| 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 |
| 27.27.605...129.1 |
$x^{27} - 81 x^{25} - 72 x^{24} + 2655 x^{23} + 4167 x^{22} - 45198 x^{21} - 97047 x^{20} + 426249 x^{19} + 1171662 x^{18} - 2179359 x^{17} - 7950852 x^{16} + 5114070 x^{15} + 31193568 x^{14} + 673551 x^{13} - 70126218 x^{12} - 30151557 x^{11} + 84666330 x^{10} + 61516056 x^{9} - 45234072 x^{8} - 47663262 x^{7} + 4603302 x^{6} + 12067416 x^{5} + 255483 x^{4} - 1327203 x^{3} + 10980 x^{2} + 61263 x - 6031$ |
$27$ |
[27,0] |
$3^{54}\cdot 19^{18}$ |
$2$ |
$64.08330623011794$ |
$75.41010411601474$ |
|
|
? |
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$7187451356185662.0$ |
| 27.27.982...001.2 |
$x^{27} - 108 x^{25} - 18 x^{24} + 4707 x^{23} + 2232 x^{22} - 109764 x^{21} - 98694 x^{20} + 1510614 x^{19} + 2133945 x^{18} - 12398832 x^{17} - 25485786 x^{16} + 55312935 x^{15} + 173500551 x^{14} - 76127436 x^{13} - 642791226 x^{12} - 369304542 x^{11} + 1056993705 x^{10} + 1580883287 x^{9} - 31929174 x^{8} - 1667662281 x^{7} - 1313738169 x^{6} + 13219668 x^{5} + 617819490 x^{4} + 433055058 x^{3} + 145257867 x^{2} + 25069374 x + 1788877$ |
$27$ |
[27,0] |
$3^{54}\cdot 37^{18}$ |
$2$ |
$99.93332221728107$ |
$117.59665155232963$ |
|
|
? |
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$2010098692253394700$ |
| 27.27.321...889.7 |
$x^{27} - 117 x^{25} - 36 x^{24} + 5238 x^{23} + 2178 x^{22} - 123963 x^{21} - 56187 x^{20} + 1744218 x^{19} + 807177 x^{18} - 15261696 x^{17} - 7048440 x^{16} + 83371158 x^{15} + 38009061 x^{14} - 276006213 x^{13} - 120997092 x^{12} + 519022485 x^{11} + 197629020 x^{10} - 508418818 x^{9} - 112614786 x^{8} + 263713383 x^{7} + 7742943 x^{6} - 65717838 x^{5} + 8944983 x^{4} + 5571624 x^{3} - 1547532 x^{2} + 95922 x - 521$ |
$27$ |
[27,0] |
$3^{66}\cdot 19^{18}$ |
$2$ |
$104.4236335758831$ |
$122.88063059438413$ |
|
|
|
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$16834279434518327000$ |
| 27.27.321...889.9 |
$x^{27} - 117 x^{25} - 9 x^{24} + 5238 x^{23} + 1575 x^{22} - 117456 x^{21} - 73008 x^{20} + 1464012 x^{19} + 1430826 x^{18} - 10397565 x^{17} - 14034969 x^{16} + 40387797 x^{15} + 72317313 x^{14} - 73318752 x^{13} - 190951476 x^{12} + 25704621 x^{11} + 238615434 x^{10} + 63425549 x^{9} - 142844067 x^{8} - 73622538 x^{7} + 35479035 x^{6} + 29346192 x^{5} - 167121 x^{4} - 3979842 x^{3} - 909036 x^{2} - 42237 x + 2843$ |
$27$ |
[27,0] |
$3^{66}\cdot 19^{18}$ |
$2$ |
$104.4236335758831$ |
$122.88063059438413$ |
|
|
? |
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$5146802035303820000$ |
| 27.27.521...441.4 |
$x^{27} - 153 x^{25} - 126 x^{24} + 9990 x^{23} + 15876 x^{22} - 358233 x^{21} - 833544 x^{20} + 7552062 x^{19} + 23609625 x^{18} - 91831401 x^{17} - 390602826 x^{16} + 545059116 x^{15} + 3816073161 x^{14} + 22287708 x^{13} - 21083544996 x^{12} - 19539617607 x^{11} + 57723169140 x^{10} + 103043855729 x^{9} - 45960476409 x^{8} - 206521848531 x^{7} - 78066883746 x^{6} + 147099542292 x^{5} + 133631033049 x^{4} - 937275522 x^{3} - 39901055706 x^{2} - 15677715069 x - 1817960563$ |
$27$ |
[27,0] |
$3^{66}\cdot 37^{18}$ |
$2$ |
$162.84117089348263$ |
$191.62353464341027$ |
|
|
? |
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$1803945263420875200000$ |
| 27.27.521...441.6 |
$x^{27} - 153 x^{25} - 153 x^{24} + 9990 x^{23} + 19656 x^{22} - 353499 x^{21} - 1052784 x^{20} + 7012764 x^{19} + 30074151 x^{18} - 67364946 x^{17} - 482652099 x^{16} - 7059159 x^{15} + 4092023583 x^{14} + 6238877085 x^{13} - 13064640816 x^{12} - 47304785295 x^{11} - 27890158797 x^{10} + 79694805080 x^{9} + 168579496998 x^{8} + 129292619823 x^{7} + 24834166434 x^{6} - 27537878124 x^{5} - 20976732495 x^{4} - 5709317640 x^{3} - 470467035 x^{2} + 51181209 x + 7086493$ |
$27$ |
[27,0] |
$3^{66}\cdot 37^{18}$ |
$2$ |
$162.84117089348263$ |
$191.62353464341027$ |
|
|
|
$C_3\wr C_3$ (as 27T19) |
trivial |
$2$ |
$26$ |
$6220276084571262000000$ |
