| 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 |
| 16.0.986...696.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 10 x^{13} + 23 x^{12} - 50 x^{11} + 52 x^{10} + 12 x^{9} + 102 x^{8} + 48 x^{7} + 190 x^{6} - 126 x^{5} - 161 x^{4} + 668 x^{3} + 664 x^{2} - 128 x + 608$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 13^{4}$ |
$4$ |
$27.3613535015$ |
$64.63622593542183$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$167392.814839$ |
| 16.0.986...696.2 |
$x^{16} - 2 x^{15} + 2 x^{14} - 18 x^{13} + 27 x^{12} - 34 x^{11} + 102 x^{10} - 122 x^{9} + 208 x^{8} - 206 x^{7} + 346 x^{6} - 306 x^{5} + 353 x^{4} - 242 x^{3} + 242 x^{2} - 128 x + 62$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 13^{4}$ |
$4$ |
$27.3613535015$ |
$64.63622593542183$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$167392.814839$ |
| 16.0.354...656.1 |
$x^{16} - 4 x^{14} - 16 x^{13} - 74 x^{12} + 180 x^{11} + 368 x^{10} - 364 x^{9} + 150 x^{8} - 408 x^{7} - 344 x^{6} - 1344 x^{5} + 3906 x^{4} + 1820 x^{3} + 2156 x^{2} - 196 x + 735$ |
$16$ |
[0,8] |
$2^{42}\cdot 7^{10}\cdot 13^{4}$ |
$3$ |
$39.5253615921$ |
$81.39057339987782$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$2973229.19903$ |
| 16.0.354...656.2 |
$x^{16} - 12 x^{14} + 98 x^{12} - 172 x^{11} - 156 x^{10} + 800 x^{9} + 6 x^{8} - 2432 x^{7} + 2236 x^{6} + 440 x^{5} - 1072 x^{4} + 280 x^{3} + 544 x^{2} + 168 x + 274$ |
$16$ |
[0,8] |
$2^{42}\cdot 7^{10}\cdot 13^{4}$ |
$3$ |
$39.5253615921$ |
$81.39057339987782$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$2973229.19903$ |
| 16.4.205...625.1 |
$x^{16} - 6 x^{14} - 21 x^{13} - 7 x^{12} + 373 x^{11} - 582 x^{10} - 109 x^{9} - 1178 x^{8} + 10930 x^{7} - 25366 x^{6} + 19300 x^{5} + 10005 x^{4} - 11956 x^{3} - 19910 x^{2} + 26387 x - 7692$ |
$16$ |
[4,6] |
$5^{4}\cdot 13^{10}\cdot 47^{8}$ |
$3$ |
$50.9337937377$ |
$84.75451298300825$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$42345641.4359$ |
| 16.4.205...625.2 |
$x^{16} - 4 x^{15} + 21 x^{14} + 3 x^{13} - 15 x^{12} + 95 x^{11} - 271 x^{10} + 233 x^{9} - 47 x^{8} - 1207 x^{7} + 517 x^{6} - 166 x^{5} - 3073 x^{4} + 6253 x^{3} - 10146 x^{2} + 8496 x - 2376$ |
$16$ |
[4,6] |
$5^{4}\cdot 13^{10}\cdot 47^{8}$ |
$3$ |
$50.9337937377$ |
$84.75451298300825$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$42345641.4359$ |
| 16.0.125...641.1 |
$x^{16} - 8 x^{15} + 19 x^{14} - 5 x^{13} + 2 x^{12} - 88 x^{11} - 268 x^{10} + 1282 x^{9} + 703 x^{8} - 5490 x^{7} + 4349 x^{6} + 3123 x^{5} + 5255 x^{4} - 4866 x^{3} - 3273 x^{2} + 4503 x + 2180$ |
$16$ |
[0,8] |
$7^{4}\cdot 19^{10}\cdot 31^{8}$ |
$3$ |
$57.0395850571$ |
$104.8895609566585$ |
|
|
|
$C_2^5:A_4$ (as 16T731) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$39206460.8793$ |
| 16.0.125...641.2 |
$x^{16} - 4 x^{15} + 22 x^{14} - 38 x^{13} + 163 x^{12} - 220 x^{11} + 845 x^{10} - 467 x^{9} + 2272 x^{8} - 24 x^{7} + 4512 x^{6} + 2011 x^{5} + 7184 x^{4} + 1337 x^{3} + 11362 x^{2} + 2128 x + 152$ |
$16$ |
[0,8] |
$7^{4}\cdot 19^{10}\cdot 31^{8}$ |
$3$ |
$57.0395850571$ |
$104.8895609566585$ |
|
|
|
$C_2^5:A_4$ (as 16T731) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$39206460.8793$ |
| 16.0.144...216.1 |
$x^{16} - 4 x^{15} + 6 x^{14} - 40 x^{13} + 67 x^{12} - 136 x^{11} + 1442 x^{10} - 1388 x^{9} - 4928 x^{8} + 4908 x^{7} + 13674 x^{6} - 4704 x^{5} - 9367 x^{4} + 9848 x^{3} + 26330 x^{2} + 9500 x + 4875$ |
$16$ |
[0,8] |
$2^{44}\cdot 31^{10}$ |
$2$ |
$57.53518935188849$ |
$78.94617922575179$ |
|
|
|
$C_2^5:A_4$ (as 16T731) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$21163657.980544407$ |
| 16.8.230...456.1 |
$x^{16} - 24 x^{14} - 16 x^{13} + 160 x^{12} + 1024 x^{11} - 4144 x^{10} + 544 x^{9} + 4024 x^{8} + 15872 x^{7} - 800 x^{6} - 67776 x^{5} + 60544 x^{4} + 26624 x^{3} - 55872 x^{2} + 23936 x - 3056$ |
$16$ |
[8,4] |
$2^{48}\cdot 31^{10}$ |
$2$ |
$68.4212565403$ |
$78.94617922575179$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$379788123.393$ |
| 16.8.230...456.2 |
$x^{16} - 8 x^{15} + 20 x^{14} - 56 x^{13} + 308 x^{12} - 992 x^{11} + 1720 x^{10} - 664 x^{9} + 6527 x^{8} - 23320 x^{7} - 20224 x^{6} + 88688 x^{5} + 13852 x^{4} - 106672 x^{3} - 1988 x^{2} + 42512 x - 1503$ |
$16$ |
[8,4] |
$2^{48}\cdot 31^{10}$ |
$2$ |
$68.4212565403$ |
$78.94617922575179$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$379788123.393$ |
| 16.4.440...000.1 |
$x^{16} + 10 x^{14} - 38 x^{13} - 29 x^{12} + 38 x^{11} - 476 x^{10} + 1528 x^{9} - 15114 x^{8} + 27802 x^{7} + 172402 x^{6} - 413268 x^{5} - 148189 x^{4} + 180204 x^{3} + 1541592 x^{2} - 1044576 x - 812916$ |
$16$ |
[4,6] |
$2^{24}\cdot 5^{8}\cdot 13^{10}\cdot 47^{4}$ |
$4$ |
$82.2752205852$ |
$239.72196346579366$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$9$ |
$578439519.726$ |
| 16.4.440...000.2 |
$x^{16} - 6 x^{15} + 30 x^{14} - 44 x^{13} + 30 x^{12} + 308 x^{11} - 1116 x^{10} + 2080 x^{9} - 6740 x^{8} + 8592 x^{7} - 15096 x^{6} + 12592 x^{5} - 10208 x^{4} + 4336 x^{3} + 32 x^{2} - 288 x + 16$ |
$16$ |
[4,6] |
$2^{24}\cdot 5^{8}\cdot 13^{10}\cdot 47^{4}$ |
$4$ |
$82.2752205852$ |
$239.72196346579366$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$9$ |
$578439519.726$ |
| 16.16.777...704.1 |
$x^{16} - 72 x^{14} - 48 x^{13} + 1532 x^{12} + 1188 x^{11} - 12571 x^{10} - 12304 x^{9} + 40011 x^{8} + 52796 x^{7} - 33882 x^{6} - 66332 x^{5} + 2440 x^{4} + 32512 x^{3} + 6624 x^{2} - 5528 x - 1812$ |
$16$ |
[16,0] |
$2^{24}\cdot 11^{8}\cdot 43^{10}$ |
$3$ |
$98.4371702869$ |
$193.63898753330463$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2, 2, 4]$ |
$2$ |
$15$ |
$84928941324.3$ |
| 16.16.777...704.2 |
$x^{16} - 61 x^{14} - 100 x^{13} + 1109 x^{12} + 3404 x^{11} - 4087 x^{10} - 26708 x^{9} - 19260 x^{8} + 51296 x^{7} + 85279 x^{6} + 7412 x^{5} - 54773 x^{4} - 22228 x^{3} + 9345 x^{2} + 4556 x + 203$ |
$16$ |
[16,0] |
$2^{24}\cdot 11^{8}\cdot 43^{10}$ |
$3$ |
$98.4371702869$ |
$193.63898753330463$ |
|
|
? |
$C_2^5:A_4$ (as 16T731) |
$[2]$ |
$[2, 2, 4]$ |
$2$ |
$15$ |
$84928941324.3$ |
| 16.0.108...241.1 |
$x^{16} - 2 x^{15} - 51 x^{14} - 367 x^{13} + 2435 x^{12} + 8924 x^{11} + 3123 x^{10} - 152375 x^{9} + 292480 x^{8} + 1235160 x^{7} + 131466 x^{6} - 1828656 x^{5} + 14098581 x^{4} + 10500354 x^{3} + 19727685 x^{2} + 7327503 x + 10697670$ |
$16$ |
[0,8] |
$3^{8}\cdot 53^{8}\cdot 61^{12}$ |
$3$ |
$275.23010665$ |
$387.6800248837557$ |
|
|
|
$C_2^5:A_4$ (as 16T731) |
$[2, 4, 4]$ |
$[2, 4, 4]$ |
$2$ |
$7$ |
$1539841823600$ |
| 16.0.108...241.2 |
$x^{16} - 2 x^{15} - 51 x^{14} + 371 x^{13} + 2027 x^{12} - 10534 x^{11} - 64806 x^{10} + 36860 x^{9} + 1048609 x^{8} + 1226340 x^{7} - 4550169 x^{6} - 11000769 x^{5} + 15502246 x^{4} + 73705032 x^{3} + 17634115 x^{2} - 77651959 x + 75128629$ |
$16$ |
[0,8] |
$3^{8}\cdot 53^{8}\cdot 61^{12}$ |
$3$ |
$275.23010665$ |
$387.6800248837557$ |
|
|
|
$C_2^5:A_4$ (as 16T731) |
$[2, 4, 4]$ |
$[2, 4, 4]$ |
$2$ |
$7$ |
$1539841823600$ |
