| 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 |
| 12.0.10312216477696.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 34 x^{8} - 48 x^{7} + 60 x^{6} - 64 x^{5} + 57 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2$ |
$12$ |
[0,6] |
$2^{32}\cdot 7^{4}$ |
$2$ |
$12.1463558875$ |
$29.27444568018377$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$8$ |
$5$ |
$347.441365493$ |
| 12.0.151336128515625.1 |
$x^{12} + 6 x^{10} - 9 x^{8} - 15 x^{7} - 43 x^{6} - 45 x^{5} + 24 x^{4} + 105 x^{3} + 126 x^{2} + 75 x + 19$ |
$12$ |
[0,6] |
$3^{18}\cdot 5^{8}$ |
$2$ |
$15.1936418545$ |
$25.058196097836525$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$532.947775068$ |
| 12.0.1283918464548864.13 |
$x^{12} - 6 x^{10} - 16 x^{9} + 12 x^{8} + 72 x^{7} + 140 x^{6} + 144 x^{5} + 183 x^{4} + 160 x^{3} + 78 x^{2} + 24 x + 4$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{14}$ |
$2$ |
$18.1570289931$ |
$30.93861708477606$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$2165.70843902$ |
| 12.0.1283918464548864.28 |
$x^{12} - 6 x^{10} - 8 x^{9} + 27 x^{8} + 36 x^{7} - 46 x^{6} - 108 x^{5} + 57 x^{4} + 140 x^{3} + 180 x^{2} - 48 x + 16$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{14}$ |
$2$ |
$18.1570289931$ |
$30.93861708477606$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$2311.10790059$ |
| 12.4.1499238400000000.1 |
$x^{12} - 2 x^{11} - 5 x^{10} + 4 x^{9} + 10 x^{7} + 48 x^{6} + 10 x^{5} + 4 x^{3} - 5 x^{2} - 2 x + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{8}\cdot 11^{4}$ |
$3$ |
$18.3931406324$ |
$46.77720696848431$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$1008.242413$ |
| 12.0.1547476985184256.2 |
$x^{12} - 4 x^{11} + 2 x^{10} + 16 x^{9} - 8 x^{8} - 52 x^{7} + 30 x^{6} + 80 x^{5} - 19 x^{4} - 64 x^{3} + 16 x^{2} + 48 x + 18$ |
$12$ |
[0,6] |
$2^{28}\cdot 7^{8}$ |
$2$ |
$18.4417451682$ |
$34.04715710793443$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[2]$ |
$2$ |
$5$ |
$2306.07563632$ |
| 12.0.2282521714753536.28 |
$x^{12} - 12 x^{10} + 18 x^{8} + 132 x^{6} + 129 x^{4} + 72 x^{2} + 16$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{12}$ |
$2$ |
$19.0488126236$ |
$36.79242356556043$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$8$ |
$5$ |
$6698.2439767$ |
| 12.0.2282521714753536.29 |
$x^{12} - 12 x^{10} + 54 x^{8} - 84 x^{6} - 63 x^{4} + 216 x^{2} + 16$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{12}$ |
$2$ |
$19.0488126236$ |
$36.79242356556043$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$8$ |
$5$ |
$6974.46025421$ |
| 12.4.7517605812240384.1 |
$x^{12} + 2 x^{10} - 4 x^{9} + 26 x^{8} + 24 x^{7} - 68 x^{6} + 128 x^{5} + 49 x^{4} - 80 x^{3} + 14 x^{2} + 4 x - 2$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$21.038105524$ |
$50.704827281493536$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$5434.84409481$ |
| 12.4.7652750400000000.1 |
$x^{12} + 3 x^{10} - 6 x^{9} - 12 x^{8} - 24 x^{7} + 20 x^{6} + 24 x^{5} - 12 x^{4} + 6 x^{3} + 3 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 3^{14}\cdot 5^{8}$ |
$3$ |
$21.069365756459888$ |
$30.755720695068224$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$1889.93528743175$ |
| 12.4.20542695432781824.4 |
$x^{12} - 6 x^{10} - 16 x^{9} - 33 x^{8} - 48 x^{7} - 64 x^{6} - 72 x^{5} - 132 x^{4} - 176 x^{3} - 96 x^{2} - 24 x - 2$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{14}$ |
$2$ |
$22.8764230319$ |
$36.79242356556043$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$9373.45565107$ |
| 12.4.20542695432781824.14 |
$x^{12} - 15 x^{8} - 48 x^{7} - 124 x^{6} - 264 x^{5} - 492 x^{4} - 624 x^{3} - 504 x^{2} - 240 x + 4$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{14}$ |
$2$ |
$22.8764230319$ |
$36.79242356556043$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$10910.4465923$ |
| 12.4.24759631762948096.1 |
$x^{12} - 10 x^{10} - 4 x^{9} + 24 x^{8} + 40 x^{7} - 48 x^{6} + 86 x^{4} - 64 x^{3} - 36 x^{2} + 88 x - 124$ |
$12$ |
[4,4] |
$2^{32}\cdot 7^{8}$ |
$2$ |
$23.2351429343$ |
$40.48912147837109$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$12903.1672214$ |
| 12.0.24759631762948096.4 |
$x^{12} - 4 x^{11} + 16 x^{10} - 64 x^{9} + 192 x^{8} - 424 x^{7} + 724 x^{6} - 984 x^{5} + 1121 x^{4} - 996 x^{3} + 556 x^{2} - 112 x + 8$ |
$12$ |
[0,6] |
$2^{32}\cdot 7^{8}$ |
$2$ |
$23.2351429343$ |
$29.27444568018377$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
$[3]$ |
$8$ |
$5$ |
$8241.18398569$ |
| 12.0.27354472316015625.1 |
$x^{12} - 6 x^{11} + 15 x^{10} - 17 x^{9} - 15 x^{8} + 150 x^{7} - 423 x^{6} + 600 x^{5} - 240 x^{4} - 1088 x^{3} + 3840 x^{2} - 6144 x + 4096$ |
$12$ |
[0,6] |
$3^{14}\cdot 5^{8}\cdot 11^{4}$ |
$3$ |
$23.4289249816$ |
$76.06024196897057$ |
✓ |
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[2]$ |
$6$ |
$5$ |
$3486.97473965$ |
| 12.0.54761930656579584.1 |
$x^{12} - 6 x^{11} + 37 x^{10} - 130 x^{9} + 422 x^{8} - 974 x^{7} + 2005 x^{6} - 3086 x^{5} + 4080 x^{4} - 3926 x^{3} + 2963 x^{2} - 1386 x + 271$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{6}\cdot 23^{4}$ |
$3$ |
$24.8240838342$ |
$94.23487803090926$ |
✓ |
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$8179.2553173$ |
| 12.0.75826372274028544.5 |
$x^{12} - 2 x^{11} + 5 x^{10} - 12 x^{9} + 71 x^{8} - 238 x^{7} + 533 x^{6} - 728 x^{5} + 568 x^{4} - 100 x^{3} - 142 x^{2} + 16 x + 92$ |
$12$ |
[0,6] |
$2^{28}\cdot 7^{10}$ |
$2$ |
$25.5065482212$ |
$34.04715710793443$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[6]$ |
$2$ |
$5$ |
$7500.15081555$ |
| 12.0.103...984.57 |
$x^{12} - 6 x^{10} + 45 x^{8} - 108 x^{7} + 126 x^{6} - 108 x^{5} + 153 x^{4} - 324 x^{3} + 540 x^{2} - 432 x + 144$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{18}$ |
$2$ |
$26.1869672633$ |
$50.414421537552215$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$10245.7701643$ |
| 12.0.103...984.67 |
$x^{12} - 6 x^{10} - 24 x^{9} + 27 x^{8} + 108 x^{7} + 146 x^{6} - 324 x^{5} - 519 x^{4} - 348 x^{3} + 1044 x^{2} + 1008 x + 784$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{18}$ |
$2$ |
$26.1869672633$ |
$50.414421537552215$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$6$ |
$5$ |
$27183.6371846$ |
| 12.0.184...416.34 |
$x^{12} - 12 x^{10} - 8 x^{9} + 72 x^{8} + 48 x^{7} - 84 x^{6} - 144 x^{5} - 15 x^{4} + 184 x^{3} + 216 x^{2} + 96 x + 32$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{16}$ |
$2$ |
$27.4731418213$ |
$56.40343465948361$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$8$ |
$5$ |
$68806.2056404$ |
| 12.0.184...416.47 |
$x^{12} - 12 x^{10} + 54 x^{8} - 20 x^{6} - 447 x^{4} + 792 x^{2} + 784$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{16}$ |
$2$ |
$27.4731418213$ |
$56.40343465948361$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$8$ |
$5$ |
$43982.1515604$ |
| 12.0.316030794822142569.2 |
$x^{12} + 21 x^{10} + 129 x^{8} + 303 x^{6} + 279 x^{4} + 90 x^{2} + 9$ |
$12$ |
[0,6] |
$3^{18}\cdot 13^{8}$ |
$2$ |
$28.72835664269688$ |
$65.49479091539757$ |
✓ |
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[6]$ |
$6$ |
$5$ |
$8916.15372658708$ |
| 12.12.876...344.1 |
$x^{12} - 22 x^{10} + 149 x^{8} - 392 x^{6} + 448 x^{4} - 216 x^{2} + 36$ |
$12$ |
[12,0] |
$2^{32}\cdot 3^{6}\cdot 23^{4}$ |
$3$ |
$31.2763857671$ |
$112.0647874357709$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$11$ |
$339092.308261$ |
| 12.4.121...704.5 |
$x^{12} - 4 x^{11} + 36 x^{9} - 151 x^{8} + 336 x^{7} - 328 x^{6} - 224 x^{5} + 1209 x^{4} - 2036 x^{3} + 1736 x^{2} - 716 x + 113$ |
$12$ |
[4,4] |
$2^{32}\cdot 7^{10}$ |
$2$ |
$32.136237014$ |
$40.48912147837109$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
$[3]$ |
$2$ |
$7$ |
$34953.0989159$ |
| 12.4.166...744.1 |
$x^{12} - 16 x^{9} - 36 x^{8} + 72 x^{7} - 48 x^{6} - 144 x^{5} + 81 x^{4} + 248 x^{3} + 1152 x^{2} + 576 x - 1472$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{18}$ |
$2$ |
$32.993511288$ |
$59.95318879120351$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$118515.791219$ |
| 12.4.166...744.79 |
$x^{12} - 12 x^{10} + 18 x^{8} + 36 x^{6} - 63 x^{4} - 216 x^{2} + 144$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{18}$ |
$2$ |
$32.993511288$ |
$59.95318879120351$ |
|
|
? |
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$7$ |
$123374.030653$ |
| 12.0.753...625.1 |
$x^{12} - 5 x^{11} + 24 x^{10} - 54 x^{9} + 147 x^{8} - 417 x^{7} + 1277 x^{6} - 1864 x^{5} + 4043 x^{4} - 3640 x^{3} + 5052 x^{2} - 2144 x + 2096$ |
$12$ |
[0,6] |
$5^{8}\cdot 19^{4}\cdot 23^{6}$ |
$3$ |
$37.41925367041402$ |
$114.18099464895768$ |
✓ |
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[9]$ |
$2$ |
$5$ |
$5327.464177374278$ |
| 12.12.234...000.1 |
$x^{12} - 6 x^{11} - 15 x^{10} + 124 x^{9} + 73 x^{8} - 946 x^{7} - 185 x^{6} + 3170 x^{5} + 502 x^{4} - 4122 x^{3} - 554 x^{2} + 1352 x - 169$ |
$12$ |
[12,0] |
$2^{18}\cdot 3^{4}\cdot 5^{8}\cdot 41^{4}$ |
$4$ |
$41.1301253923$ |
$194.77013349422438$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$11$ |
$950637.357809$ |
| 12.0.432...384.1 |
$x^{12} + 12 x^{10} - 6 x^{9} + 108 x^{8} - 54 x^{7} + 437 x^{6} - 324 x^{5} + 1326 x^{4} - 636 x^{3} + 396 x^{2} + 36 x + 4$ |
$12$ |
[0,6] |
$2^{4}\cdot 3^{18}\cdot 17^{8}$ |
$3$ |
$43.283711622$ |
$99.59686195719284$ |
✓ |
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
$[11]$ |
$6$ |
$5$ |
$64963.27378587159$ |
| 12.12.798...000.1 |
$x^{12} - 5 x^{11} - 27 x^{10} + 154 x^{9} + 173 x^{8} - 1579 x^{7} + 620 x^{6} + 5919 x^{5} - 7507 x^{4} - 4264 x^{3} + 13243 x^{2} - 8405 x + 1681$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{8}\cdot 41^{8}$ |
$3$ |
$55.18942946790709$ |
$98.3443829914461$ |
|
|
|
$C_2\times C_3^2:C_4$ (as 12T40) |
trivial |
$2$ |
$11$ |
$8782047.5467148$ |
