| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 21.3.287...408.1 |
$x^{21} - 3 x^{20} - 6 x^{19} + 10 x^{18} + 60 x^{17} - 15 x^{16} - 161 x^{15} - 318 x^{14} + 216 x^{13} + 899 x^{12} + 1398 x^{11} - 1833 x^{10} - 3947 x^{9} - 1857 x^{8} + 6708 x^{7} + 4309 x^{6} - 4260 x^{5} - 12447 x^{4} - 7163 x^{3} - 2730 x^{2} + 819 x + 279$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{6}$ |
$4$ |
$31.48208999031069$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
trivial |
trivial |
$2$ |
$11$ |
$62868196.45248938$ |
| 21.3.134...152.1 |
$x^{21} - 6 x^{20} + 15 x^{19} + 27 x^{18} - 303 x^{17} - 63 x^{16} + 3104 x^{15} - 1299 x^{14} - 22305 x^{13} + 5836 x^{12} + 128607 x^{11} + 66183 x^{10} - 469881 x^{9} - 549753 x^{8} + 859986 x^{7} + 2022197 x^{6} - 470280 x^{5} - 4074150 x^{4} - 3964116 x^{3} - 741048 x^{2} - 264204 x - 259212$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{24}\cdot 7^{7}\cdot 29^{12}$ |
$4$ |
$73.00009801119556$ |
|
|
|
|
$C_7^2:D_6$ (as 21T23) |
trivial |
trivial |
$2$ |
$11$ |
$2533394128009.0625$ |
| 21.3.171...968.1 |
$x^{21} - 6 x^{19} - 88 x^{18} + 39 x^{17} + 180 x^{16} + 2226 x^{15} - 3639 x^{14} + 525 x^{13} - 27802 x^{12} + 75852 x^{11} - 83598 x^{10} + 216851 x^{9} - 585924 x^{8} + 738249 x^{7} - 566225 x^{6} + 341556 x^{5} + 132618 x^{4} - 369807 x^{3} + 46656 x^{2} + 6636 x - 917$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{12}$ |
$4$ |
$82.3932351005181$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
trivial |
trivial |
$2$ |
$11$ |
$1342136518659.229$ |
| 21.3.170...552.1 |
$x^{21} - 9 x^{20} + 30 x^{19} - 199 x^{18} + 1092 x^{17} - 1755 x^{16} + 4451 x^{15} - 25701 x^{14} - 22737 x^{13} + 135768 x^{12} + 318663 x^{11} + 345774 x^{10} - 878835 x^{9} - 6057429 x^{8} - 14183334 x^{7} + 14847566 x^{6} + 61785606 x^{5} + 82913100 x^{4} + 48856772 x^{3} - 175571604 x^{2} - 47075184 x - 182586944$ |
$21$ |
(3, 9) |
$-\,2^{8}\cdot 3^{21}\cdot 7^{10}\cdot 11^{14}\cdot 29^{6}$ |
$5$ |
$127.73701873743101$ |
|
|
|
|
$C_7^3:C_3^2:D_6$ (as 21T82) |
trivial |
trivial |
$2$ |
$11$ |
$898219691494869.9$ |
| 21.3.101...728.1 |
$x^{21} - 3 x^{20} - 75 x^{19} + 18 x^{18} + 2550 x^{17} + 2268 x^{16} - 37881 x^{15} - 71979 x^{14} + 275952 x^{13} + 642992 x^{12} - 376269 x^{11} + 684714 x^{10} - 5272466 x^{9} - 35340678 x^{8} + 19353819 x^{7} + 139133726 x^{6} + 44938068 x^{5} - 303848790 x^{4} + 1014692 x^{3} + 60157839 x^{2} - 586686408 x - 868818657$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
|
$S_3\times D_7$ (as 21T8) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$14422580697878034$ |
| 21.3.101...728.2 |
$x^{21} - 9 x^{20} - 27 x^{19} + 341 x^{18} + 936 x^{17} - 8502 x^{16} - 24694 x^{15} + 151107 x^{14} + 489174 x^{13} - 2318013 x^{12} - 3671184 x^{11} + 9720984 x^{10} + 46144588 x^{9} - 29676336 x^{8} - 183614883 x^{7} - 551192359 x^{6} - 105424728 x^{5} + 62428278 x^{4} + 805420790 x^{3} - 155313876 x^{2} - 101077488 x - 28199601$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$8763119106525316.0$ |
| 21.3.101...728.3 |
$x^{21} - 174 x^{18} + 87 x^{17} + 2784 x^{16} + 14964 x^{15} - 6699 x^{14} - 330513 x^{13} - 618976 x^{12} + 1907388 x^{11} + 15107724 x^{10} + 12962333 x^{9} - 117158028 x^{8} - 272128257 x^{7} + 92312365 x^{6} + 1063848180 x^{5} + 1669524606 x^{4} + 1044605259 x^{3} + 31608144 x^{2} - 110628504 x + 13828563$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$6505962221998820.0$ |
| 21.3.101...728.4 |
$x^{21} - 3 x^{20} - 33 x^{19} + 92 x^{18} + 2526 x^{17} + 11403 x^{16} - 58980 x^{15} - 546234 x^{14} - 114045 x^{13} + 15340470 x^{12} + 21607908 x^{11} - 264670614 x^{10} - 213258450 x^{9} + 1969037874 x^{8} + 1883149065 x^{7} - 7708919702 x^{6} - 6117904524 x^{5} + 6653872905 x^{4} + 5671508995 x^{3} + 10106386557 x^{2} + 465351837 x + 353146803$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$7636639207361091.0$ |
| 21.3.101...728.5 |
$x^{21} - 174 x^{18} + 174 x^{17} - 522 x^{16} + 13311 x^{15} - 26883 x^{14} - 487780 x^{12} - 363312 x^{11} + 4662504 x^{10} - 1602105 x^{9} + 47437446 x^{8} - 148228773 x^{7} + 111847954 x^{6} - 816690054 x^{5} + 1379344284 x^{4} - 1541214077 x^{3} + 4228833099 x^{2} - 5216733933 x + 2421998423$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
? |
$C_7^3:D_6$ (as 21T37) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$4889700521205931.0$ |
| 21.3.101...728.6 |
$x^{21} - 6 x^{20} + 90 x^{19} - 4 x^{18} + 945 x^{17} + 9240 x^{16} + 688 x^{15} + 124320 x^{14} - 899385 x^{13} - 138774 x^{12} + 14321466 x^{11} - 41404908 x^{10} - 83631921 x^{9} + 258284556 x^{8} + 642697968 x^{7} - 370879024 x^{6} - 31727542848 x^{5} - 107343299664 x^{4} - 252801298380 x^{3} - 229594109448 x^{2} - 294148045392 x + 156767332912$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 29^{18}$ |
$4$ |
$215.63514977622526$ |
|
|
|
|
$C_7^2:D_6$ (as 21T23) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$738366451048665100$ |
| 21.3.218...368.1 |
$x^{21} - 24 x^{19} - 14 x^{18} - 3084 x^{17} - 56784 x^{16} - 503796 x^{15} - 3520848 x^{14} - 22938600 x^{13} - 145278408 x^{12} - 865798224 x^{11} - 4515165216 x^{10} - 19297709104 x^{9} - 54651878976 x^{8} + 37264166880 x^{7} + 1511902686560 x^{6} + 9619188568512 x^{5} + 35979580335168 x^{4} + 83800780183488 x^{3} + 119536414109568 x^{2} + 111180142596096 x + 57833371300608$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 11^{8}\cdot 29^{18}$ |
$5$ |
$537.5768742043803$ |
|
|
|
? |
$C_7^3:C_3^2:D_6$ (as 21T82) |
$[7]$ |
$[7]$ |
$2$ |
$11$ |
$201657442127625650000$ |
| 21.3.386...448.1 |
$x^{21} - 132 x^{19} - 1264 x^{18} + 15285 x^{17} + 306498 x^{16} + 1724169 x^{15} + 17632854 x^{14} + 194395803 x^{13} + 904165436 x^{12} - 7110430428 x^{11} - 40109446740 x^{10} + 813372660322 x^{9} + 4583695583820 x^{8} - 12839910577851 x^{7} - 83196487657120 x^{6} + 35205316248351 x^{5} + 339896682248592 x^{4} + 577123926068385 x^{3} + 942453063154974 x^{2} - 600376794302430 x - 3983694435282250$ |
$21$ |
(3, 9) |
$-\,2^{14}\cdot 3^{21}\cdot 7^{10}\cdot 11^{14}\cdot 29^{18}$ |
$5$ |
$1066.5503066312406$ |
|
|
|
? |
$C_7^3:C_3^2:D_6$ (as 21T82) |
not computed |
not computed |
$2$ |
$11$ |
|
