| 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 $p$ |
| 16.12.791...584.1 |
$x^{16} - 12 x^{14} + 52 x^{12} - 96 x^{10} + 63 x^{8} + 4 x^{4} - 12 x^{2} + 1$ |
$16$ |
(12, 2) |
$2^{48}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$26.9865214329$ |
$87.45705441086021$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$13$ |
$955677.748689$ |
$11$ |
$23$ |
| 16.0.791...584.1 |
$x^{16} + 12 x^{14} + 52 x^{12} + 96 x^{10} + 63 x^{8} + 4 x^{4} + 12 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$26.9865214329$ |
$87.45705441086021$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$26081.4796809$ |
$0$ |
$23$ |
| 16.4.791...584.1 |
$x^{16} + 4 x^{14} + 4 x^{12} - 20 x^{10} - 71 x^{8} - 80 x^{6} + 64 x^{4} + 256 x^{2} + 256$ |
$16$ |
(4, 6) |
$2^{48}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$26.9865214329$ |
$87.45705441086021$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$9$ |
$581374.39206$ |
$3$ |
$23$ |
| 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 |
$[2]$ |
$2$ |
$13$ |
$1924241.55705$ |
$11$ |
$3$ |
| 16.0.153...104.1 |
$x^{16} - 8 x^{13} - 4 x^{12} + 24 x^{11} + 96 x^{10} - 336 x^{9} + 612 x^{8} - 1376 x^{7} + 2856 x^{6} - 3624 x^{5} + 2988 x^{4} - 1816 x^{3} + 1128 x^{2} - 16 x + 337$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.1238436786$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$41062.2575942$ |
$0$ |
$3$ |
| 16.4.153...104.2 |
$x^{16} - 8 x^{14} - 8 x^{13} + 16 x^{12} + 24 x^{11} - 80 x^{10} - 336 x^{9} - 314 x^{8} + 944 x^{7} + 3520 x^{6} + 5776 x^{5} + 6164 x^{4} + 4864 x^{3} + 2728 x^{2} + 1264 x + 478$ |
$16$ |
(4, 6) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.1238436786$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$9$ |
$283940.790469$ |
$3$ |
$3$ |
| 16.12.153...104.3 |
$x^{16} - 16 x^{14} - 8 x^{13} + 68 x^{12} + 24 x^{11} - 208 x^{10} - 336 x^{9} - 44 x^{8} + 864 x^{7} + 1336 x^{6} + 344 x^{5} - 732 x^{4} - 664 x^{3} - 200 x^{2} - 16 x + 1$ |
$16$ |
(12, 2) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$13$ |
$1925513.952814602$ |
$11$ |
$3$ |
| 16.4.153...104.11 |
$x^{16} - 16 x^{14} - 16 x^{13} + 104 x^{12} + 216 x^{11} - 184 x^{10} - 984 x^{9} - 1028 x^{8} - 96 x^{7} + 544 x^{6} + 640 x^{5} + 672 x^{4} + 376 x^{3} - 8 x^{2} - 56 x - 23$ |
$16$ |
(4, 6) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$9$ |
$435269.3871581764$ |
$3$ |
$3$ |
| 16.0.153...104.96 |
$x^{16} + 8 x^{14} - 8 x^{13} + 8 x^{12} + 24 x^{11} + 32 x^{10} - 336 x^{9} + 862 x^{8} - 1296 x^{7} + 1504 x^{6} - 1840 x^{5} + 2340 x^{4} - 2368 x^{3} + 1576 x^{2} - 592 x + 94$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$58311.88908906106$ |
$0$ |
$3$ |
| 16.0.153...104.97 |
$x^{16} + 8 x^{14} - 16 x^{13} + 44 x^{12} - 120 x^{11} + 272 x^{10} - 480 x^{9} + 898 x^{8} - 720 x^{7} + 88 x^{6} + 112 x^{5} - 60 x^{4} + 112 x^{3} + 184 x^{2} - 176 x + 94$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$51122.0008617326$ |
$0$ |
$3$ |
| 16.0.153...104.142 |
$x^{16} + 16 x^{14} - 16 x^{13} + 112 x^{12} - 168 x^{11} + 520 x^{10} - 792 x^{9} + 1468 x^{8} - 1952 x^{7} + 2272 x^{6} - 1984 x^{5} + 1352 x^{4} - 1288 x^{3} + 1720 x^{2} - 1336 x + 409$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$47326.53557770333$ |
$0$ |
$3$ |
| 16.0.140...064.1 |
$x^{16} + 12 x^{14} + 24 x^{12} - 36 x^{10} + 189 x^{8} + 648 x^{6} - 540 x^{4} + 324$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$32.3055690086$ |
$179.60432689710672$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$275151.857337$ |
$0$ |
$97$ |
| 16.8.140...064.1 |
$x^{16} - 12 x^{14} - 12 x^{12} + 144 x^{10} + 351 x^{8} - 2592 x^{6} + 7236 x^{4} - 3564 x^{2} + 81$ |
$16$ |
(8, 4) |
$2^{48}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$32.3055690086$ |
$179.60432689710672$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1847252.6064$ |
$7$ |
$97$ |
| 16.0.140...064.2 |
$x^{16} + 12 x^{14} - 12 x^{12} - 144 x^{10} + 351 x^{8} + 2592 x^{6} + 7236 x^{4} + 3564 x^{2} + 81$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$32.3055690086$ |
$179.60432689710672$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$84259.0044281$ |
$0$ |
$97$ |
| 16.8.140...064.2 |
$x^{16} - 12 x^{14} + 24 x^{12} + 36 x^{10} + 189 x^{8} - 648 x^{6} - 540 x^{4} + 324$ |
$16$ |
(8, 4) |
$2^{48}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$32.3055690086$ |
$179.60432689710672$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$11$ |
$3528599.13688$ |
$7$ |
$97$ |
| 16.0.562...256.1 |
$x^{16} + 52 x^{12} - 48 x^{10} + 438 x^{8} + 96 x^{6} + 508 x^{4} + 1200 x^{2} + 625$ |
$16$ |
(0, 8) |
$2^{50}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$35.229472812$ |
$195.8599073014336$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 12]$ |
$[2, 12]$ |
$2$ |
$7$ |
$45687.5845647$ |
$0$ |
$97$ |
| 16.16.562...256.1 |
$x^{16} - 24 x^{14} + 172 x^{12} - 552 x^{10} + 870 x^{8} - 648 x^{6} + 196 x^{4} - 24 x^{2} + 1$ |
$16$ |
(16, 0) |
$2^{50}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$35.229472812$ |
$195.8599073014336$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$28246056.1969$ |
$14$ |
$97$ |
| 16.0.562...256.2 |
$x^{16} + 52 x^{12} + 48 x^{10} + 438 x^{8} - 96 x^{6} + 508 x^{4} - 1200 x^{2} + 625$ |
$16$ |
(0, 8) |
$2^{50}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$35.229472812$ |
$195.8599073014336$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$166995.738124$ |
$0$ |
$97$ |
| 16.0.562...256.3 |
$x^{16} + 24 x^{14} + 172 x^{12} + 552 x^{10} + 870 x^{8} + 648 x^{6} + 196 x^{4} + 24 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{50}\cdot 3^{12}\cdot 97^{2}$ |
$3$ |
$35.229472812$ |
$195.8599073014336$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 12]$ |
$[2, 12]$ |
$2$ |
$7$ |
$27485.952385$ |
$0$ |
$97$ |
| 16.16.127...144.1 |
$x^{16} - 44 x^{14} - 80 x^{13} + 436 x^{12} + 1224 x^{11} - 752 x^{10} - 4488 x^{9} - 1568 x^{8} + 5384 x^{7} + 3820 x^{6} - 2048 x^{5} - 2008 x^{4} + 256 x^{3} + 376 x^{2} - 8 x - 23$ |
$16$ |
(16, 0) |
$2^{52}\cdot 3^{12}\cdot 73^{2}$ |
$3$ |
$37.0769314888$ |
$185.28909367485454$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$39169340.8767$ |
$14$ |
$73$ |
| 16.0.810...016.1 |
$x^{16} - 8 x^{15} + 24 x^{14} - 16 x^{13} - 60 x^{12} + 48 x^{11} + 568 x^{10} - 2248 x^{9} + 4884 x^{8} - 8456 x^{7} + 16000 x^{6} - 33984 x^{5} + 63540 x^{4} - 89216 x^{3} + 89520 x^{2} - 57592 x + 19297$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.618905494$ |
$160.39694500305947$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[6, 12]$ |
$[6, 12]$ |
$2$ |
$7$ |
$45687.5845647$ |
$0$ |
$23$ |
| 16.16.810...016.1 |
$x^{16} - 8 x^{15} + 128 x^{13} - 180 x^{12} - 720 x^{11} + 1528 x^{10} + 1544 x^{9} - 5052 x^{8} - 248 x^{7} + 7144 x^{6} - 2688 x^{5} - 3708 x^{4} + 1984 x^{3} + 672 x^{2} - 376 x - 23$ |
$16$ |
(16, 0) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$127518766.58957401$ |
$14$ |
$23$ |
| 16.8.810...016.1 |
$x^{16} - 16 x^{14} - 8 x^{13} + 128 x^{12} - 24 x^{11} - 496 x^{10} + 336 x^{9} + 1582 x^{8} - 1968 x^{7} - 1184 x^{6} + 3680 x^{5} - 4860 x^{4} - 1984 x^{3} + 4984 x^{2} + 752 x - 914$ |
$16$ |
(8, 4) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$15612030.939096455$ |
$6$ |
$23$ |
| 16.8.810...016.2 |
$x^{16} - 24 x^{14} - 24 x^{13} + 196 x^{12} + 408 x^{11} - 480 x^{10} - 2400 x^{9} - 2028 x^{8} + 2880 x^{7} + 8160 x^{6} + 7272 x^{5} + 172 x^{4} - 6648 x^{3} - 7080 x^{2} - 3120 x - 503$ |
$16$ |
(8, 4) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$9889938.307322176$ |
$7$ |
$23$ |
| 16.0.810...016.2 |
$x^{16} + 16 x^{14} - 24 x^{13} + 96 x^{12} - 264 x^{11} + 520 x^{10} - 1392 x^{9} + 2230 x^{8} - 3312 x^{7} + 5040 x^{6} - 3408 x^{5} + 6588 x^{4} - 5184 x^{3} + 72 x^{2} - 576 x + 846$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$676806.3546003123$ |
$0$ |
$23$ |
| 16.16.810...016.2 |
$x^{16} - 32 x^{14} - 16 x^{13} + 340 x^{12} + 264 x^{11} - 1448 x^{10} - 1200 x^{9} + 2746 x^{8} + 1936 x^{7} - 2456 x^{6} - 1072 x^{5} + 956 x^{4} + 80 x^{3} - 152 x^{2} + 32 x - 2$ |
$16$ |
(16, 0) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$97751967.49566491$ |
$14$ |
$23$ |
| 16.8.810...016.3 |
$x^{16} - 8 x^{14} - 8 x^{13} + 40 x^{12} - 24 x^{11} - 56 x^{10} + 96 x^{9} + 982 x^{8} - 4624 x^{7} + 7024 x^{6} + 544 x^{5} - 10756 x^{4} + 8128 x^{3} - 152 x^{2} - 1568 x + 382$ |
$16$ |
(8, 4) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$6500801.080357627$ |
$7$ |
$23$ |
| 16.0.810...016.3 |
$x^{16} - 24 x^{13} - 20 x^{12} - 72 x^{11} + 96 x^{10} + 432 x^{9} + 1140 x^{8} + 2784 x^{7} + 2952 x^{6} + 3624 x^{5} + 4588 x^{4} - 5880 x^{3} - 7368 x^{2} + 1680 x + 2113$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$625772.9258235572$ |
$0$ |
$23$ |
| 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...016.4 |
$x^{16} - 8 x^{15} + 24 x^{14} - 16 x^{13} - 60 x^{12} + 168 x^{11} - 272 x^{10} + 32 x^{9} + 1074 x^{8} - 896 x^{7} + 40 x^{6} - 1104 x^{5} + 5220 x^{4} - 11216 x^{3} + 13320 x^{2} - 8512 x + 4222$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
✓ |
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2, 12]$ |
$[2, 12]$ |
$2$ |
$7$ |
$114624.6980098966$ |
$0$ |
$23$ |
| 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) |
$[2, 30]$ |
$[2, 30]$ |
$2$ |
$7$ |
$45687.584564657765$ |
$0$ |
$23$ |
