| 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 |
| 14.2.152...352.1 |
$x^{14} - 132$ |
$14$ |
[2,6] |
$2^{12}\cdot 3^{13}\cdot 7^{14}\cdot 11^{13}$ |
$4$ |
$325.966079449$ |
$410.9408534700397$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[21]$ |
$2$ |
$7$ |
$205124867932.8738$ |
| 14.2.130...704.1 |
$x^{14} - 288684$ |
$14$ |
[2,6] |
$2^{20}\cdot 3^{12}\cdot 7^{14}\cdot 11^{13}$ |
$4$ |
$447.826160283$ |
$564.5681440961255$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[21]$ |
$2$ |
$7$ |
$1237103268266.4392$ |
| 14.0.167...112.1 |
$x^{14} + 36951552$ |
$14$ |
[0,7] |
$-\,2^{27}\cdot 3^{12}\cdot 7^{14}\cdot 11^{13}$ |
$4$ |
$633.321829457$ |
$798.4199262645484$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[42]$ |
$2$ |
$6$ |
$3018334253596.328$ |
| 14.2.116...784.1 |
$x^{14} - 154 x^{12} + 8316 x^{10} - 251174 x^{8} + 1847384 x^{6} + 125641362 x^{4} - 1580335988 x^{2} - 27024383386$ |
$14$ |
[2,6] |
$2^{27}\cdot 3^{12}\cdot 7^{15}\cdot 11^{13}$ |
$4$ |
$727.7607065591901$ |
$798.4199262645484$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[42]$ |
$2$ |
$7$ |
$32173555967169.406$ |
| 14.0.319...328.1 |
$x^{14} - 500742 x^{7} + 80813044224$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 3^{12}\cdot 7^{14}\cdot 11^{13}\cdot 13^{7}$ |
$5$ |
$1086.58572593$ |
$1369.843347927244$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[2, 14, 210]$ |
$2$ |
$6$ |
$4251654694196.4424$ |
| 21.5.382...816.1 |
$x^{21} - 6 x^{20} - 32 x^{19} + 220 x^{18} - 71 x^{17} - 902 x^{16} + 5320 x^{15} - 32524 x^{14} + 54335 x^{13} + 52730 x^{12} - 451160 x^{11} + 2325392 x^{10} - 6659517 x^{9} + 11243466 x^{8} - 15644640 x^{7} + 4239088 x^{6} + 54407188 x^{5} - 141705136 x^{4} + 265754960 x^{3} - 413258960 x^{2} + 333108324 x - 162458072$ |
$21$ |
[5,8] |
$2^{36}\cdot 11^{19}\cdot 71^{7}$ |
$3$ |
$118.946034221$ |
$350.64554459156545$ |
|
|
|
$\PSL(3,4).C_2$ (as 21T85) |
trivial |
$2$ |
$12$ |
$2512137314520000$ |
| 21.1.559...000.1 |
$x^{21} - 660 x^{14} + 22192610 x^{7} + 133100000$ |
$21$ |
[1,10] |
$2^{33}\cdot 5^{19}\cdot 7^{21}\cdot 11^{19}$ |
$4$ |
$781.19424998$ |
$1387.7584075789991$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
| 21.1.123...168.1 |
$x^{21} - 814968 x^{14} + 216165139344 x^{7} - 2103437831970816$ |
$21$ |
[1,10] |
$2^{33}\cdot 3^{18}\cdot 7^{21}\cdot 11^{19}\cdot 13^{7}\cdot 29^{7}$ |
$6$ |
$3373.64305848$ |
$15502.510788689044$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
| 21.3.281...672.1 |
$x^{21} - 7 x^{20} - 973 x^{19} + 10787 x^{18} + 379421 x^{17} - 6163507 x^{16} - 65283267 x^{15} + 1772163547 x^{14} + 724282426 x^{13} - 274594499130 x^{12} + 1717423940624 x^{11} + 16979256988064 x^{10} - 237142301741940 x^{9} - 67722425026340 x^{8} + 17216475270041488 x^{7} - 113614134852063972 x^{6} + 61794351643866044 x^{5} + 2944808825056049252 x^{4} - 18315053480332654276 x^{3} + 70401309849385147724 x^{2} - 140518746032233545508 x + 225250264020821840164$ |
$21$ |
[3,9] |
$-\,2^{33}\cdot 3^{19}\cdot 7^{17}\cdot 11^{19}\cdot 19^{19}$ |
$5$ |
$4875.68039142$ |
$7625.510649732338$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$11$ |
|
| 21.1.106...272.1 |
$x^{21} - 7 x^{20} - 287 x^{19} + 217 x^{18} + 45647 x^{17} + 200263 x^{16} - 3562629 x^{15} - 36090861 x^{14} + 65413572 x^{13} + 2598847636 x^{12} + 10392408656 x^{11} - 66770308976 x^{10} - 761127721760 x^{9} - 1522762878112 x^{8} + 14927125793824 x^{7} + 116086483927680 x^{6} + 256562417172096 x^{5} - 970514714615040 x^{4} - 8380568286220032 x^{3} - 25844320743720192 x^{2} - 42235199862831360 x - 32112348692007168$ |
$21$ |
[1,10] |
$2^{26}\cdot 3^{19}\cdot 7^{21}\cdot 11^{19}\cdot 13^{7}\cdot 181^{7}$ |
$6$ |
$5194.80661094$ |
$29621.52561819821$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
| 21.1.147...248.1 |
$x^{21} - 7 x^{20} - 203 x^{19} + 3577 x^{18} + 4571 x^{17} - 504497 x^{16} + 3401223 x^{15} + 23857779 x^{14} - 435708840 x^{13} + 1190532028 x^{12} + 19675217744 x^{11} - 180093096848 x^{10} + 131433585472 x^{9} + 6334083644672 x^{8} - 37927992475328 x^{7} - 9875246516352 x^{6} + 1153537138204416 x^{5} - 4848630637165056 x^{4} - 165598058723328 x^{3} + 67288149908775936 x^{2} - 254693431382971392 x + 378173306864249856$ |
$21$ |
[1,10] |
$2^{33}\cdot 3^{19}\cdot 7^{21}\cdot 11^{19}\cdot 2381^{7}$ |
$5$ |
$6570.90526472$ |
$42139.672348053486$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
| 21.1.162...568.1 |
$x^{21} - 343 x^{19} - 1162 x^{18} + 50421 x^{17} + 341628 x^{16} - 3539039 x^{15} - 41773926 x^{14} + 59992415 x^{13} + 2617225520 x^{12} + 8927122659 x^{11} - 63601829382 x^{10} - 500020233713 x^{9} + 343600855164 x^{8} + 14413854343811 x^{7} + 58121867075622 x^{6} + 69534025707132 x^{5} - 474189524383064 x^{4} - 3007387918123568 x^{3} - 7993067522148464 x^{2} - 4353580806135904 x - 862855657735952$ |
$21$ |
[1,10] |
$2^{33}\cdot 7^{15}\cdot 11^{19}\cdot 13^{19}\cdot 239^{7}$ |
$5$ |
$6600.1504014$ |
$29880.55290223505$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
| 21.1.477...672.1 |
$x^{21} - 217 x^{19} - 2366 x^{18} + 20181 x^{17} + 440076 x^{16} + 1356439 x^{15} - 34100808 x^{14} - 339540985 x^{13} + 60041590 x^{12} + 22586633601 x^{11} + 134959190184 x^{10} - 246731376353 x^{9} - 7180157032902 x^{8} - 31305447146011 x^{7} + 65735000288916 x^{6} + 1298708257358232 x^{5} + 4533527410038662 x^{4} - 3560502436425872 x^{3} - 87526563039797182 x^{2} - 321470307054447124 x - 507583980506499514$ |
$21$ |
[1,10] |
$2^{18}\cdot 7^{40}\cdot 11^{19}\cdot 29^{7}\cdot 83^{7}$ |
$5$ |
$8651.81828165$ |
$38534.16451467704$ |
|
|
? |
$S_3\times F_7$ (as 21T15) |
not computed |
$2$ |
$10$ |
|
