| 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 |
| 12.0.858246278477.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 13 x^{9} + 17 x^{8} - 18 x^{7} + 18 x^{6} - 15 x^{5} + 11 x^{4} - 7 x^{3} + x^{2} + x + 1$ |
$12$ |
[0,6] |
$7^{8}\cdot 53^{3}$ |
$2$ |
$9.87342111674$ |
$26.640147687438905$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$5$ |
$7.51675464389$ |
| 12.6.14501103264256.1 |
$x^{12} - x^{11} - 7 x^{10} + 6 x^{9} + 13 x^{8} - 16 x^{7} - x^{6} + 19 x^{5} - 17 x^{4} - 5 x^{3} + 13 x^{2} - 3 x - 1$ |
$12$ |
[6,3] |
$-\,2^{9}\cdot 7^{8}\cdot 17^{3}$ |
$3$ |
$12.4963569039$ |
$42.67447112735335$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$93.643207835$ |
| 12.6.22039921152000.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 12 x^{8} - 25 x^{6} + 12 x^{5} + 24 x^{4} - 16 x^{3} - 6 x^{2} + 6 x - 1$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 3^{16}\cdot 5^{3}$ |
$3$ |
$12.9399968231$ |
$27.364761579423373$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$138.651675632$ |
| 12.0.69229431796189.1 |
$x^{12} - 4 x^{9} + 13 x^{8} - 11 x^{6} + 5 x^{5} + 26 x^{4} + x^{3} - x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$7^{8}\cdot 229^{3}$ |
$2$ |
$14.2350030301$ |
$55.3753436647046$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$5$ |
$58.4689097655$ |
| 12.6.213838914125824.1 |
$x^{12} - 6 x^{11} + 15 x^{10} - 18 x^{9} - 4 x^{8} + 50 x^{7} - 89 x^{6} + 124 x^{5} - 135 x^{4} + 86 x^{3} - 44 x^{2} + 24 x - 5$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 13^{8}$ |
$2$ |
$15.637736649622886$ |
$22.11509925471549$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$561.9137686720087$ |
| 12.6.464767295827968.1 |
$x^{12} - 2 x^{11} - 8 x^{10} + 6 x^{9} + 10 x^{8} - 20 x^{7} - 12 x^{6} + 22 x^{5} + 19 x^{4} + 4 x^{3} - 4 x^{2} - 4 x + 1$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{8}$ |
$3$ |
$16.682826379104554$ |
$18.725839469079336$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$732.2564009514388$ |
| 12.12.5576647516812869.1 |
$x^{12} - x^{11} - 16 x^{10} + 9 x^{9} + 90 x^{8} - 16 x^{7} - 225 x^{6} - 26 x^{5} + 249 x^{4} + 81 x^{3} - 97 x^{2} - 47 x - 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 23^{3}\cdot 43^{3}$ |
$3$ |
$20.5209643664$ |
$115.07920132818636$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$6486.54804926$ |
| 12.12.18053582868392517.1 |
$x^{12} - 3 x^{11} - 12 x^{10} + 32 x^{9} + 48 x^{8} - 111 x^{7} - 69 x^{6} + 150 x^{5} + 12 x^{4} - 71 x^{3} + 18 x^{2} + 3 x - 1$ |
$12$ |
[12,0] |
$3^{20}\cdot 173^{3}$ |
$2$ |
$22.6315144524$ |
$92.7339193741872$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$20749.7660725$ |
| 12.12.18626210017276736.1 |
$x^{12} - 5 x^{11} - 6 x^{10} + 59 x^{9} - 18 x^{8} - 234 x^{7} + 146 x^{6} + 404 x^{5} - 232 x^{4} - 304 x^{3} + 88 x^{2} + 80 x + 8$ |
$12$ |
[12,0] |
$2^{6}\cdot 7^{10}\cdot 101^{3}$ |
$3$ |
$22.690481295808528$ |
$80.74129623043368$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$14515.643674724211$ |
| 12.12.224...688.1 |
$x^{12} - 2 x^{11} - 24 x^{10} + 44 x^{9} + 197 x^{8} - 370 x^{7} - 696 x^{6} + 1478 x^{5} + 934 x^{4} - 2798 x^{3} + 148 x^{2} + 2012 x - 923$ |
$12$ |
[12,0] |
$2^{18}\cdot 7^{8}\cdot 53^{3}$ |
$3$ |
$27.92625210063111$ |
$75.34971632639669$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$58639.698672698236$ |
| 12.6.369...832.10 |
$x^{12} - 12 x^{10} - 24 x^{9} + 192 x^{7} + 160 x^{6} - 948 x^{4} + 256 x^{3} - 288 x^{2} + 672 x - 136$ |
$12$ |
[6,3] |
$-\,2^{33}\cdot 3^{16}$ |
$2$ |
$29.106779845745038$ |
$29.106779845745038$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$30512.39561200712$ |
| 12.0.435848050125000000.1 |
$x^{12} + 3 x^{10} - x^{9} - 21 x^{8} + 84 x^{7} - 12 x^{6} + 318 x^{5} + 285 x^{4} - 1184 x^{3} + 1149 x^{2} - 1137 x + 971$ |
$12$ |
[0,6] |
$2^{6}\cdot 3^{20}\cdot 5^{9}$ |
$3$ |
$29.508327325118774$ |
$37.4222358010528$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
$[8]$ |
$2$ |
$5$ |
$1362.5474857609888$ |
| 12.12.174...077.1 |
$x^{12} - 6 x^{11} - 7 x^{10} + 84 x^{9} - 8 x^{8} - 426 x^{7} + 118 x^{6} + 915 x^{5} - 147 x^{4} - 767 x^{3} - 76 x^{2} + 165 x + 41$ |
$12$ |
[12,0] |
$43^{8}\cdot 53^{3}$ |
$2$ |
$33.11676740288559$ |
$89.35459797694433$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$163180.5159869209$ |
| 12.12.981...000.1 |
$x^{12} - 40 x^{10} - 6 x^{9} + 452 x^{8} - 84 x^{7} - 1902 x^{6} + 804 x^{5} + 3073 x^{4} - 1716 x^{3} - 1342 x^{2} + 732 x - 61$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{3}\cdot 61^{8}$ |
$3$ |
$46.343879551622635$ |
$77.78691605847096$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$1471754.2045208085$ |
| 12.12.808...584.3 |
$x^{12} - 36 x^{10} - 24 x^{9} + 432 x^{8} + 576 x^{7} - 1728 x^{6} - 3744 x^{5} - 108 x^{4} + 4992 x^{3} + 4752 x^{2} + 1728 x + 216$ |
$12$ |
[12,0] |
$2^{33}\cdot 3^{23}$ |
$2$ |
$55.24778780238397$ |
$72.71017779983123$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$11$ |
$7190264.729428787$ |
| 12.0.190...533.3 |
$x^{12} - 2 x^{11} + 41 x^{10} - 10 x^{9} + 777 x^{8} - 543 x^{7} + 6808 x^{6} + 356 x^{5} + 31934 x^{4} + 25815 x^{3} - 208162 x^{2} + 249588 x + 805384$ |
$12$ |
[0,6] |
$7^{8}\cdot 53^{9}$ |
$2$ |
$71.87959071301479$ |
$71.87959071301479$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
$[32]$ |
$2$ |
$5$ |
$48715.36358081249$ |
| 12.12.857...216.1 |
$x^{12} - 6 x^{11} - 90 x^{10} + 264 x^{9} + 2685 x^{8} - 2862 x^{7} - 30858 x^{6} + 9030 x^{5} + 146718 x^{4} - 8722 x^{3} - 285480 x^{2} + 177957$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{19}\cdot 23^{9}$ |
$3$ |
$119.61010160912983$ |
$139.32681210085573$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
$[2]$ |
$2$ |
$11$ |
$334329203.2735909$ |
| 12.12.802...857.3 |
$x^{12} - 4 x^{11} - 152 x^{10} + 748 x^{9} + 5649 x^{8} - 39624 x^{7} + 11800 x^{6} + 403933 x^{5} - 1025690 x^{4} + 553946 x^{3} + 1041834 x^{2} - 1517303 x + 565118$ |
$12$ |
[12,0] |
$17^{9}\cdot 127^{8}$ |
$2$ |
$211.53026087633702$ |
$211.53026087633702$ |
|
|
|
$C_3\times S_4$ (as 12T45) |
$[4]$ |
$2$ |
$11$ |
$22019643173.340816$ |
