| 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 |
| 12.4.124...136.1 |
$x^{12} - 6 x^{11} + 13 x^{10} + 2524 x^{9} - 17319 x^{8} + 46464 x^{7} + 1203181 x^{6} - 9811932 x^{5} + 31542997 x^{4} - 83848558 x^{3} + 167284857 x^{2} - 172666322 x + 211707700$ |
$12$ |
[4,4] |
$2^{4}\cdot 3^{6}\cdot 7^{10}\cdot 181^{10}$ |
$4$ |
$840.5259734815883$ |
$1058.9963669728331$ |
|
|
|
$S_3\times D_6$ (as 12T37) |
$[3, 3, 3]$ |
$[3, 6, 6]$ |
$2$ |
$7$ |
$5700170311303.9795$ |
| 12.4.124...136.2 |
$x^{12} - 6 x^{11} + 13 x^{10} + 2524 x^{9} - 17319 x^{8} + 46464 x^{7} - 2699179 x^{6} + 19775052 x^{5} - 61936263 x^{4} + 163561066 x^{3} - 326612015 x^{2} + 337301178 x + 418887540$ |
$12$ |
[4,4] |
$2^{4}\cdot 3^{6}\cdot 7^{10}\cdot 181^{10}$ |
$4$ |
$840.5259734815883$ |
$1058.9963669728331$ |
|
|
|
$S_3\times D_6$ (as 12T37) |
$[3, 3, 3]$ |
$[3, 6, 6]$ |
$2$ |
$7$ |
$3604644688029.8984$ |
| 12.4.103...144.1 |
$x^{12} - 6 x^{11} - 377 x^{10} + 492 x^{9} + 173850 x^{8} - 694074 x^{7} - 21012689 x^{6} + 443688 x^{5} + 4848871342 x^{4} - 24924809490 x^{3} - 46044538197 x^{2} + 258630537564 x - 208255070079$ |
$12$ |
[4,4] |
$2^{16}\cdot 3^{6}\cdot 7^{8}\cdot 181^{10}$ |
$4$ |
$1215.4342230722195$ |
$1681.0519469631765$ |
|
|
? |
$S_3\times D_6$ (as 12T37) |
$[6]$ |
$[2, 12]$ |
$2$ |
$7$ |
$56411363733056.39$ |
| 12.4.814...896.1 |
$x^{12} - 4 x^{10} - 3372 x^{8} - 277432 x^{6} + 2870368 x^{4} + 325351584 x^{2} + 9308390400$ |
$12$ |
[4,4] |
$2^{20}\cdot 3^{6}\cdot 7^{10}\cdot 181^{10}$ |
$4$ |
$2117.9927339456663$ |
$2377.366462449021$ |
|
|
? |
$S_3\times D_6$ (as 12T37) |
$[3, 6, 6]$ |
$[6, 6, 12]$ |
$2$ |
$7$ |
$481614365859644.3$ |
| 12.0.814...896.1 |
$x^{12} + 4 x^{10} - 3372 x^{8} + 277432 x^{6} + 2870368 x^{4} - 325351584 x^{2} + 9308390400$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{6}\cdot 7^{10}\cdot 181^{10}$ |
$4$ |
$2117.9927339456663$ |
$2377.366462449021$ |
|
|
? |
$S_3\times D_6$ (as 12T37) |
$[3, 3, 3, 30, 180]$ |
$[3, 3, 3, 30, 180]$ |
$2$ |
$5$ |
$337066535001.9145$ |
| 12.0.503...216.1 |
$x^{12} - 6 x^{11} + 25 x^{10} - 70 x^{9} + 2208 x^{8} - 8478 x^{7} - 379331 x^{6} + 1167438 x^{5} + 9182773 x^{4} - 20321060 x^{3} + 498298500 x^{2} - 487942000 x + 58535290000$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 17^{8}\cdot 181^{10}$ |
$4$ |
$2464.925026003026$ |
$3952.5605746032343$ |
|
|
|
$S_3\times D_6$ (as 12T37) |
$[2, 2, 4, 84]$ |
$[2, 2, 4, 84]$ |
$2$ |
$5$ |
$44526403357293.09$ |
| 12.0.162...664.1 |
$x^{12} - 6 x^{11} + 45 x^{10} + 6346 x^{9} - 28632 x^{8} + 56838 x^{7} + 20608493 x^{6} - 62855850 x^{5} - 485618601 x^{4} + 33838345412 x^{3} - 45847562742 x^{2} - 446214581256 x + 25518486110788$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{20}\cdot 19^{6}\cdot 181^{10}$ |
$4$ |
$5854.943352522696$ |
$7031.417842506584$ |
|
|
|
$S_3\times D_6$ (as 12T37) |
$[6, 6, 72]$ |
$[6, 6, 72]$ |
$2$ |
$5$ |
$1054956121597384.5$ |
| 12.0.162...664.2 |
$x^{12} - 6 x^{11} + 45 x^{10} + 58474 x^{9} - 263208 x^{8} + 525990 x^{7} + 1574303081 x^{6} - 4732227966 x^{5} - 32775894435 x^{4} + 21042562267484 x^{3} - 31210015827924 x^{2} - 283365049551600 x + 128001124123458832$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{20}\cdot 19^{6}\cdot 181^{10}$ |
$4$ |
$5854.943352522696$ |
$7031.417842506584$ |
|
|
|
$S_3\times D_6$ (as 12T37) |
not computed |
not computed |
$2$ |
$5$ |
|
| 18.0.574...952.1 |
$x^{18} - 3 x^{17} + 20 x^{16} + 1362 x^{15} - 16869 x^{14} + 78771 x^{13} + 219275 x^{12} - 11754783 x^{11} + 107551277 x^{10} - 547425153 x^{9} + 1564985171 x^{8} + 4765766637 x^{7} - 32351937940 x^{6} + 7695601410 x^{5} + 281898472227 x^{4} - 3456002831025 x^{3} - 4258366333978 x^{2} + 64823516991216 x + 145789851946348$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{6}\cdot 7^{15}\cdot 181^{14}$ |
$4$ |
$660.613848489$ |
$1058.9963669728331$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 9, 72]$ |
$[3, 9, 72]$ |
$2$ |
$8$ |
$11818497877709620$ |
| 18.2.155...704.1 |
$x^{18} - 3 x^{17} - 43 x^{16} + 1530 x^{15} + 14211 x^{14} - 3367 x^{13} + 441798 x^{12} + 14232059 x^{11} + 62764507 x^{10} + 120304518 x^{9} + 8996989 x^{8} + 16779559799 x^{7} + 175986117153 x^{6} + 894155090640 x^{5} + 3706321588712 x^{4} + 18967648445288 x^{3} + 61040515529776 x^{2} + 91761067945264 x + 371842144156624$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{9}\cdot 7^{15}\cdot 181^{14}$ |
$4$ |
$793.355583751$ |
$1058.9963669728331$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 3, 3, 24]$ |
$[3, 3, 6, 24]$ |
$2$ |
$9$ |
$72580827066460660$ |
| 18.2.155...704.3 |
$x^{18} - 3 x^{17} - 43 x^{16} + 1530 x^{15} - 16197 x^{14} + 47313 x^{13} + 178262 x^{12} - 10195701 x^{11} + 76159231 x^{10} - 353497734 x^{9} + 502346517 x^{8} + 16201007055 x^{7} - 77557079187 x^{6} + 502850396412 x^{5} + 241150905864 x^{4} - 15229612161144 x^{3} + 23226191597664 x^{2} + 23567257290672 x + 29904908758992$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{9}\cdot 7^{15}\cdot 181^{14}$ |
$4$ |
$793.355583751$ |
$1058.9963669728331$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 18, 72]$ |
$[6, 18, 72]$ |
$2$ |
$9$ |
$25227093628066316$ |
| 18.2.396...224.1 |
$x^{18} - 3 x^{17} - 43 x^{16} - 1004 x^{15} - 19998 x^{14} + 177814 x^{13} + 3735998 x^{12} - 13131340 x^{11} + 383548635 x^{10} - 6810881065 x^{9} - 20419393889 x^{8} + 515818017892 x^{7} + 2265758897542 x^{6} - 45951945609794 x^{5} + 171298725341122 x^{4} - 151679387579436 x^{3} - 50466723050367 x^{2} - 693532074002715 x + 906603033880125$ |
$18$ |
[2,8] |
$2^{20}\cdot 3^{9}\cdot 7^{15}\cdot 181^{14}$ |
$4$ |
$1079.59034495$ |
$1681.0519469631765$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 24]$ |
$[6, 24]$ |
$2$ |
$9$ |
$26521687306898375000$ |
| 18.0.464...144.1 |
$x^{18} - 6 x^{17} + 71 x^{16} - 1726 x^{15} - 4422 x^{14} - 21938 x^{13} + 592725 x^{12} + 10137390 x^{11} + 75176574 x^{10} + 210305386 x^{9} + 936182385 x^{8} + 563115470 x^{7} + 27331479833 x^{6} + 166066463052 x^{5} + 340843100314 x^{4} - 646478742144 x^{3} + 4039579519356 x^{2} - 40722759376416 x + 299480417841240$ |
$18$ |
[0,9] |
$-\,2^{33}\cdot 3^{9}\cdot 7^{14}\cdot 181^{14}$ |
$4$ |
$1598.52581136$ |
$2377.366462449021$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
$[3, 6, 6, 18, 180]$ |
$[3, 6, 6, 18, 180]$ |
$2$ |
$8$ |
$241814465131864350$ |
| 18.2.464...144.1 |
$x^{18} - 6 x^{17} - 37 x^{16} - 1150 x^{15} - 5862 x^{14} + 30982 x^{13} + 172221 x^{12} + 8777598 x^{11} + 22636422 x^{10} + 99933154 x^{9} - 459220119 x^{8} - 16495586098 x^{7} - 18228023191 x^{6} - 427536662700 x^{5} + 1460718484342 x^{4} + 15093050892288 x^{3} + 4666131046140 x^{2} - 29995375012704 x + 38248316595432$ |
$18$ |
[2,8] |
$2^{33}\cdot 3^{9}\cdot 7^{14}\cdot 181^{14}$ |
$4$ |
$1598.52581136$ |
$2377.366462449021$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
$[6, 36, 36]$ |
$[2, 6, 36, 36]$ |
$2$ |
$9$ |
$11980234096981277000$ |
| 18.0.598...256.1 |
$x^{18} - 9 x^{17} + 51 x^{16} - 204 x^{15} - 5508 x^{14} + 41412 x^{13} + 13138994 x^{12} - 79378950 x^{11} + 10923486 x^{10} + 674026948 x^{9} + 36636764328 x^{8} - 151466109924 x^{7} + 39944056206445 x^{6} - 119298331344081 x^{5} + 318200659662687 x^{4} - 437749263098552 x^{3} + 1592931307768140 x^{2} - 1393914218595264 x + 508135996832752$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 17^{15}\cdot 181^{14}$ |
$4$ |
$2093.8084544$ |
$3952.5605746032343$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
not computed |
not computed |
$2$ |
$8$ |
|
| 18.0.634...736.1 |
$x^{18} - 9 x^{17} + 159 x^{16} + 2190 x^{15} - 14367 x^{14} + 164157 x^{13} + 3722336 x^{12} - 25129761 x^{11} + 3585945 x^{10} + 3344464060 x^{9} - 14691916371 x^{8} - 127221531561 x^{7} + 1831690168033 x^{6} - 763095139824 x^{5} - 76729321661868 x^{4} + 357817977035260 x^{3} + 1224625809441876 x^{2} - 13118235143169264 x + 32955441712928752$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{32}\cdot 19^{9}\cdot 181^{14}$ |
$4$ |
$3504.24598956$ |
$7031.417842506584$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
not computed |
not computed |
$2$ |
$8$ |
|
| 18.0.634...736.2 |
$x^{18} - 3 x^{17} - 51 x^{16} - 3106 x^{15} + 9963 x^{14} + 45381 x^{13} + 4287342 x^{12} - 3250713 x^{11} + 27409683 x^{10} - 3144312126 x^{9} + 310914417 x^{8} - 73465223577 x^{7} + 1748550612057 x^{6} - 3000923737680 x^{5} + 36493650483372 x^{4} - 285215996340224 x^{3} + 1083488517567408 x^{2} - 5496601090738560 x + 27750861942498304$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{32}\cdot 19^{9}\cdot 181^{14}$ |
$4$ |
$3504.24598956$ |
$7031.417842506584$ |
|
|
|
$S_3\times D_6$ (as 18T29) |
not computed |
not computed |
$2$ |
$8$ |
|
