| 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 |
| 12.4.756680642578125.1 |
$x^{12} - 7 x^{9} + 14 x^{6} - 8 x^{3} + 1$ |
$12$ |
[4,4] |
$3^{18}\cdot 5^{9}$ |
$2$ |
$17.3743827793$ |
$27.182670372565486$ |
|
|
✓ |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$2$ |
$7$ |
$616.448428077$ |
| 12.4.756680642578125.3 |
$x^{12} - x^{9} - 4 x^{6} + 4 x^{3} + 1$ |
$12$ |
[4,4] |
$3^{18}\cdot 5^{9}$ |
$2$ |
$17.3743827793$ |
$27.182670372565486$ |
|
|
✓ |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$2$ |
$7$ |
$595.763948625$ |
| 12.0.6643012500000000.1 |
$x^{12} - 135 x^{6} - 270 x^{5} + 225 x^{4} + 1040 x^{3} + 1080 x^{2} + 480 x + 80$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$20.8223826158$ |
$43.62779101665627$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$10$ |
$5$ |
$4454.21449848$ |
| 12.0.6643012500000000.2 |
$x^{12} - 15 x^{10} + 90 x^{8} - 290 x^{6} - 90 x^{5} + 405 x^{4} + 730 x^{3} + 1620 x^{2} + 2040 x + 880$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$20.8223826158$ |
$43.62779101665627$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$10$ |
$5$ |
$5824.34466735$ |
| 12.0.15196929064453125.1 |
$x^{12} - 11 x^{9} + 51 x^{6} - 121 x^{3} + 121$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$22.3089768604$ |
$82.50875193999316$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$10$ |
$5$ |
$8255.75011032$ |
| 12.0.15196929064453125.2 |
$x^{12} - 28 x^{9} + 259 x^{6} - 902 x^{3} + 1331$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$22.3089768604$ |
$82.50875193999316$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$10$ |
$5$ |
$7472.62786974$ |
| 12.0.71228826095703125.2 |
$x^{12} - 5 x^{11} + 10 x^{10} + 28 x^{9} - 95 x^{8} + 45 x^{7} + 494 x^{6} - 95 x^{5} - 445 x^{4} + 1972 x^{3} + 4135 x^{2} + 2795 x + 671$ |
$12$ |
[0,6] |
$5^{9}\cdot 19^{4}\cdot 23^{4}$ |
$3$ |
$25.37394430342993$ |
$114.18099464895768$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
$[3]$ |
$10$ |
$5$ |
$5061.858110935322$ |
| 12.0.456488925854205933.2 |
$x^{12} - 7 x^{9} + 33 x^{6} - 45 x^{3} + 27$ |
$12$ |
[0,6] |
$3^{16}\cdot 13^{9}$ |
$2$ |
$29.622328050127763$ |
$65.49479091539757$ |
|
|
|
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$2$ |
$5$ |
$43888.17342090075$ |
| 12.12.155...000.1 |
$x^{12} - 90 x^{10} - 120 x^{9} + 3015 x^{8} + 8040 x^{7} - 39450 x^{6} - 178200 x^{5} + 17985 x^{4} + 1215280 x^{3} + 2504700 x^{2} + 2032800 x + 590480$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{12}\cdot 5^{11}\cdot 11^{4}$ |
$4$ |
$58.3451350475$ |
$215.78686932416204$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$2$ |
$11$ |
$7041584.90614$ |
| 12.12.137...000.1 |
$x^{12} - 78 x^{10} - 90 x^{9} + 2124 x^{8} + 4830 x^{7} - 20347 x^{6} - 73080 x^{5} + 2001 x^{4} + 213150 x^{3} + 151380 x^{2} - 100920 x - 67280$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{18}\cdot 5^{9}\cdot 29^{4}$ |
$4$ |
$84.7348467641$ |
$513.1615556142547$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$2$ |
$11$ |
$60617990.1421$ |
| 12.12.179...568.1 |
$x^{12} - 4 x^{11} - 114 x^{10} + 388 x^{9} + 4891 x^{8} - 13592 x^{7} - 100664 x^{6} + 210024 x^{5} + 1068015 x^{4} - 1422372 x^{3} - 5623062 x^{2} + 3341012 x + 11302711$ |
$12$ |
[12,0] |
$2^{35}\cdot 3^{6}\cdot 23^{4}\cdot 37^{6}$ |
$4$ |
$226.2428807829799$ |
$643.4046580852108$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
$[2]$ |
$2$ |
$11$ |
$45887579848.0333$ |
