$ |
$[3, 3, 3, 3, 18, 18]$ |
$6$ |
$8$ |
$815207056414.5446$ |
18.0.896...000.1 |
$x^{18} - 60 x^{15} - 28551 x^{12} + 1705300 x^{9} + 313150767 x^{6} - 184875000 x^{3} + 40353607$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{39}\cdot 5^{12}\cdot 19^{12}$ |
$4$ |
$357.216726122$ |
$387.502136220015$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 6, 18]$ |
$[3, 3, 3, 3, 6, 18]$ |
$6$ |
$8$ |
$4411949748464.114$ |
18.0.158...848.1 |
$x^{18} - 9 x^{17} + 39 x^{16} + 90 x^{15} - 1191 x^{14} + 4365 x^{13} + 3940 x^{12} - 44235 x^{11} + 89241 x^{10} + 663882 x^{9} - 2055975 x^{8} + 1561365 x^{7} + 48365515 x^{6} - 130560552 x^{5} + 146010546 x^{4} + 514036110 x^{3} - 952674696 x^{2} + 374601564 x + 2314764156$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 11^{12}\cdot 19^{12}$ |
$4$ |
$418.960572972$ |
$604.2457063439533$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 9, 9]$ |
$[3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$31268530013404.87$ |
18.0.522...107.1 |
$x^{18} - 96 x^{15} + 3849 x^{12} + 74482 x^{9} + 224141118 x^{6} + 33589614 x^{3} + 17373979$ |
$18$ |
[0,9] |
$-\,3^{39}\cdot 17^{12}\cdot 19^{12}$ |
$3$ |
$508.82026535$ |
$508.82026534963563$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 9, 9, 27]$ |
$[3, 3, 3, 3, 9, 9, 27]$ |
$6$ |
$8$ |
$2807605647887.7075$ |
18.0.809...043.2 |
$x^{18} - 9 x^{17} + 39 x^{16} + 63 x^{15} - 1020 x^{14} + 3870 x^{13} - 2378 x^{12} + 513 x^{11} - 41691 x^{10} + 408012 x^{9} - 205674 x^{8} - 2349711 x^{7} + 61018867 x^{6} - 167179851 x^{5} + 206732358 x^{4} + 134872806 x^{3} - 587584620 x^{2} + 354328425 x + 678127017$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 19^{12}\cdot 37^{12}$ |
$3$ |
$592.5056786001568$ |
$854.5410603657755$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 3, 3, 9, 9]$ |
$[3, 3, 3, 3, 3, 3, 9, 9]$ |
$6$ |
$8$ |
$51642889179696.195$ |
18.0.517...728.1 |
$x^{18} - 9 x^{17} + 39 x^{16} + 18 x^{15} - 849 x^{14} + 3843 x^{13} - 28406 x^{12} + 92007 x^{11} - 95403 x^{10} - 448638 x^{9} - 900645 x^{8} + 7936227 x^{7} + 281242081 x^{6} - 884819106 x^{5} + 1203660630 x^{4} + 111900570 x^{3} - 1123085628 x^{2} + 404543268 x + 888131124$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 7^{12}\cdot 71^{12}$ |
$4$ |
$746.414194769$ |
$1076.5155516772218$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 3, 3, 3, 3, 3]$ |
$[3, 3, 3, 3, 3, 3, 3, 3, 3]$ |
$6$ |
$8$ |
$3506023773867162.0$ |
18.0.125...000.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 18 x^{15} - 489 x^{14} + 2259 x^{13} - 30962 x^{12} + 131103 x^{11} - 233499 x^{10} - 812226 x^{9} + 3378711 x^{8} - 4698873 x^{7} + 272888029 x^{6} - 810558162 x^{5} + 1079608554 x^{4} - 805226586 x^{3} + 468467820 x^{2} - 202915692 x + 51961428$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 5^{12}\cdot 107^{12}$ |
$4$ |
$783.991737085$ |
$1130.71174593506$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 6, 6]$ |
$[3, 3, 3, 6, 6]$ |
$6$ |
$8$ |
$181961253025547170$ |
18.0.590...347.1 |
$x^{18} - 60 x^{15} + 2229 x^{12} + 3025762 x^{9} + 1020101190 x^{6} + 51364578 x^{3} + 40353607$ |
$18$ |
[0,9] |
$-\,3^{39}\cdot 19^{12}\cdot 37^{12}$ |
$3$ |
$854.541060366$ |
$854.5410603657755$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 9, 9, 9, 18, 54]$ |
$[3, 3, 3, 3, 9, 9, 9, 18, 54]$ |
$6$ |
$8$ |
$2535693926127.3457$ |
18.0.195...000.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 18 x^{15} - 489 x^{14} + 2259 x^{13} - 46082 x^{12} + 294723 x^{11} - 868809 x^{10} - 832476 x^{9} + 9141591 x^{8} - 21041973 x^{7} + 634588399 x^{6} - 1846066752 x^{5} + 2444612454 x^{4} - 2002296426 x^{3} + 1157395500 x^{2} - 374881932 x + 57871188$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 5^{12}\cdot 163^{12}$ |
$4$ |
$1037.96020526$ |
$1496.9976600338653$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 18, 18]$ |
$[3, 3, 3, 3, 18, 18]$ |
$6$ |
$8$ |
$78531702270513380$ |
18.0.554...568.1 |
$x^{18} - 9 x^{17} + 39 x^{16} + 18 x^{15} - 795 x^{14} + 3465 x^{13} - 17408 x^{12} + 110313 x^{11} - 382071 x^{10} - 1046958 x^{9} + 7983021 x^{8} - 18695511 x^{7} + 227790487 x^{6} - 633662316 x^{5} + 831229938 x^{4} - 969139794 x^{3} + 983394720 x^{2} - 427567140 x + 256690812$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 7^{12}\cdot 127^{12}$ |
$4$ |
$1099.87535633$ |
$1586.2947600616906$ |
|
|
|
$C_3^2:C_6$ (as 18T23) |
$[3, 3, 3, 3, 3, 3, 9, 18, 18]$ |
$[3, 3, 3, 3, 3, 3, 9, 18, 18]$ |
$6$ |
$8$ |
$1521039359576000.2$ |
18.0.208...875.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 63 x^{15} - 588 x^{14} + 4122 x^{13} + 65374 x^{12} - 404667 x^{11} + 1068837 x^{10} - 8088882 x^{9} + 36038982 x^{8} - 79679565 x^{7} - 143151569 x^{6} + 541076877 x^{5} - 81393138 x^{4} + 14258110416 x^{3} - 14623618176 x^{2} + 99972009 x + 522764442927$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 5^{12}\cdot 397^{12}$ |
$3$ |
$1183.66636724$ |
$1707.1423095326381$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
not computed |
not computed |
$6$ |
$8$ |
|
18.0.139...875.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 63 x^{15} + 627 x^{14} - 4383 x^{13} + 170809 x^{12} - 1036062 x^{11} + 3126507 x^{10} - 25029222 x^{9} + 89645457 x^{8} - 160156980 x^{7} - 1758315869 x^{6} + 6138070497 x^{5} - 4922138088 x^{4} + 134538470331 x^{3} - 132534531936 x^{2} - 1368271656 x + 9167365520487$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 5^{12}\cdot 683^{12}$ |
$3$ |
$1699.48018637$ |
$2451.0745685348866$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
not computed |
not computed |
$6$ |
$8$ |
|