| 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 |
Unit signature rank |
Max $p$ |
| 16.12.153...104.1 |
$x^{16} - 24 x^{14} - 16 x^{13} + 212 x^{12} + 264 x^{11} - 768 x^{10} - 1440 x^{9} + 714 x^{8} + 2672 x^{7} + 600 x^{6} - 1680 x^{5} - 828 x^{4} + 304 x^{3} + 216 x^{2} + 16 x - 2$ |
$16$ |
(12, 2) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.1238436786$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$13$ |
$1924241.55705$ |
$11$ |
$3$ |
| 16.8.810...016.4 |
$x^{16} - 8 x^{15} + 8 x^{14} + 48 x^{13} - 36 x^{12} - 88 x^{11} - 176 x^{10} + 64 x^{9} + 442 x^{8} + 192 x^{7} + 648 x^{6} - 368 x^{5} - 2556 x^{4} + 2448 x^{3} + 1192 x^{2} - 2336 x + 766$ |
$16$ |
(8, 4) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$17231940.423891354$ |
$6$ |
$23$ |
| 16.0.810...016.5 |
$x^{16} - 16 x^{13} + 56 x^{12} + 120 x^{11} + 456 x^{10} - 72 x^{9} - 276 x^{8} - 3232 x^{7} - 1920 x^{6} - 2496 x^{5} + 9936 x^{4} + 12952 x^{3} + 22872 x^{2} + 12184 x + 4393$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 30]$ |
$[2, 30]$ |
$2$ |
$7$ |
$45687.584564657765$ |
$0$ |
$23$ |
| 16.16.515...656.1 |
$x^{16} - 744 x^{14} + 205956 x^{12} - 26464968 x^{10} + 1632317382 x^{8} - 44854306200 x^{6} + 426672111492 x^{4} - 1327838774328 x^{2} + 301569017409$ |
$16$ |
(16, 0) |
$2^{58}\cdot 3^{10}\cdot 11^{10}\cdot 43^{8}$ |
$4$ |
$719.513877106$ |
$1324.6798063293725$ |
|
|
|
$C_2^6.(C_2\times D_4)$ (as 16T1143) |
$[2, 2, 4]$ |
$[2, 2, 2, 4, 4]$ |
$2$ |
$15$ |
$225315666778000000$ |
$13$ |
$43$ |
| 16.16.515...656.2 |
$x^{16} - 8 x^{15} - 808 x^{14} + 5432 x^{13} + 257160 x^{12} - 1508608 x^{11} - 41530872 x^{10} + 219388000 x^{9} + 3647178732 x^{8} - 17547819704 x^{7} - 173061975672 x^{6} + 742299743672 x^{5} + 4178139743672 x^{4} - 14747590543552 x^{3} - 45224122241960 x^{2} + 96367168970464 x + 202542606718753$ |
$16$ |
(16, 0) |
$2^{58}\cdot 3^{10}\cdot 11^{10}\cdot 43^{8}$ |
$4$ |
$719.513877106$ |
$1324.6798063293725$ |
|
|
? |
$C_2^6.(C_2\times D_4)$ (as 16T1143) |
$[2, 2, 4]$ |
$[2, 2, 2, 4, 4]$ |
$2$ |
$15$ |
$139846139231000000$ |
$13$ |
$43$ |
| 18.2.327...544.1 |
$x^{18} + 63 x^{16} + 1280 x^{14} + 5952 x^{12} - 101894 x^{10} - 1333706 x^{8} - 5720064 x^{6} - 9320640 x^{4} - 3409879 x^{2} - 441$ |
$18$ |
(2, 8) |
$2^{58}\cdot 31^{6}\cdot 71^{6}$ |
$3$ |
$121.392602557$ |
|
|
|
|
$C_2^8.F_9:C_2$ (as 18T692) |
trivial |
trivial |
$2$ |
$9$ |
$3337505864640$ |
$2$ |
$71$ |
| 18.2.262...352.1 |
$x^{18} + 40 x^{16} - 184 x^{14} - 19688 x^{12} - 282638 x^{10} - 1912696 x^{8} - 7060792 x^{6} - 14329000 x^{4} - 14621983 x^{2} - 5617952$ |
$18$ |
(2, 8) |
$2^{61}\cdot 31^{6}\cdot 71^{6}$ |
$3$ |
$136.258589316$ |
|
|
|
? |
$C_2^8.F_9:C_2$ (as 18T695) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$4662143947070$ |
$2$ |
$71$ |
| 20.0.600...096.1 |
$x^{20} - 10 x^{18} + 69 x^{16} - 160 x^{14} + 396 x^{12} - 664 x^{10} + 952 x^{8} - 784 x^{6} + 380 x^{4} + 296 x^{2} + 36$ |
$20$ |
(0, 10) |
$2^{58}\cdot 113^{6}$ |
$2$ |
$30.8255277343$ |
|
|
|
|
$C_2^9.S_6:C_2$ (as 20T952) |
trivial |
trivial |
$2$ |
$9$ |
$229273124.817$ |
$0$ |
$113$ |
| 20.0.192...072.1 |
$x^{20} + 7 x^{18} + 10 x^{16} + 120 x^{14} + 210 x^{12} + 270 x^{10} + 1100 x^{8} + 728 x^{6} + 193 x^{4} + 23 x^{2} + 2$ |
$20$ |
(0, 10) |
$2^{63}\cdot 113^{6}$ |
$2$ |
$36.6579369053$ |
|
|
|
|
$C_2^9.S_6:C_2$ (as 20T951) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$227962863.737$ |
$0$ |
$113$ |
| 20.0.192...072.2 |
$x^{20} - 6 x^{18} + 20 x^{16} - 40 x^{14} + 6 x^{12} + 236 x^{10} - 524 x^{8} - 72 x^{6} + 737 x^{4} + 298 x^{2} + 32$ |
$20$ |
(0, 10) |
$2^{63}\cdot 113^{6}$ |
$2$ |
$36.6579369053$ |
|
|
|
|
$C_2^9.S_6:C_2$ (as 20T951) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$98230094.892$ |
$0$ |
$113$ |
