| 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 |
| 16.2.145380128593826227.1 |
$x^{16} - x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 7 x^{11} + 5 x^{10} - 24 x^{9} + x^{8} + 35 x^{7} - 15 x^{6} - 42 x^{5} + 36 x^{4} + 23 x^{3} - 28 x^{2} + 6 x - 1$ |
$16$ |
(2, 7) |
$-\,283^{7}$ |
$1$ |
$11.8210639157$ |
$68.99852815152498$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
trivial |
$2$ |
$8$ |
$96.9580135951$ |
$2$ |
| 16.2.538...816.2 |
$x^{16} + 2 x^{14} - 4 x^{10} - x^{8} + 12 x^{6} - 14 x^{4} + 6 x^{2} - 1$ |
$16$ |
(2, 7) |
$-\,2^{36}\cdot 23^{8}$ |
$2$ |
$22.8129478795$ |
|
|
|
|
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
trivial |
$2$ |
$8$ |
$39478.2220757$ |
$2$ |
| 16.2.538...816.3 |
$x^{16} - 2 x^{14} + 4 x^{10} - x^{8} - 12 x^{6} - 14 x^{4} - 6 x^{2} - 1$ |
$16$ |
(2, 7) |
$-\,2^{36}\cdot 23^{8}$ |
$2$ |
$22.812947879511295$ |
|
|
|
|
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
trivial |
$2$ |
$8$ |
$27991.764000997155$ |
$2$ |
| 16.2.516...472.1 |
$x^{16} - 6 x^{14} + 33 x^{12} - 76 x^{10} + 90 x^{8} + 150 x^{6} - 828 x^{4} - 216 x^{2} - 27$ |
$16$ |
(2, 7) |
$-\,2^{24}\cdot 3^{15}\cdot 11^{8}$ |
$3$ |
$26.274987154219783$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2]$ |
$2$ |
$8$ |
$220561.73470157915$ |
$1$ |
| 16.0.127...953.1 |
$x^{16} - x^{15} + 3 x^{14} - 18 x^{13} - 9 x^{12} - 37 x^{11} + 113 x^{10} + 91 x^{9} + 365 x^{8} + 238 x^{7} + 801 x^{6} + 231 x^{5} + 793 x^{4} - 314 x^{3} + 562 x^{2} - 545 x + 164$ |
$16$ |
(0, 8) |
$2777^{7}$ |
$1$ |
$32.1043918392$ |
$382.54445375465184$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[9]$ |
$[9]$ |
$2$ |
$7$ |
$167279.883422$ |
$0$ |
| 16.0.127...953.2 |
$x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 22 x^{12} - 32 x^{11} + 67 x^{10} - 96 x^{9} + 131 x^{8} + 300 x^{7} - 567 x^{6} + 700 x^{5} - 736 x^{4} - 531 x^{3} + 1619 x^{2} - 2285 x + 1838$ |
$16$ |
(0, 8) |
$2777^{7}$ |
$1$ |
$32.1043918392$ |
$382.54445375465184$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[9]$ |
$[9]$ |
$2$ |
$7$ |
$136017.205956$ |
$0$ |
| 16.0.226...864.1 |
$x^{16} - 2 x^{15} + 10 x^{14} - 20 x^{13} + 34 x^{12} - 156 x^{11} - 20 x^{10} + 488 x^{9} + 1144 x^{8} + 2296 x^{7} - 280 x^{6} - 32 x^{5} + 384 x^{4} + 2136 x^{3} + 2824 x^{2} - 4144 x + 1960$ |
$16$ |
(0, 8) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.4280143385$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1404863.99526$ |
$0$ |
| 16.8.226...864.1 |
$x^{16} - 2 x^{15} - 20 x^{14} + 26 x^{13} + 168 x^{12} - 88 x^{11} - 954 x^{10} + 354 x^{9} + 3140 x^{8} - 3928 x^{7} + 1446 x^{6} + 7320 x^{5} - 22258 x^{4} + 12224 x^{3} + 13240 x^{2} - 10076 x - 658$ |
$16$ |
(8, 4) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.4280143385$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2]$ |
$2$ |
$11$ |
$27599165.1239$ |
$7$ |
| 16.4.226...864.2 |
$x^{16} - 6 x^{15} + 18 x^{14} - 48 x^{13} + 78 x^{12} + 104 x^{11} - 1044 x^{10} + 3168 x^{9} - 4684 x^{8} + 568 x^{7} + 13104 x^{6} - 32800 x^{5} + 44784 x^{4} - 38232 x^{3} + 19992 x^{2} - 3392 x - 1816$ |
$16$ |
(4, 6) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.4280143385$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$2964541.47936$ |
$4$ |
| 16.0.226...864.2 |
$x^{16} - 8 x^{15} + 38 x^{14} - 122 x^{13} + 294 x^{12} - 554 x^{11} + 972 x^{10} - 1434 x^{9} + 2414 x^{8} - 2720 x^{7} + 3986 x^{6} - 2768 x^{5} + 3578 x^{4} - 584 x^{3} + 1368 x^{2} + 648 x + 82$ |
$16$ |
(0, 8) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.4280143385$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1396585.91218$ |
$0$ |
| 16.4.226...864.3 |
$x^{16} - 6 x^{15} + 8 x^{14} + 20 x^{13} - 110 x^{12} + 174 x^{11} + 100 x^{10} - 512 x^{9} + 868 x^{8} + 230 x^{7} - 1572 x^{6} - 24 x^{5} + 498 x^{4} - 2574 x^{3} - 1040 x^{2} + 108 x + 395$ |
$16$ |
(4, 6) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.4280143385$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$2950341.45664$ |
$4$ |
| 16.4.226...864.6 |
$x^{16} - 6 x^{15} + 10 x^{14} + 6 x^{13} - 46 x^{12} + 98 x^{11} + 294 x^{10} + 28 x^{9} - 44 x^{8} + 482 x^{7} - 5000 x^{6} + 122 x^{5} + 4306 x^{4} + 3706 x^{3} - 276 x^{2} - 2368 x - 1255$ |
$16$ |
(4, 6) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.42801433846924$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$3226835.9701734046$ |
$4$ |
| 16.4.226...864.7 |
$x^{16} - 2 x^{15} - 2 x^{14} + 18 x^{13} - 46 x^{12} + 34 x^{11} + 106 x^{10} - 534 x^{9} + 564 x^{8} + 262 x^{7} - 1374 x^{6} + 2282 x^{5} - 1630 x^{4} + 754 x^{3} - 346 x^{2} - 126 x - 37$ |
$16$ |
(4, 6) |
$2^{24}\cdot 389^{7}$ |
$2$ |
$38.42801433846924$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2]$ |
$2$ |
$9$ |
$3711217.4783385145$ |
$3$ |
| 16.4.904...456.1 |
$x^{16} - 2 x^{15} - 22 x^{13} + 36 x^{12} - 26 x^{11} + 128 x^{10} - 230 x^{9} + 102 x^{8} - 278 x^{7} + 528 x^{6} - 514 x^{5} - 796 x^{4} - 238 x^{3} + 304 x^{2} + 350 x + 49$ |
$16$ |
(4, 6) |
$2^{26}\cdot 389^{7}$ |
$2$ |
$41.9060467871$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$4168611.87282$ |
$4$ |
| 16.8.904...456.1 |
$x^{16} - 2 x^{15} - 14 x^{14} + 34 x^{13} + 34 x^{12} - 188 x^{11} + 76 x^{10} + 116 x^{9} - 188 x^{8} + 426 x^{7} - 652 x^{6} + 434 x^{5} + 234 x^{4} - 524 x^{3} + 434 x^{2} - 188 x + 25$ |
$16$ |
(8, 4) |
$2^{26}\cdot 389^{7}$ |
$2$ |
$41.9060467871$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$16570294.3703$ |
$8$ |
| 16.4.904...456.2 |
$x^{16} - 6 x^{15} + 32 x^{14} - 132 x^{13} + 412 x^{12} - 900 x^{11} + 1184 x^{10} - 1196 x^{9} + 1596 x^{8} - 2684 x^{7} + 2872 x^{6} - 1392 x^{5} - 372 x^{4} + 456 x^{3} + 8 x^{2} + 16 x + 4$ |
$16$ |
(4, 6) |
$2^{26}\cdot 389^{7}$ |
$2$ |
$41.9060467871$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$5854631.85707$ |
$4$ |
| 16.8.904...456.4 |
$x^{16} - 2 x^{15} - 20 x^{14} - 2 x^{13} + 214 x^{12} + 420 x^{11} - 1058 x^{10} - 3884 x^{9} + 600 x^{8} + 12906 x^{7} + 9314 x^{6} - 11338 x^{5} - 12758 x^{4} + 3176 x^{3} + 5184 x^{2} - 272 x - 631$ |
$16$ |
(8, 4) |
$2^{26}\cdot 389^{7}$ |
$2$ |
$41.9060467870721$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$16139630.540766995$ |
$8$ |
| 16.8.334...192.1 |
$x^{16} - 4 x^{15} - 12 x^{14} - 10 x^{13} + 429 x^{12} - 270 x^{11} + 262 x^{10} - 6158 x^{9} - 35517 x^{8} + 84174 x^{7} + 219840 x^{6} - 105174 x^{5} - 1172115 x^{4} + 381168 x^{3} + 1533654 x^{2} - 411480 x - 40257$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{16}\cdot 173^{7}$ |
$3$ |
$80.874464551$ |
|
|
|
|
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$9831405234.4$ |
$6$ |
| 16.8.334...192.2 |
$x^{16} - 8 x^{14} - 486 x^{12} + 4144 x^{10} + 23023 x^{8} - 16776 x^{6} - 153194 x^{4} - 124112 x^{2} + 1557$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{16}\cdot 173^{7}$ |
$3$ |
$80.874464551$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$4959484238.44$ |
$6$ |
| 16.8.334...192.3 |
$x^{16} - 42 x^{14} + 137 x^{12} + 3752 x^{10} - 12606 x^{8} - 27446 x^{6} + 13912 x^{4} + 16416 x^{2} + 173$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{16}\cdot 173^{7}$ |
$3$ |
$80.8744645510216$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$4636491365.775628$ |
$6$ |
| 16.8.334...192.4 |
$x^{16} + 6 x^{14} - 217 x^{12} - 2228 x^{10} - 1347 x^{8} + 36404 x^{6} + 52051 x^{4} - 68994 x^{2} + 173$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{16}\cdot 173^{7}$ |
$3$ |
$80.8744645510216$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$4665595581.437905$ |
$6$ |
| 16.16.213...848.1 |
$x^{16} - 56 x^{14} + 1142 x^{12} - 10626 x^{10} + 46031 x^{8} - 89398 x^{6} + 76759 x^{4} - 26466 x^{2} + 2777$ |
$16$ |
(16, 0) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
$1081.9991094208717$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$78595180540.2$ |
$13$ |
| 16.0.213...848.1 |
$x^{16} + 56 x^{14} + 1142 x^{12} + 10626 x^{10} + 46031 x^{8} + 89398 x^{6} + 76759 x^{4} + 26466 x^{2} + 2777$ |
$16$ |
(0, 8) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
$1081.9991094208717$ |
✓ |
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2, 804]$ |
$[2, 804]$ |
$2$ |
$7$ |
$1177443.7333$ |
$0$ |
| 16.12.213...848.1 |
$x^{16} - 6 x^{15} - 26 x^{14} + 218 x^{13} + 189 x^{12} - 4880 x^{11} + 2 x^{10} + 78932 x^{9} + 19066 x^{8} - 662478 x^{7} - 272302 x^{6} + 2586552 x^{5} + 1183325 x^{4} - 4338242 x^{3} - 1977696 x^{2} + 2413344 x + 1300042$ |
$16$ |
(12, 2) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
$1081.9991094208717$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2, 4]$ |
$2$ |
$13$ |
$12710080147.1$ |
$10$ |
| 16.4.213...848.1 |
$x^{16} + 64 x^{14} + 998 x^{12} + 3694 x^{10} - 12797 x^{8} - 37650 x^{6} - 25053 x^{4} - 190 x^{2} + 2777$ |
$16$ |
(4, 6) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$2729919382.61$ |
$3$ |
| 16.8.213...848.1 |
$x^{16} + 16 x^{14} - 428 x^{12} - 1824 x^{10} + 17966 x^{8} + 22224 x^{6} - 62940 x^{4} + 16576 x^{2} + 2777$ |
$16$ |
(8, 4) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$6291105028.27$ |
$7$ |
| 16.8.213...848.2 |
$x^{16} - 16 x^{14} - 428 x^{12} + 1824 x^{10} + 17966 x^{8} - 22224 x^{6} - 62940 x^{4} - 16576 x^{2} + 2777$ |
$16$ |
(8, 4) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$12453085640.0$ |
$6$ |
| 16.12.213...848.2 |
$x^{16} - 46 x^{14} + 163 x^{12} + 3994 x^{10} - 29905 x^{8} + 47118 x^{6} + 32362 x^{4} - 31272 x^{2} + 2777$ |
$16$ |
(12, 2) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$26420670568.5$ |
$10$ |
| 16.0.213...848.2 |
$x^{16} - 4 x^{14} - 38 x^{13} + 163 x^{12} + 2904 x^{11} + 11016 x^{10} - 14346 x^{9} - 26204 x^{8} + 328526 x^{7} - 127400 x^{6} - 812470 x^{5} + 2172477 x^{4} - 1095064 x^{3} + 1738888 x^{2} - 846456 x + 682568$ |
$16$ |
(0, 8) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
✓ |
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2, 880]$ |
$[2, 880]$ |
$2$ |
$7$ |
$1177443.7333$ |
$0$ |
| 16.4.213...848.2 |
$x^{16} - 6 x^{15} - 14 x^{14} + 186 x^{13} - 951 x^{12} + 4000 x^{11} - 13558 x^{10} + 41228 x^{9} - 90086 x^{8} + 238146 x^{7} - 586206 x^{6} + 599580 x^{5} - 2327335 x^{4} + 2146782 x^{3} - 2500620 x^{2} + 6390268 x - 3549766$ |
$16$ |
(4, 6) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
$1081.9991094208717$ |
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2, 4]$ |
$2$ |
$9$ |
$2096543856.81$ |
$2$ |
| 16.16.213...848.2 |
$x^{16} - 92 x^{14} - 16 x^{13} + 2647 x^{12} - 342 x^{11} - 31052 x^{10} + 10374 x^{9} + 157346 x^{8} - 62988 x^{7} - 317096 x^{6} + 91478 x^{5} + 243709 x^{4} - 49184 x^{3} - 59172 x^{2} + 8816 x + 3364$ |
$16$ |
(16, 0) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327014$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$70152924710.2$ |
$13$ |
| 16.12.213...848.3 |
$x^{16} - 64 x^{14} + 998 x^{12} - 3694 x^{10} - 12797 x^{8} + 37650 x^{6} - 25053 x^{4} + 190 x^{2} + 2777$ |
$16$ |
(12, 2) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327013685$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$31532548839.535828$ |
$10$ |
| 16.4.213...848.3 |
$x^{16} + 46 x^{14} + 163 x^{12} - 3994 x^{10} - 29905 x^{8} - 47118 x^{6} + 32362 x^{4} + 31272 x^{2} + 2777$ |
$16$ |
(4, 6) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327013685$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$1968236113.7083936$ |
$3$ |
| 16.8.213...848.3 |
$x^{16} + 8 x^{14} - 550 x^{12} - 4938 x^{10} + 9563 x^{8} + 39746 x^{6} + 3471 x^{4} - 14506 x^{2} + 2777$ |
$16$ |
(8, 4) |
$2^{24}\cdot 2777^{7}$ |
$2$ |
$90.8049327013685$ |
|
|
|
? |
$C_2^7.\GL(2,3)$ (as 16T1691) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$11300290319.772436$ |
$6$ |
