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 |
21.3.396...527.1 |
$x^{21} - 5 x^{20} + 11 x^{19} - 20 x^{18} + 37 x^{17} - 68 x^{16} + 120 x^{15} - 168 x^{14} + 237 x^{13} - 331 x^{12} + 362 x^{11} - 431 x^{10} + 452 x^{9} - 381 x^{8} + 350 x^{7} - 238 x^{6} + 169 x^{5} - 90 x^{4} + 43 x^{3} + 6 x^{2} + 27$ |
$21$ |
[3,9] |
$-\,13^{2}\cdot 1801^{2}\cdot 193327^{3}$ |
$3$ |
$14.8362250548$ |
$359846.7897340511$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$11$ |
$6158.71427835$ |
21.3.930...607.1 |
$x^{21} - 5 x^{20} + 36 x^{18} - 35 x^{17} - 108 x^{16} + 155 x^{15} + 176 x^{14} - 338 x^{13} - 129 x^{12} + 413 x^{11} - 50 x^{10} - 234 x^{9} + 162 x^{8} - 66 x^{7} - 51 x^{6} + 196 x^{5} - 92 x^{4} - 98 x^{3} + 71 x^{2} - 10 x - 25$ |
$21$ |
[3,9] |
$-\,151^{2}\cdot 2377^{2}\cdot 193327^{3}$ |
$3$ |
$19.2412307236$ |
$2220668.2086930433$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$11$ |
$99654.8309357$ |
21.9.184...873.1 |
$x^{21} - 2 x^{20} - 2 x^{19} + 12 x^{18} - 25 x^{17} + x^{16} + 48 x^{15} - 91 x^{14} + 103 x^{13} - 12 x^{12} - 110 x^{11} + 272 x^{10} - 277 x^{9} - 78 x^{8} + 278 x^{7} - 46 x^{6} + 11 x^{5} - 114 x^{4} + 3 x^{3} + 93 x^{2} - 19 x - 23$ |
$21$ |
[9,6] |
$71^{3}\cdot 8623^{3}\cdot 283573^{2}$ |
$3$ |
$22.1821586762$ |
$3377289.469795227$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$1614740.57391$ |
21.9.778...553.1 |
$x^{21} - 8 x^{20} + 15 x^{19} + 42 x^{18} - 181 x^{17} + 43 x^{16} + 664 x^{15} - 785 x^{14} - 999 x^{13} + 2386 x^{12} - 12 x^{11} - 3337 x^{10} + 2186 x^{9} + 1818 x^{8} - 2845 x^{7} + 445 x^{6} + 1349 x^{5} - 754 x^{4} - 347 x^{3} + 279 x^{2} + 76 x + 1$ |
$21$ |
[9,6] |
$71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3}$ |
$4$ |
$23.7555403331$ |
$5456272.155977658$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$3400600.48543$ |
21.15.303...199.1 |
$x^{21} - 7 x^{20} + 4 x^{19} + 78 x^{18} - 172 x^{17} - 227 x^{16} + 1027 x^{15} - 237 x^{14} - 2424 x^{13} + 2147 x^{12} + 2451 x^{11} - 3882 x^{10} - 561 x^{9} + 3295 x^{8} - 1120 x^{7} - 1109 x^{6} + 907 x^{5} - 79 x^{4} - 154 x^{3} + 74 x^{2} - 14 x + 1$ |
$21$ |
[15,3] |
$-\,107^{3}\cdot 313^{2}\cdot 5023^{2}\cdot 21557^{3}$ |
$4$ |
$31.5601884029$ |
$20534827.556795347$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$17$ |
$239141569.892$ |
21.15.383...559.1 |
$x^{21} - 7 x^{20} + 4 x^{19} + 76 x^{18} - 158 x^{17} - 247 x^{16} + 951 x^{15} + 33 x^{14} - 2574 x^{13} + 1625 x^{12} + 3365 x^{11} - 4136 x^{10} - 1183 x^{9} + 3929 x^{8} - 1250 x^{7} - 1233 x^{6} + 995 x^{5} - 101 x^{4} - 152 x^{3} + 74 x^{2} - 14 x + 1$ |
$21$ |
[15,3] |
$-\,107^{3}\cdot 21557^{3}\cdot 1767079^{2}$ |
$3$ |
$31.9133777479$ |
$22198486.248570334$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$17$ |
$267663117.46$ |
21.21.840...873.1 |
$x^{21} - 8 x^{20} + 8 x^{19} + 94 x^{18} - 269 x^{17} - 195 x^{16} + 1577 x^{15} - 1066 x^{14} - 3297 x^{13} + 4973 x^{12} + 1604 x^{11} - 7061 x^{10} + 2541 x^{9} + 3722 x^{8} - 3133 x^{7} - 183 x^{6} + 1045 x^{5} - 344 x^{4} - 56 x^{3} + 58 x^{2} - 13 x + 1$ |
$21$ |
[21,0] |
$71^{3}\cdot 109^{2}\cdot 29437^{2}\cdot 283583^{3}$ |
$4$ |
$46.0330043159$ |
$97614867.21334988$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$20$ |
$54641615186.6$ |
21.21.123...257.1 |
$x^{21} - 6 x^{20} - 6 x^{19} + 102 x^{18} - 113 x^{17} - 557 x^{16} + 1235 x^{15} + 876 x^{14} - 4391 x^{13} + 1595 x^{12} + 6346 x^{11} - 6325 x^{10} - 2479 x^{9} + 6202 x^{8} - 1793 x^{7} - 1829 x^{6} + 1407 x^{5} - 158 x^{4} - 178 x^{3} + 84 x^{2} - 15 x + 1$ |
$21$ |
[21,0] |
$71^{3}\cdot 283583^{3}\cdot 3892951^{2}$ |
$3$ |
$46.8883990697$ |
$111042329.03007942$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$20$ |
$50400436611.9$ |