| 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 |
| 12.0.271...125.1 |
$x^{12} - x^{11} + 53 x^{10} - 11 x^{9} + 1303 x^{8} + 438 x^{7} + 18804 x^{6} + 9784 x^{5} + 170686 x^{4} + 49088 x^{3} + 900838 x^{2} + 99987 x + 2139101$ |
$12$ |
[0,6] |
$5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$3$ |
$50.4487787342$ |
$50.448778734178404$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[962]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.12.133...125.1 |
$x^{12} - x^{11} - 152 x^{10} + 151 x^{9} + 8594 x^{8} - 8443 x^{7} - 228593 x^{6} + 234291 x^{5} + 2932130 x^{4} - 3275066 x^{3} - 15786160 x^{2} + 17913708 x + 16784881$ |
$12$ |
[12,0] |
$5^{9}\cdot 7^{10}\cdot 17^{6}$ |
$3$ |
$69.7750779953$ |
$69.77507799528695$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$6790562.47053$ |
| 12.0.384...125.1 |
$x^{12} - x^{11} + 45 x^{10} - 15 x^{9} + 1141 x^{8} + 680 x^{7} + 18214 x^{6} + 13740 x^{5} + 178606 x^{4} + 104830 x^{3} + 1201400 x^{2} + 851959 x + 4264781$ |
$12$ |
[0,6] |
$5^{9}\cdot 13^{8}\cdot 17^{6}$ |
$3$ |
$76.2220922079$ |
$76.22209220793223$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 10, 130]$ |
$2$ |
$5$ |
$615.54450504$ |
| 12.12.198...125.1 |
$x^{12} - x^{11} - 202 x^{10} + 74 x^{9} + 15753 x^{8} + 1798 x^{7} - 599316 x^{6} - 252696 x^{5} + 11554141 x^{4} + 6283413 x^{3} - 104562232 x^{2} - 45628823 x + 334724041$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$4$ |
$87.3798479474$ |
$87.37984794739731$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$18345440.8395$ |
| 12.0.800...125.1 |
$x^{12} - x^{11} + 37 x^{10} + 21 x^{9} + 997 x^{8} + 268 x^{7} + 16408 x^{6} + 7328 x^{5} + 208512 x^{4} - 219292 x^{3} + 2113070 x^{2} - 1950049 x + 6498881$ |
$12$ |
[0,6] |
$5^{9}\cdot 17^{6}\cdot 19^{8}$ |
$3$ |
$98.164478691$ |
$98.16447869097495$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2834]$ |
$2$ |
$5$ |
$1234.55163261$ |
| 12.12.111...000.1 |
$x^{12} - 4 x^{11} - 257 x^{10} + 874 x^{9} + 25914 x^{8} - 71452 x^{7} - 1309383 x^{6} + 2723614 x^{5} + 34749905 x^{4} - 47923684 x^{3} - 453217430 x^{2} + 304232502 x + 2215713361$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$4$ |
$100.897557468$ |
$100.89755746835681$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$54495459.0657$ |
| 12.0.429...997.1 |
$x^{12} - x^{11} + 150 x^{10} + 168 x^{9} + 6499 x^{8} + 17779 x^{7} + 113305 x^{6} + 399401 x^{5} + 930866 x^{4} + 2425574 x^{3} + 5043531 x^{2} + 4720833 x + 2845051$ |
$12$ |
[0,6] |
$17^{6}\cdot 37^{11}$ |
$2$ |
$112.912677966$ |
$112.9126779663512$ |
✓ |
✓ |
|
$C_{12}$ (as 12T1) |
$[19546]$ |
$2$ |
$5$ |
$2518.23324049$ |
| 12.0.649...125.1 |
$x^{12} - x^{11} + 270 x^{10} - 275 x^{9} + 20801 x^{8} - 24235 x^{7} + 615964 x^{6} - 658945 x^{5} + 8871411 x^{4} - 3368575 x^{3} + 65405755 x^{2} + 15856409 x + 249089881$ |
$12$ |
[0,6] |
$5^{9}\cdot 13^{10}\cdot 17^{6}$ |
$3$ |
$116.87943159$ |
$116.87943159008147$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 2, 5746]$ |
$2$ |
$5$ |
$615.54450504$ |
| 12.0.970...125.1 |
$x^{12} - x^{11} + 443 x^{10} - 444 x^{9} + 72854 x^{8} - 73298 x^{7} + 5685112 x^{6} - 6113764 x^{5} + 223464715 x^{4} - 256778386 x^{3} + 4246142315 x^{2} - 4044668347 x + 31633408171$ |
$12$ |
[0,6] |
$3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6}$ |
$4$ |
$120.85398019$ |
$120.85398018991815$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 35906]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.12.280...125.1 |
$x^{12} - x^{11} - 210 x^{10} + 70 x^{9} + 16611 x^{8} + 1360 x^{7} - 624896 x^{6} - 200970 x^{5} + 11417901 x^{4} + 4551265 x^{3} - 90501020 x^{2} - 23480651 x + 233001991$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 13^{8}\cdot 17^{6}$ |
$4$ |
$132.020536363$ |
$132.02053636333846$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$427202136.726$ |
| 12.0.402...125.1 |
$x^{12} - x^{11} + 21 x^{10} + 33 x^{9} + 898 x^{8} + 137 x^{7} + 14950 x^{6} + 14307 x^{5} + 235426 x^{4} - 424511 x^{3} + 3757769 x^{2} - 2920010 x + 16177451$ |
$12$ |
[0,6] |
$5^{9}\cdot 17^{6}\cdot 31^{8}$ |
$3$ |
$136.048291783$ |
$136.04829178250532$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[11714]$ |
$2$ |
$5$ |
$4882.16021651$ |
| 12.0.545...000.1 |
$x^{12} + 595 x^{10} + 131495 x^{8} + 13756400 x^{6} + 716192575 x^{4} + 17393248250 x^{2} + 147842610125$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6}$ |
$4$ |
$139.550155991$ |
$139.5501559905739$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 201994]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.0.712...000.1 |
$x^{12} - 4 x^{11} + 508 x^{10} - 1676 x^{9} + 104199 x^{8} - 273412 x^{7} + 10968102 x^{6} - 21538616 x^{5} + 623909300 x^{4} - 819565924 x^{3} + 18410523340 x^{2} - 12257477028 x + 222965992201$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$4$ |
$142.690694182$ |
$142.69069418206897$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[18, 16866]$ |
$2$ |
$5$ |
$104.882003477$ |
| 12.12.712...000.1 |
$x^{12} - 4 x^{11} - 512 x^{10} + 1724 x^{9} + 103859 x^{8} - 281572 x^{7} - 10644338 x^{6} + 21700544 x^{5} + 578712080 x^{4} - 784199124 x^{3} - 15736799340 x^{2} + 10519199812 x + 166108823761$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6}$ |
$4$ |
$142.690694182$ |
$142.69069418206897$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$320040330.009$ |
| 12.12.844...625.1 |
$x^{12} - x^{11} - 285 x^{10} + 285 x^{9} + 27236 x^{8} - 33450 x^{7} - 1015091 x^{6} + 1882750 x^{5} + 13705706 x^{4} - 36747465 x^{3} - 37348115 x^{2} + 178599199 x - 130101919$ |
$12$ |
[12,0] |
$5^{9}\cdot 13^{11}\cdot 17^{6}$ |
$3$ |
$144.732713189$ |
$144.7327131886099$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$2$ |
$11$ |
$544261614.045$ |
| 12.12.844...625.2 |
$x^{12} - x^{11} - 285 x^{10} + 285 x^{9} + 27236 x^{8} - 6930 x^{7} - 1152111 x^{6} - 702950 x^{5} + 20667206 x^{4} + 25065130 x^{3} - 101392810 x^{2} - 59815601 x + 123164081$ |
$12$ |
[12,0] |
$5^{9}\cdot 13^{11}\cdot 17^{6}$ |
$3$ |
$144.732713189$ |
$144.7327131886099$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
$[2, 10]$ |
$2$ |
$11$ |
$101052811.273$ |
| 20.10.447...552.1 |
$x^{20} - 4 x^{19} - 192 x^{18} - 368 x^{17} + 5900 x^{16} + 11612 x^{15} - 82376 x^{14} - 147412 x^{13} + 496249 x^{12} + 5837552 x^{11} + 28472784 x^{10} + 9581508 x^{9} - 257955946 x^{8} - 848288280 x^{7} - 488954264 x^{6} + 5231676656 x^{5} + 10164474572 x^{4} - 6966146992 x^{3} - 22153914848 x^{2} - 5610833232 x + 1443605144$ |
$20$ |
[10,5] |
$-\,2^{38}\cdot 17^{8}\cdot 23^{5}\cdot 881^{8}$ |
$4$ |
$382.436101742$ |
$11049.38055118573$ |
|
|
? |
$C_2^8.(S_3\times A_5)$ (as 20T754) |
trivial |
$2$ |
$14$ |
$12096615465700000000$ |
| 24.0.177...625.3 |
$x^{24} - x^{23} - 20 x^{22} + 20 x^{21} + 320 x^{20} - 219 x^{19} - 4901 x^{18} + 14901 x^{17} + 60299 x^{16} - 248180 x^{15} - 836019 x^{14} + 3276519 x^{13} + 13401461 x^{12} - 39585781 x^{11} - 30241579 x^{10} + 249183880 x^{9} - 136356881 x^{8} - 463267559 x^{7} + 1148300059 x^{6} - 13723758699 x^{5} + 13110121180 x^{4} + 71729555620 x^{3} - 174821473680 x^{2} - 220712110521 x + 1061520150601$ |
$24$ |
[0,12] |
$5^{18}\cdot 7^{20}\cdot 17^{12}$ |
$3$ |
$69.7750779953$ |
$69.77507799528695$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
not computed |
$14$ |
$11$ |
|
