| 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 |
Unit signature rank |
| 12.0.100...000.1 |
$x^{12} - 4 x^{11} + 32 x^{10} - 23 x^{9} + 303 x^{8} - 38 x^{7} + 3223 x^{6} - 10028 x^{5} + 28963 x^{4} - 82513 x^{3} + 121977 x^{2} - 15829 x + 6311$ |
$12$ |
(0, 6) |
$2^{8}\cdot 5^{9}\cdot 17^{10}$ |
$3$ |
$56.2714709902$ |
$56.27147099020761$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2, 2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$5$ |
$7502.80335755$ |
$0$ |
| 12.12.258...000.1 |
$x^{12} - 6 x^{11} - 92 x^{10} + 430 x^{9} + 3051 x^{8} - 8900 x^{7} - 47648 x^{6} + 52988 x^{5} + 313291 x^{4} + 62090 x^{3} - 503040 x^{2} - 410810 x - 71455$ |
$12$ |
(12, 0) |
$2^{16}\cdot 5^{9}\cdot 17^{10}$ |
$3$ |
$89.3253922457$ |
$89.32539224565357$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$11$ |
$63369775.7088$ |
$7$ |
| 12.12.734...000.1 |
$x^{12} - 4 x^{11} - 138 x^{10} + 317 x^{9} + 6593 x^{8} - 8198 x^{7} - 124787 x^{6} + 108972 x^{5} + 789883 x^{4} - 840543 x^{3} + 122997 x^{2} + 100791 x - 27009$ |
$12$ |
(12, 0) |
$2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 17^{10}$ |
$4$ |
$97.4650467717$ |
$97.46504677167775$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$11$ |
$72708176.852$ |
$7$ |
| 12.0.165...000.1 |
$x^{12} + 170 x^{10} + 10880 x^{8} + 331500 x^{6} + 5057500 x^{4} + 36125000 x^{2} + 90312500$ |
$12$ |
(0, 6) |
$2^{22}\cdot 5^{9}\cdot 17^{10}$ |
$3$ |
$126.325181178$ |
$126.32518117809978$ |
✓ |
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2, 2, 2, 2, 18, 18]$ |
$[2, 2, 2, 2, 18, 18]$ |
$2$ |
$5$ |
$7502.80335755$ |
$0$ |
| 12.12.165...000.1 |
$x^{12} - 170 x^{10} + 10880 x^{8} - 331500 x^{6} + 5057500 x^{4} - 36125000 x^{2} + 90312500$ |
$12$ |
(12, 0) |
$2^{22}\cdot 5^{9}\cdot 17^{10}$ |
$3$ |
$126.325181178$ |
$126.32518117809978$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$11$ |
$456041034.146$ |
$7$ |
| 12.4.384...125.1 |
$x^{12} - 4 x^{11} - 38 x^{10} - 175 x^{9} + 450 x^{8} + 5030 x^{7} + 405 x^{6} - 46890 x^{5} - 78950 x^{4} + 28775 x^{3} + 143790 x^{2} + 13540 x - 61595$ |
$12$ |
(4, 4) |
$5^{19}\cdot 17^{10}$ |
$2$ |
$135.54284840658144$ |
$244.54884140016014$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$85555778.2735486$ |
$4$ |
| 12.4.384...125.2 |
$x^{12} - 6 x^{11} - 26 x^{10} + 185 x^{9} + 185 x^{8} - 1916 x^{7} + 126 x^{6} + 7171 x^{5} - 4350 x^{4} - 5890 x^{3} + 5856 x^{2} - 1336 x + 339$ |
$12$ |
(4, 4) |
$5^{19}\cdot 17^{10}$ |
$2$ |
$135.54284840658144$ |
$244.54884140016014$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$170756284.89580935$ |
$4$ |
| 12.4.384...125.5 |
$x^{12} - 25 x^{10} - 200 x^{8} - 510 x^{7} + 875 x^{6} + 1250 x^{4} + 19125 x^{3} - 12850 x^{2} - 42500 x + 54375$ |
$12$ |
(4, 4) |
$5^{19}\cdot 17^{10}$ |
$2$ |
$135.54284840658144$ |
$244.54884140016014$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$170756284.89580935$ |
$4$ |
| 12.4.384...125.6 |
$x^{12} - 6 x^{11} - 26 x^{10} + 185 x^{9} + 185 x^{8} - 1916 x^{7} - 1149 x^{6} + 10996 x^{5} + 7125 x^{4} - 35215 x^{3} + 22091 x^{2} - 2271 x + 70379$ |
$12$ |
(4, 4) |
$5^{19}\cdot 17^{10}$ |
$2$ |
$135.54284840658144$ |
$244.54884140016014$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$85555778.2735486$ |
$4$ |
| 12.12.118...000.1 |
$x^{12} - 4 x^{11} - 308 x^{10} + 657 x^{9} + 33113 x^{8} - 36078 x^{7} - 1438037 x^{6} + 1349632 x^{5} + 21624743 x^{4} - 36044313 x^{3} - 17439873 x^{2} + 13770491 x + 4815101$ |
$12$ |
(12, 0) |
$2^{8}\cdot 5^{9}\cdot 7^{6}\cdot 17^{10}$ |
$4$ |
$148.880318148$ |
$148.88031814787485$ |
|
✓ |
? |
$C_3 : C_4$ (as 12T5) |
$[2]$ |
$[2, 2, 2, 2, 2, 2]$ |
$2$ |
$11$ |
$1004442899.46$ |
$7$ |
| 16.0.806...000.1 |
$x^{16} - x^{15} + 8 x^{14} + 4 x^{13} + 19 x^{11} - 22 x^{10} - 75 x^{9} + 57 x^{8} + 389 x^{7} + 656 x^{6} + 635 x^{5} + 408 x^{4} + 180 x^{3} + 52 x^{2} + 9 x + 1$ |
$16$ |
(0, 8) |
$2^{12}\cdot 5^{10}\cdot 17^{10}$ |
$3$ |
$27.0183812315$ |
$79.57987744903578$ |
|
|
? |
$C_2^4.S_4$ (as 16T737) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$40610.993319$ |
$0$ |
| 16.0.397...616.1 |
$x^{16} - 2 x^{15} - 16 x^{13} + 90 x^{12} + 40 x^{11} - 38 x^{10} - 132 x^{9} + 70 x^{8} + 3498 x^{7} - 2176 x^{6} - 6040 x^{5} + 3565 x^{4} + 1290 x^{3} + 2794 x^{2} - 4334 x + 3779$ |
$16$ |
(0, 8) |
$2^{24}\cdot 7^{6}\cdot 17^{10}$ |
$3$ |
$34.4736552631$ |
$94.34646087898356$ |
|
|
? |
$C_2^7:S_4$ (as 16T1530) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$234797.970125$ |
$0$ |
| 16.4.311...944.2 |
$x^{16} - 2 x^{15} - 14 x^{14} + 72 x^{13} - 174 x^{12} + 320 x^{11} + 152 x^{10} - 1148 x^{9} - 2430 x^{8} + 1820 x^{7} + 4024 x^{6} + 304 x^{5} - 2828 x^{4} - 584 x^{3} + 720 x^{2} + 72 x - 108$ |
$16$ |
(4, 6) |
$2^{28}\cdot 7^{8}\cdot 17^{10}$ |
$3$ |
$52.2855990584$ |
$94.34646087898356$ |
|
|
? |
$C_2^7:S_4$ (as 16T1525) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$20484100.4919$ |
$2$ |
| 20.2.130...528.1 |
$x^{20} - 2 x^{19} - 16 x^{17} - 64 x^{16} + 160 x^{15} + 304 x^{14} + 724 x^{13} + 2770 x^{12} + 4912 x^{11} + 5488 x^{10} + 15660 x^{9} + 11230 x^{8} + 8296 x^{7} + 23152 x^{6} - 380 x^{5} - 14045 x^{4} + 14286 x^{3} - 6944 x^{2} - 28772 x - 10826$ |
$20$ |
(2, 9) |
$-\,2^{52}\cdot 3^{15}\cdot 17^{10}$ |
$3$ |
$56.9827481499$ |
|
|
|
? |
$C_2^{10}.C_3^4:(S_3\times A_5)$ (as 20T1047) |
trivial |
trivial |
$2$ |
$10$ |
$10509374314.8$ |
$2$ |
| 20.2.521...112.1 |
$x^{20} - 2 x^{19} + 12 x^{17} - 115 x^{16} - 164 x^{15} + 528 x^{14} + 480 x^{13} - 636 x^{12} - 220 x^{11} - 448 x^{10} - 696 x^{9} + 520 x^{8} + 332 x^{7} + 512 x^{6} + 328 x^{5} + 93 x^{4} - 14 x^{3} - 4 x + 1$ |
$20$ |
(2, 9) |
$-\,2^{54}\cdot 3^{15}\cdot 17^{10}$ |
$3$ |
$61.0725972894$ |
|
|
|
? |
$C_2^{10}.C_3^4:(S_3\times A_5)$ (as 20T1047) |
trivial |
$[2]$ |
$2$ |
$10$ |
$16610928505.8$ |
$1$ |
