| 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 |
| 12.0.1511207993344.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 6 x^{9} + 18 x^{8} - 24 x^{7} - 18 x^{6} + 12 x^{5} + 57 x^{4} - 76 x^{3} + 40 x^{2} - 10 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}$ |
$2$ |
$10.350079528$ |
$10.350079527967589$ |
|
✓ |
? |
$A_4$ (as 12T4) |
trivial |
trivial |
$2$ |
$5$ |
$12.7907966811$ |
| 12.0.11284439629824.1 |
$x^{12} - 2 x^{9} + 18 x^{8} - 18 x^{7} + 14 x^{6} - 30 x^{5} + 45 x^{4} - 52 x^{3} + 42 x^{2} - 18 x + 3$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{16}$ |
$2$ |
$12.2378934159$ |
$12.237893415933033$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
trivial |
$2$ |
$5$ |
$90.7922965712$ |
| 12.0.12745792515625.1 |
$x^{12} - 5 x^{11} + 12 x^{10} - 24 x^{9} + 48 x^{8} - 66 x^{7} + 53 x^{6} - 36 x^{5} + 42 x^{4} - 41 x^{3} + 23 x^{2} - 7 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 13^{8}$ |
$2$ |
$12.3627163157$ |
$12.362716315674692$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$21.2498556899$ |
| 12.0.27825593350009.1 |
$x^{12} - 3 x^{11} + 5 x^{10} - 13 x^{9} + 36 x^{8} - 72 x^{7} + 115 x^{6} - 150 x^{5} + 144 x^{4} - 92 x^{3} + 38 x^{2} - 9 x + 1$ |
$12$ |
[0,6] |
$7^{8}\cdot 13^{6}$ |
$2$ |
$13.1938143701$ |
$13.193814370085985$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$39.6447347937$ |
| 12.0.213838914125824.2 |
$x^{12} - 2 x^{11} - 12 x^{9} + 18 x^{8} - 26 x^{7} + 110 x^{6} - 50 x^{5} + 165 x^{4} - 228 x^{3} + 212 x^{2} - 156 x + 47$ |
$12$ |
[0,6] |
$2^{18}\cdot 13^{8}$ |
$2$ |
$15.6377366496$ |
$15.637736649622886$ |
|
✓ |
? |
$A_4$ (as 12T4) |
trivial |
trivial |
$2$ |
$5$ |
$167.105330062$ |
| 12.0.1039043198361249.1 |
$x^{12} + 6 x^{10} - x^{9} + 33 x^{8} - 27 x^{7} + 89 x^{6} - 186 x^{5} + 219 x^{4} - 341 x^{3} + 396 x^{2} - 252 x + 72$ |
$12$ |
[0,6] |
$3^{16}\cdot 17^{6}$ |
$2$ |
$17.8396419506$ |
$17.839641950637386$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$708.950206538$ |
| 12.0.1998099208210609.2 |
$x^{12} - 4 x^{11} + 7 x^{10} - 19 x^{9} + 46 x^{8} - 38 x^{7} + 62 x^{6} - 61 x^{5} + 181 x^{4} - 11 x^{3} - 38 x^{2} + 133 x + 133$ |
$12$ |
[0,6] |
$7^{6}\cdot 19^{8}$ |
$2$ |
$18.8387212751$ |
$18.838721275076466$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$263.701558623$ |
| 12.0.2025170913606201.2 |
$x^{12} - 6 x^{10} - 11 x^{9} + 21 x^{8} + 39 x^{7} + 14 x^{6} - 27 x^{5} + 72 x^{4} + 20 x^{3} - 129 x^{2} - 297 x + 327$ |
$12$ |
[0,6] |
$3^{16}\cdot 19^{6}$ |
$2$ |
$18.859860385$ |
$18.859860385004858$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$538.58951047$ |
| 12.0.3429038075724121.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 15 x^{9} + 31 x^{8} - 49 x^{7} + 69 x^{6} - 60 x^{5} + 179 x^{4} - 143 x^{3} + 462 x^{2} - 612 x + 216$ |
$12$ |
[0,6] |
$7^{8}\cdot 29^{6}$ |
$2$ |
$19.7059643282$ |
$19.705964328162043$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$560.923582639$ |
| 12.0.3493441689358336.15 |
$x^{12} - 3 x^{10} - 2 x^{8} + 102 x^{6} - 255 x^{4} + 157 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{8}$ |
$2$ |
$19.7365448064$ |
$19.736544806437948$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$4903.16351074$ |
| 12.0.4452139149819904.7 |
$x^{12} - 8 x^{10} + 34 x^{8} - 26 x^{6} - 247 x^{4} + 722 x^{2} + 361$ |
$12$ |
[0,6] |
$2^{18}\cdot 19^{8}$ |
$2$ |
$20.1394401761$ |
$20.13944017607579$ |
|
✓ |
? |
$A_4$ (as 12T4) |
trivial |
trivial |
$2$ |
$5$ |
$761.462514223$ |
| 12.12.139...849.1 |
$x^{12} - 4 x^{11} - 17 x^{10} + 68 x^{9} + 108 x^{8} - 416 x^{7} - 314 x^{6} + 1129 x^{5} + 358 x^{4} - 1353 x^{3} - 36 x^{2} + 540 x - 72$ |
$12$ |
[12,0] |
$3^{6}\cdot 61^{8}$ |
$2$ |
$26.8398767603$ |
$26.839876760292654$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$55324.635116$ |
| 12.12.223...504.1 |
$x^{12} - 2 x^{11} - 27 x^{10} + 70 x^{9} + 183 x^{8} - 604 x^{7} - 300 x^{6} + 1896 x^{5} - 467 x^{4} - 2170 x^{3} + 1207 x^{2} + 602 x - 373$ |
$12$ |
[12,0] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$27.911689339648817$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$86712.0400607$ |
| 12.0.223580268118933504.8 |
$x^{12} + 6 x^{10} + 34 x^{8} + 96 x^{6} + 177 x^{4} + 178 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$27.911689339648817$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$4311.11312563$ |
| 12.12.551...041.1 |
$x^{12} - 3 x^{11} - 39 x^{10} + 92 x^{9} + 543 x^{8} - 882 x^{7} - 3153 x^{6} + 2880 x^{5} + 7236 x^{4} - 1899 x^{3} - 4212 x^{2} + 324 x + 648$ |
$12$ |
[12,0] |
$3^{16}\cdot 71^{6}$ |
$2$ |
$36.4578326691$ |
$36.45783266912841$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1188211.01781$ |
| 12.12.879...209.1 |
$x^{12} - 39 x^{10} - 10 x^{9} + 455 x^{8} + 156 x^{7} - 1895 x^{6} - 988 x^{5} + 3133 x^{4} + 2276 x^{3} - 1521 x^{2} - 1638 x - 351$ |
$12$ |
[12,0] |
$13^{8}\cdot 47^{6}$ |
$2$ |
$37.903370486$ |
$37.90337048597898$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$552184.780497$ |
| 12.0.143...256.9 |
$x^{12} + 6 x^{10} - 38 x^{8} + 1110 x^{6} - 3159 x^{4} + 3568 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{24}\cdot 31^{8}$ |
$2$ |
$39.4730896129$ |
$39.473089612875896$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2, 2, 2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$5$ |
$14852.4986279$ |
| 12.0.143...256.83 |
$x^{12} + 6 x^{10} - 38 x^{8} + 366 x^{6} - 183 x^{4} - 152 x^{2} + 13456$ |
$12$ |
[0,6] |
$2^{24}\cdot 31^{8}$ |
$2$ |
$39.4730896129$ |
$39.473089612875896$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2, 2, 2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$5$ |
$23246.9438193$ |
| 12.12.125...569.1 |
$x^{12} - 3 x^{11} - 44 x^{10} + 224 x^{9} + 117 x^{8} - 2771 x^{7} + 6359 x^{6} - 4427 x^{5} - 1991 x^{4} + 3249 x^{3} - 434 x^{2} - 280 x + 56$ |
$12$ |
[12,0] |
$7^{8}\cdot 167^{6}$ |
$2$ |
$47.2886514151$ |
$47.28865141512203$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2838054.22304$ |
| 12.12.198...641.1 |
$x^{12} - x^{11} - 59 x^{10} + 148 x^{9} + 952 x^{8} - 4185 x^{7} + 530 x^{6} + 25121 x^{5} - 58645 x^{4} + 60947 x^{3} - 31956 x^{2} + 7830 x - 675$ |
$12$ |
[12,0] |
$13^{8}\cdot 79^{6}$ |
$2$ |
$49.1408254335$ |
$49.14082543353559$ |
|
✓ |
|
$A_4$ (as 12T4) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2942733.53438$ |
| 12.12.202...881.2 |
$x^{12} - x^{11} - 61 x^{10} + 120 x^{9} + 1142 x^{8} - 3153 x^{7} - 6342 x^{6} + 25793 x^{5} - 4597 x^{4} - 53239 x^{3} + 53940 x^{2} - 9900 x - 3375$ |
$12$ |
[12,0] |
$7^{8}\cdot 181^{6}$ |
$2$ |
$49.230923296$ |
$49.23092329595919$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[4]$ |
$[4]$ |
$2$ |
$11$ |
$923852.467934$ |
| 12.12.165...889.2 |
$x^{12} - 91 x^{10} - 74 x^{9} + 2450 x^{8} + 868 x^{7} - 29502 x^{6} + 11907 x^{5} + 147462 x^{4} - 165829 x^{3} - 117600 x^{2} + 193200 x - 56000$ |
$12$ |
[12,0] |
$7^{8}\cdot 13^{6}\cdot 29^{6}$ |
$3$ |
$71.0508648177$ |
$71.05086481765254$ |
|
✓ |
|
$A_4$ (as 12T4) |
$[2, 2]$ |
$[2, 2, 4, 4]$ |
$2$ |
$11$ |
$12581501.4645$ |
