| 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 |
| 12.0.1600000000000000.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 10 x^{9} + 15 x^{8} - 38 x^{7} - 24 x^{6} + 72 x^{5} + 30 x^{4} - 80 x^{3} - 34 x^{2} + 38 x + 31$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{14}$ |
$2$ |
$18.493111943$ |
$22.91954538992328$ |
|
|
? |
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$5$ |
$534.541702856$ |
| 12.0.1828652958613504.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 19 x^{8} - 12 x^{7} - 4 x^{6} - 12 x^{5} + 19 x^{4} + 2 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 17^{8}$ |
$2$ |
$18.7001148748$ |
$18.700114874768015$ |
|
|
? |
$A_5$ (as 12T33) |
$[5]$ |
$2$ |
$5$ |
$291.266472164$ |
| 12.0.4452139149819904.2 |
$x^{12} + 4 x^{10} + 10 x^{8} - 10 x^{6} + 17 x^{4} + 10 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 19^{8}$ |
$2$ |
$20.1394401761$ |
$29.822762797001236$ |
|
|
? |
$A_5$ (as 12T33) |
trivial |
$2$ |
$5$ |
$1500.58669489$ |
| 12.0.40000000000000000.2 |
$x^{12} + 4 x^{10} - 10 x^{8} + 30 x^{6} + 65 x^{4} + 34 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{16}$ |
$2$ |
$24.1827117512$ |
$37.14471242937835$ |
|
|
? |
$A_5$ (as 12T33) |
trivial |
$2$ |
$5$ |
$5593.24772239$ |
| 12.0.40000000000000000.5 |
$x^{12} - 6 x^{11} + 24 x^{10} - 60 x^{9} + 110 x^{8} - 134 x^{7} + 114 x^{6} - 46 x^{5} + 5 x^{4} + 36 x^{2} - 36 x + 19$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{16}$ |
$2$ |
$24.1827117512$ |
$37.14471242937835$ |
|
|
? |
$A_5$ (as 12T33) |
trivial |
$2$ |
$5$ |
$5347.50227078$ |
| 12.0.40000000000000000.11 |
$x^{12} + 10 x^{10} + 50 x^{8} + 180 x^{6} + 345 x^{4} + 274 x^{2} + 100$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{16}$ |
$2$ |
$24.1827117512$ |
$37.14471242937835$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$5$ |
$7105.60969015$ |
| 12.0.131136595679248384.3 |
$x^{12} + 10 x^{8} + 22 x^{6} + 9 x^{4} + 142 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{18}\cdot 29^{8}$ |
$2$ |
$26.697893242$ |
$41.82764291976793$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$5$ |
$9842.51001576$ |
| 12.0.131136595679248384.6 |
$x^{12} + 2 x^{8} + 58 x^{6} + 301 x^{4} + 174 x^{2} + 25$ |
$12$ |
[0,6] |
$2^{18}\cdot 29^{8}$ |
$2$ |
$26.697893242$ |
$26.697893241960433$ |
|
|
? |
$A_5$ (as 12T33) |
$[5]$ |
$2$ |
$5$ |
$2302.05567158$ |
| 12.0.223...504.14 |
$x^{12} - 4 x^{11} + 10 x^{10} - 22 x^{9} + 46 x^{8} - 80 x^{7} + 92 x^{6} - 70 x^{5} + 61 x^{4} - 86 x^{3} + 94 x^{2} - 8 x + 31$ |
$12$ |
[0,6] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$44.119882642841475$ |
|
|
? |
$A_5$ (as 12T33) |
trivial |
$2$ |
$5$ |
$7108.11455748$ |
| 12.0.256...000.23 |
$x^{12} + 2 x^{10} - 10 x^{8} - 10 x^{6} + 25 x^{4} + 68 x^{2} + 196$ |
$12$ |
[0,6] |
$2^{24}\cdot 5^{16}$ |
$2$ |
$34.1995189335$ |
$52.53055608807534$ |
|
|
|
$A_5$ (as 12T33) |
$[2, 2]$ |
$2$ |
$5$ |
$31927.4420841$ |
| 12.12.629...656.1 |
$x^{12} - 6 x^{11} - 17 x^{10} + 140 x^{9} + 20 x^{8} - 986 x^{7} + 323 x^{6} + 3136 x^{5} - 920 x^{4} - 4850 x^{3} + 115 x^{2} + 3044 x + 1055$ |
$12$ |
[12,0] |
$2^{8}\cdot 199^{8}$ |
$2$ |
$54.1072400204$ |
$109.58954527670048$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$6474868.58794$ |
| 12.12.734...544.1 |
$x^{12} - 35 x^{10} - 52 x^{9} + 308 x^{8} + 808 x^{7} - 249 x^{6} - 2810 x^{5} - 3596 x^{4} - 1830 x^{3} - 267 x^{2} + 54 x + 9$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 89^{8}$ |
$3$ |
$54.8075803091$ |
$99.71472513477265$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$8958450.47427$ |
| 12.12.265...000.1 |
$x^{12} - x^{11} - 46 x^{10} + 105 x^{9} + 580 x^{8} - 2123 x^{7} - 417 x^{6} + 10028 x^{5} - 14340 x^{4} + 5300 x^{3} + 2816 x^{2} - 2156 x + 244$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{14}\cdot 19^{8}$ |
$3$ |
$73.90163885190631$ |
$135.62837243568117$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$57646491.00673672$ |
| 12.12.896...625.1 |
$x^{12} - 70 x^{10} - 35 x^{9} + 1465 x^{8} + 1200 x^{7} - 11435 x^{6} - 12425 x^{5} + 32075 x^{4} + 40150 x^{3} - 20295 x^{2} - 21925 x + 7350$ |
$12$ |
[12,0] |
$5^{14}\cdot 59^{8}$ |
$2$ |
$99.09072656748337$ |
$211.51570293565203$ |
|
|
? |
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$771396558.2358254$ |
| 12.12.610...000.1 |
$x^{12} - 55 x^{10} - 120 x^{9} + 750 x^{8} + 2844 x^{7} - 1055 x^{6} - 16800 x^{5} - 18810 x^{4} + 17820 x^{3} + 47993 x^{2} + 31020 x + 6325$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{6}\cdot 5^{16}\cdot 11^{8}$ |
$4$ |
$116.27037870803834$ |
$245.87447533561422$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$2398757681.8762155$ |
| 12.12.925...625.1 |
$x^{12} - 3 x^{11} - 89 x^{10} + 125 x^{9} + 2810 x^{8} - 584 x^{7} - 38503 x^{6} - 30504 x^{5} + 204740 x^{4} + 338110 x^{3} - 94356 x^{2} - 408797 x - 176251$ |
$12$ |
[12,0] |
$5^{14}\cdot 79^{8}$ |
$2$ |
$120.37872318003083$ |
$267.15461364932094$ |
|
|
|
$A_5$ (as 12T33) |
$[4]$ |
$2$ |
$11$ |
$510849558.74388$ |
| 12.12.149...856.1 |
$x^{12} - 4 x^{11} - 71 x^{10} + 342 x^{9} + 1036 x^{8} - 6880 x^{7} + 5953 x^{6} + 6222 x^{5} - 6572 x^{4} - 604 x^{3} + 1057 x^{2} - 30 x - 9$ |
$12$ |
[12,0] |
$2^{8}\cdot 701^{8}$ |
$2$ |
$125.26565369164506$ |
$300.09660215338573$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$1397721578.3085644$ |
| 12.12.209...601.1 |
$x^{12} - 113 x^{10} + 4482 x^{8} - 72251 x^{6} + 388968 x^{4} - 48712 x^{2} + 1225$ |
$12$ |
[12,0] |
$1951^{8}$ |
$1$ |
$156.13664610561165$ |
$428.75166098858034$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$8824810032.071943$ |
| 12.12.311...000.1 |
$x^{12} - 99 x^{10} + 3535 x^{8} - 56445 x^{6} + 430800 x^{4} - 1511156 x^{2} + 1898884$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{16}\cdot 41^{8}$ |
$3$ |
$161.3748707260082$ |
$406.6921185224303$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$6767810532.056657$ |
| 12.12.441...921.1 |
$x^{12} - 111 x^{10} + 3535 x^{8} - 33095 x^{6} + 100794 x^{4} - 108353 x^{2} + 26244$ |
$12$ |
[12,0] |
$2141^{8}$ |
$1$ |
$166.11586482031228$ |
$461.8419028397104$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$31886286099.988056$ |
| 12.12.165...625.1 |
$x^{12} - 6 x^{11} - 119 x^{10} + 650 x^{9} + 515 x^{8} - 6026 x^{7} + 1166 x^{6} + 20389 x^{5} - 7885 x^{4} - 26575 x^{3} + 9381 x^{2} + 8509 x - 954$ |
$12$ |
[12,0] |
$5^{16}\cdot 101^{8}$ |
$2$ |
$185.42754779106332$ |
$526.9981685865927$ |
|
|
? |
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$19976632467.314842$ |
| 12.12.132...625.1 |
$x^{12} - 104 x^{10} - 10 x^{9} + 3150 x^{8} + 643 x^{7} - 31425 x^{6} + 6348 x^{5} + 108215 x^{4} - 78845 x^{3} - 22893 x^{2} + 14840 x + 2672$ |
$12$ |
[12,0] |
$5^{16}\cdot 131^{8}$ |
$2$ |
$220.5333135599178$ |
$648.8869551830437$ |
|
|
|
$A_5$ (as 12T33) |
trivial |
$2$ |
$11$ |
$243827836201.38577$ |
| 12.12.481...625.1 |
$x^{12} - 5 x^{11} - 140 x^{10} + 590 x^{9} + 7135 x^{8} - 21050 x^{7} - 170605 x^{6} + 214825 x^{5} + 1931350 x^{4} + 651875 x^{3} - 6937760 x^{2} - 9899675 x - 3759725$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{14}\cdot 101^{8}$ |
$3$ |
$245.60651433044995$ |
$563.2208608229729$ |
|
|
? |
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$121886096245.05731$ |
| 12.12.135...000.1 |
$x^{12} - 6 x^{11} - 161 x^{10} + 860 x^{9} + 5190 x^{8} - 25986 x^{7} - 61299 x^{6} + 278526 x^{5} + 387670 x^{4} - 1271620 x^{3} - 1451761 x^{2} + 2138586 x + 2493431$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{14}\cdot 131^{8}$ |
$3$ |
$267.7107840175872$ |
$635.5719264451167$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$115276886013.08443$ |
| 12.12.654...625.1 |
$x^{12} - x^{11} - 236 x^{10} - 130 x^{9} + 17755 x^{8} + 32901 x^{7} - 429781 x^{6} - 1246906 x^{5} + 1377075 x^{4} + 5122970 x^{3} - 300291 x^{2} - 5570744 x - 1811584$ |
$12$ |
[12,0] |
$5^{14}\cdot 11^{8}\cdot 29^{8}$ |
$3$ |
$305.25219374974677$ |
$816.0063757822372$ |
|
|
? |
$A_5$ (as 12T33) |
$[4]$ |
$2$ |
$11$ |
$208600330475.23264$ |
| 12.12.593...625.1 |
$x^{12} - 2 x^{11} - 142 x^{10} - 75 x^{9} + 5705 x^{8} + 13521 x^{7} - 56212 x^{6} - 220467 x^{5} - 118450 x^{4} + 278650 x^{3} + 264997 x^{2} - 35339 x - 56659$ |
$12$ |
[12,0] |
$5^{16}\cdot 281^{8}$ |
$2$ |
$366.8013164789806$ |
$1194.8601107286643$ |
|
|
|
$A_5$ (as 12T33) |
$[2]$ |
$2$ |
$11$ |
$499849527217.84595$ |
