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 |
21.21.319...896.1 |
$x^{21} - 7 x^{20} - 13 x^{19} + 208 x^{18} - 267 x^{17} - 1890 x^{16} + 5310 x^{15} + 4781 x^{14} - 31996 x^{13} + 16294 x^{12} + 77939 x^{11} - 103109 x^{10} - 52599 x^{9} + 164304 x^{8} - 52267 x^{7} - 74030 x^{6} + 58226 x^{5} - 9947 x^{4} - 1399 x^{3} + 399 x^{2} - 10 x - 1$ |
$21$ |
[21,0] |
$2^{18}\cdot 73^{14}$ |
$2$ |
$31.6403260824$ |
$31.640326082417378$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$802783691.084$ |
21.21.289...944.1 |
$x^{21} - 7 x^{20} - 21 x^{19} + 238 x^{18} - 245 x^{17} - 1848 x^{16} + 4732 x^{15} + 1861 x^{14} - 18536 x^{13} + 16856 x^{12} + 14819 x^{11} - 32431 x^{10} + 8897 x^{9} + 16660 x^{8} - 13533 x^{7} + 392 x^{6} + 3514 x^{5} - 1547 x^{4} + 161 x^{3} + 49 x^{2} - 14 x + 1$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{32}$ |
$2$ |
$35.1393846905$ |
$35.13938469045169$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$3144548714.36$ |
21.21.866...889.1 |
$x^{21} - 6 x^{20} - 33 x^{19} + 233 x^{18} + 329 x^{17} - 3262 x^{16} - 1293 x^{15} + 23199 x^{14} + 2230 x^{13} - 94736 x^{12} - 9112 x^{11} + 230162 x^{10} + 58671 x^{9} - 317626 x^{8} - 158283 x^{7} + 200827 x^{6} + 166516 x^{5} - 10000 x^{4} - 42256 x^{3} - 13584 x^{2} - 1600 x - 64$ |
$21$ |
[21,0] |
$313^{14}$ |
$1$ |
$46.0995010635$ |
$46.09950106351405$ |
|
✓ |
|
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$97964797589.8$ |
21.21.988...136.1 |
$x^{21} - 7 x^{20} - 45 x^{19} + 362 x^{18} + 799 x^{17} - 7508 x^{16} - 7656 x^{15} + 79875 x^{14} + 49998 x^{13} - 459906 x^{12} - 252543 x^{11} + 1367403 x^{10} + 782753 x^{9} - 1809622 x^{8} - 897807 x^{7} + 1116746 x^{6} + 430780 x^{5} - 303555 x^{4} - 87913 x^{3} + 25235 x^{2} + 7546 x + 343$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{14}\cdot 11^{18}$ |
$3$ |
$51.7662500108$ |
$51.766250010785875$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$452833489306$ |
21.21.400...944.1 |
$x^{21} - 5 x^{20} - 63 x^{19} + 346 x^{18} + 1377 x^{17} - 8838 x^{16} - 12180 x^{15} + 107597 x^{14} + 26142 x^{13} - 675808 x^{12} + 238721 x^{11} + 2184149 x^{10} - 1549027 x^{9} - 3422708 x^{8} + 3271777 x^{7} + 2382104 x^{6} - 2931914 x^{5} - 581659 x^{4} + 1163183 x^{3} - 57751 x^{2} - 168018 x + 32573$ |
$21$ |
[21,0] |
$2^{18}\cdot 199^{14}$ |
$2$ |
$61.7439526498$ |
$61.743952649783516$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$1272666465930$ |
21.21.453...264.1 |
$x^{21} - 90 x^{19} - 54 x^{18} + 3180 x^{17} + 3024 x^{16} - 58772 x^{15} - 67734 x^{14} + 629568 x^{13} + 784368 x^{12} - 4069848 x^{11} - 5110992 x^{10} + 15949576 x^{9} + 19347408 x^{8} - 36320292 x^{7} - 42371712 x^{6} + 42009624 x^{5} + 50881608 x^{4} - 15240528 x^{3} - 26180496 x^{2} - 5843664 x - 190728$ |
$21$ |
[21,0] |
$2^{18}\cdot 3^{28}\cdot 31^{14}$ |
$3$ |
$77.3443355287$ |
$77.34433552870686$ |
|
✓ |
|
$C_7:C_3$ (as 21T2) |
$[3]$ |
$2$ |
$20$ |
$65890265440600$ |
21.21.131...944.1 |
$x^{21} - x^{20} - 85 x^{19} - 44 x^{18} + 2809 x^{17} + 5152 x^{16} - 41166 x^{15} - 131957 x^{14} + 189850 x^{13} + 1279532 x^{12} + 1063163 x^{11} - 3442335 x^{10} - 8884217 x^{9} - 7903686 x^{8} - 1827259 x^{7} + 1604980 x^{6} + 1042524 x^{5} + 68775 x^{4} - 81417 x^{3} - 15141 x^{2} + 1372 x + 343$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{14}\cdot 43^{14}$ |
$3$ |
$81.3585826825$ |
$81.35858268246776$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
$[3]$ |
$2$ |
$20$ |
$18989130461400$ |
21.21.562...216.1 |
$x^{21} - 105 x^{19} - 119 x^{18} + 4599 x^{17} + 10290 x^{16} - 103334 x^{15} - 360885 x^{14} + 1118670 x^{13} + 6432475 x^{12} - 1703289 x^{11} - 58140705 x^{10} - 81978176 x^{9} + 197166396 x^{8} + 700361361 x^{7} + 439003348 x^{6} - 1276860228 x^{5} - 3090183579 x^{4} - 3073057932 x^{3} - 1588530069 x^{2} - 391156857 x - 28779219$ |
$21$ |
[21,0] |
$2^{18}\cdot 3^{28}\cdot 7^{26}$ |
$3$ |
$87.1965380585$ |
$87.19653805851985$ |
|
✓ |
|
$C_7:C_3$ (as 21T2) |
$[3]$ |
$2$ |
$20$ |
$218203272125000$ |
21.21.159...009.1 |
$x^{21} - 9 x^{20} - 70 x^{19} + 768 x^{18} + 1466 x^{17} - 25320 x^{16} + 779 x^{15} + 409371 x^{14} - 412080 x^{13} - 3420406 x^{12} + 5652363 x^{11} + 14095477 x^{10} - 32356568 x^{9} - 22553276 x^{8} + 85473488 x^{7} - 10352270 x^{6} - 87722101 x^{5} + 49086315 x^{4} + 6245027 x^{3} - 3047523 x^{2} - 337401 x + 1593$ |
$21$ |
[21,0] |
$877^{14}$ |
$1$ |
$91.6219918212$ |
$91.62199182116717$ |
|
✓ |
|
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$199665489400000$ |
21.21.576...464.1 |
$x^{21} - 4 x^{20} - 127 x^{19} + 339 x^{18} + 6077 x^{17} - 8442 x^{16} - 135842 x^{15} + 57349 x^{14} + 1461398 x^{13} + 149067 x^{12} - 7801639 x^{11} - 2592179 x^{10} + 21127316 x^{9} + 8554392 x^{8} - 28090537 x^{7} - 10678784 x^{6} + 16344264 x^{5} + 4723953 x^{4} - 3302816 x^{3} - 671223 x^{2} + 33705 x + 189$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{14}\cdot 23^{18}$ |
$3$ |
$97.4136221104$ |
$97.41362211039652$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
trivial |
$2$ |
$20$ |
$434748805809000$ |
21.21.781...736.1 |
$x^{21} - 7 x^{20} - 85 x^{19} + 600 x^{18} + 2969 x^{17} - 20148 x^{16} - 58666 x^{15} + 340921 x^{14} + 762604 x^{13} - 3106176 x^{12} - 6541447 x^{11} + 14463151 x^{10} + 32672825 x^{9} - 27520996 x^{8} - 75363341 x^{7} + 12806508 x^{6} + 63845912 x^{5} - 2336541 x^{4} - 19620833 x^{3} + 1847525 x^{2} + 1883508 x - 325961$ |
$21$ |
[21,0] |
$2^{18}\cdot 13^{14}\cdot 31^{14}$ |
$3$ |
$98.8315806676$ |
$98.83158066757649$ |
|
✓ |
? |
$C_7:C_3$ (as 21T2) |
$[3]$ |
$2$ |
$20$ |
$107348023084000$ |