| 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 |
| 21.3.366...608.1 |
$x^{21} - 7 x^{19} - 42 x^{18} + 21 x^{17} + 364 x^{16} + 749 x^{15} - 454 x^{14} - 4781 x^{13} - 9016 x^{12} - 1813 x^{11} + 8106 x^{10} + 2471 x^{9} - 39956 x^{8} + 12367 x^{7} + 34118 x^{6} - 37072 x^{5} - 7392 x^{4} + 11424 x^{3} + 448 x^{2} - 1792 x - 512$ |
$21$ |
[3,9] |
$-\,2^{36}\cdot 7^{23}\cdot 11^{7}$ |
$3$ |
$61.4845337197$ |
$117.0742228154606$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$11$ |
$2390509249850$ |
| 21.3.609...656.1 |
$x^{21} - 7 x^{20} - 7 x^{19} + 175 x^{18} - 301 x^{17} - 1659 x^{16} + 7147 x^{15} - 2403 x^{14} - 36253 x^{13} + 42441 x^{12} + 180299 x^{11} - 484547 x^{10} - 15883 x^{9} + 1455531 x^{8} - 1731731 x^{7} - 623189 x^{6} + 3164084 x^{5} - 2658810 x^{4} - 245532 x^{3} + 1776908 x^{2} - 1293152 x + 262088$ |
$21$ |
[3,9] |
$-\,2^{33}\cdot 7^{23}\cdot 11^{10}$ |
$3$ |
$78.4389880814$ |
$117.0742228154606$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$11$ |
$51859841553800$ |
| 21.7.310...000.1 |
$x^{21} - 63 x^{19} - 84 x^{18} + 1512 x^{17} + 3850 x^{16} - 15029 x^{15} - 63668 x^{14} + 19355 x^{13} + 408198 x^{12} + 542696 x^{11} - 448728 x^{10} - 1801933 x^{9} - 2364768 x^{8} - 3841877 x^{7} - 7427812 x^{6} - 9136848 x^{5} - 5209666 x^{4} + 684425 x^{3} + 2417492 x^{2} + 819441 x - 32894$ |
$21$ |
[7,7] |
$-\,2^{20}\cdot 5^{7}\cdot 7^{35}$ |
$3$ |
$84.7582475598$ |
$129.90531209989487$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$13$ |
$84536711969500$ |
| 21.1.606...000.1 |
$x^{21} + 63 x^{19} - 56 x^{18} + 1610 x^{17} - 2520 x^{16} + 23121 x^{15} - 46272 x^{14} + 210994 x^{13} - 459704 x^{12} + 1276149 x^{11} - 2623516 x^{10} + 5090785 x^{9} - 8563100 x^{8} + 12268682 x^{7} - 15308580 x^{6} + 15211588 x^{5} - 11151728 x^{4} + 5522776 x^{3} - 1800400 x^{2} + 419328 x - 65792$ |
$21$ |
[1,10] |
$2^{14}\cdot 5^{10}\cdot 7^{35}$ |
$3$ |
$87.5036676122$ |
$129.90531209989487$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$10$ |
$16696091809800$ |
| 21.7.569...976.1 |
$x^{21} - 49 x^{19} - 98 x^{18} + 826 x^{17} + 2968 x^{16} - 7448 x^{15} - 44616 x^{14} + 22197 x^{13} + 371224 x^{12} + 210063 x^{11} - 1736602 x^{10} - 2769312 x^{9} + 3364144 x^{8} + 7470434 x^{7} - 27811420 x^{6} - 80806096 x^{5} + 4000752 x^{4} + 229127416 x^{3} + 240065168 x^{2} - 1757728 x - 66831808$ |
$21$ |
[7,7] |
$-\,2^{36}\cdot 3^{7}\cdot 7^{35}$ |
$3$ |
$121.223989536$ |
$201.24844413870787$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$13$ |
$23977211379700000$ |
| 21.1.192...544.1 |
$x^{21} - 14 x^{19} - 112 x^{18} - 336 x^{17} + 4564 x^{16} + 1708 x^{15} + 24636 x^{14} - 16562 x^{13} - 6692 x^{12} - 289520 x^{11} + 264516 x^{10} + 115752 x^{9} + 1883644 x^{8} - 889788 x^{7} - 3541916 x^{6} - 12439007 x^{5} + 416388 x^{4} + 19645038 x^{3} + 30658572 x^{2} + 19299672 x + 7270992$ |
$21$ |
[1,10] |
$2^{33}\cdot 3^{10}\cdot 7^{35}$ |
$3$ |
$128.453063676$ |
$201.24844413870787$ |
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[3]$ |
$2$ |
$10$ |
$27379099210300000$ |
