| 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 |
| 16.0.494...201.1 |
$x^{16} - 8 x^{15} + 30 x^{14} - 70 x^{13} + 109 x^{12} - 108 x^{11} - 22 x^{10} + 385 x^{9} - 411 x^{8} - 710 x^{7} + 1946 x^{6} - 1731 x^{5} - 1705 x^{4} + 4698 x^{3} - 1838 x^{2} - 566 x + 4483$ |
$16$ |
[0,8] |
$3^{8}\cdot 16573^{4}$ |
$2$ |
$19.6521879931$ |
$222.97757734803739$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$6$ |
$7$ |
$17187.0222201$ |
| 16.0.494...201.2 |
$x^{16} - 5 x^{15} + 20 x^{14} - 75 x^{13} + 156 x^{12} - 325 x^{11} + 548 x^{10} - 279 x^{9} + 554 x^{8} + 51 x^{7} - 1277 x^{6} - 2053 x^{5} - 1505 x^{4} + 1586 x^{3} + 4632 x^{2} + 3971 x + 2749$ |
$16$ |
[0,8] |
$3^{8}\cdot 16573^{4}$ |
$2$ |
$19.6521879931$ |
$222.97757734803739$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$6$ |
$7$ |
$12143.537393$ |
| 16.0.147...625.1 |
$x^{16} - 3 x^{15} + 5 x^{14} - 29 x^{13} + 90 x^{12} - 159 x^{11} + 382 x^{10} - 821 x^{9} + 901 x^{8} - 1151 x^{7} + 2315 x^{6} - 2337 x^{5} + 1761 x^{4} - 2270 x^{3} + 2929 x^{2} - 2150 x + 625$ |
$16$ |
[0,8] |
$5^{8}\cdot 7841^{4}$ |
$2$ |
$21.0415566474$ |
$1863.21766288455$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$7$ |
$9609.8559606$ |
| 16.0.474...625.1 |
$x^{16} - x^{15} + 3 x^{14} - 16 x^{13} + 51 x^{12} - 123 x^{11} + 265 x^{10} - 562 x^{9} + 1131 x^{8} - 1606 x^{7} + 1567 x^{6} - 2429 x^{5} + 3069 x^{4} + 3438 x^{3} - 7695 x^{2} - 279 x + 3491$ |
$16$ |
[0,8] |
$5^{8}\cdot 10501^{4}$ |
$2$ |
$22.6356341908$ |
$229.13969538253298$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$7$ |
$16571.2730232$ |
| 16.0.474...625.2 |
$x^{16} - 5 x^{15} + 9 x^{14} - 12 x^{13} + 8 x^{12} - 14 x^{11} + 135 x^{10} - 160 x^{9} + 266 x^{8} - 293 x^{7} + 298 x^{6} - 447 x^{5} + 984 x^{4} - 1378 x^{3} + 3524 x^{2} + 1390 x + 1555$ |
$16$ |
[0,8] |
$5^{8}\cdot 10501^{4}$ |
$2$ |
$22.635634190782866$ |
$229.13969538253298$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$7$ |
$14786.829106607225$ |
| 16.0.196...625.1 |
$x^{16} - 3 x^{15} + 9 x^{14} - 20 x^{13} + 57 x^{12} - 154 x^{11} + 890 x^{10} - 2775 x^{9} + 5444 x^{8} - 7210 x^{7} + 9714 x^{6} - 10126 x^{5} + 14764 x^{4} - 14510 x^{3} + 14457 x^{2} - 20828 x + 39019$ |
$16$ |
[0,8] |
$5^{8}\cdot 31^{4}\cdot 859^{4}$ |
$3$ |
$28.5643086113$ |
$4661.236573643297$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2]$ |
$2$ |
$7$ |
$35623.8314936$ |
| 16.4.226...625.1 |
$x^{16} - 3 x^{15} + 13 x^{14} - 17 x^{13} - 41 x^{12} + 265 x^{11} - 1141 x^{10} + 2371 x^{9} - 4122 x^{8} + 3160 x^{7} + 3681 x^{6} - 18463 x^{5} + 38654 x^{4} - 52041 x^{3} + 47410 x^{2} - 26237 x + 8521$ |
$16$ |
[4,6] |
$5^{8}\cdot 27581^{4}$ |
$2$ |
$28.8162527173$ |
$371.35562470494506$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$9$ |
$132373.178239$ |
| 16.4.226...625.2 |
$x^{16} - 3 x^{15} + 8 x^{14} - 37 x^{13} + 37 x^{12} + 43 x^{11} - 193 x^{10} + 890 x^{9} - 945 x^{8} - 389 x^{7} + 268 x^{6} - 1721 x^{5} - 1079 x^{4} + 372 x^{3} + 21369 x^{2} - 25449 x + 16969$ |
$16$ |
[4,6] |
$5^{8}\cdot 27581^{4}$ |
$2$ |
$28.8162527173$ |
$371.35562470494506$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$9$ |
$150633.324393$ |
| 16.4.237...625.1 |
$x^{16} - 6 x^{15} + 26 x^{14} - 52 x^{13} + 80 x^{12} + 68 x^{11} - 314 x^{10} + 1115 x^{9} - 1113 x^{8} + 993 x^{7} + 349 x^{6} + 279 x^{5} - 4943 x^{4} + 11070 x^{3} - 19806 x^{2} + 14673 x - 2389$ |
$16$ |
[4,6] |
$5^{12}\cdot 9929^{4}$ |
$2$ |
$33.3775058678$ |
$3325.8804652021704$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$9$ |
$734836.868092$ |
| 16.8.237...625.1 |
$x^{16} - 10 x^{14} - 30 x^{13} - 38 x^{12} + 250 x^{11} + 495 x^{10} - 205 x^{9} - 1906 x^{8} - 4170 x^{7} + 1860 x^{6} + 16415 x^{5} + 21733 x^{4} + 3975 x^{3} - 40155 x^{2} - 42635 x - 2609$ |
$16$ |
[8,4] |
$5^{12}\cdot 9929^{4}$ |
$2$ |
$33.3775058678$ |
$3325.8804652021704$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$1625744.92823$ |
| 16.0.237...625.2 |
$x^{16} - x^{15} + 19 x^{14} - 17 x^{13} + 159 x^{12} - 64 x^{11} + 886 x^{10} + 317 x^{9} + 3641 x^{8} + 2710 x^{7} + 9575 x^{6} + 6550 x^{5} + 14055 x^{4} + 7275 x^{3} + 10625 x^{2} + 2550 x + 3100$ |
$16$ |
[0,8] |
$5^{12}\cdot 9929^{4}$ |
$2$ |
$33.3775058678$ |
$3325.8804652021704$ |
|
|
|
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2]$ |
$2$ |
$7$ |
$200448.051572$ |
| 16.4.237...625.2 |
$x^{16} - 3 x^{15} + 11 x^{14} - 37 x^{13} + 74 x^{12} - 57 x^{11} - 168 x^{10} + 1319 x^{9} - 4769 x^{8} + 8355 x^{7} - 9298 x^{6} + 4549 x^{5} + 19594 x^{4} - 65145 x^{3} + 103105 x^{2} - 90016 x + 32756$ |
$16$ |
[4,6] |
$5^{12}\cdot 9929^{4}$ |
$2$ |
$33.3775058678$ |
$3325.8804652021704$ |
|
|
|
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$9$ |
$1064406.05241$ |
| 16.0.604...000.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 64 x^{13} + 6 x^{12} - 570 x^{11} + 888 x^{10} + 5130 x^{9} + 1390 x^{8} - 13266 x^{7} - 9170 x^{6} + 118200 x^{5} + 448796 x^{4} + 68274 x^{3} - 2070881 x^{2} - 867030 x + 4273025$ |
$16$ |
[0,8] |
$2^{12}\cdot 5^{8}\cdot 7841^{4}$ |
$3$ |
$35.3875391123$ |
$726.2764648261364$ |
|
|
|
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$7$ |
$1358570.75849$ |
| 16.0.604...000.2 |
$x^{16} - 3 x^{15} - 22 x^{14} + 95 x^{13} + 307 x^{12} - 1596 x^{11} - 2156 x^{10} + 15748 x^{9} + 8573 x^{8} - 98637 x^{7} - 3020 x^{6} + 324405 x^{5} + 39628 x^{4} - 327971 x^{3} - 291719 x^{2} - 2518894 x + 5375956$ |
$16$ |
[0,8] |
$2^{12}\cdot 5^{8}\cdot 7841^{4}$ |
$3$ |
$35.3875391123$ |
$726.2764648261364$ |
|
|
|
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$7$ |
$1100568.72659$ |
| 16.4.805...625.1 |
$x^{16} - x^{15} + 18 x^{14} + 31 x^{13} - 57 x^{12} + 677 x^{11} - 2446 x^{10} + 5995 x^{9} - 23176 x^{8} + 48188 x^{7} - 121259 x^{6} + 220610 x^{5} - 300350 x^{4} + 404439 x^{3} - 184740 x^{2} + 186782 x + 146959$ |
$16$ |
[4,6] |
$5^{8}\cdot 119851^{4}$ |
$2$ |
$41.6049895889$ |
$774.1156244386235$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2]$ |
$2$ |
$9$ |
$1983016.07231$ |
| 16.4.805...625.2 |
$x^{16} - x^{15} + 12 x^{14} - 22 x^{13} - 175 x^{12} - 578 x^{11} - 3517 x^{10} - 9030 x^{9} - 27574 x^{8} - 63964 x^{7} - 136379 x^{6} - 239398 x^{5} - 381259 x^{4} - 573105 x^{3} - 408453 x^{2} - 763918 x - 89701$ |
$16$ |
[4,6] |
$5^{8}\cdot 119851^{4}$ |
$2$ |
$41.6049895889$ |
$774.1156244386235$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2]$ |
$2$ |
$9$ |
$2166260.67427$ |
| 16.8.122...625.1 |
$x^{16} - 4 x^{15} - 10 x^{14} + 148 x^{13} - 420 x^{12} - 761 x^{11} + 5351 x^{10} - 7759 x^{9} - 12884 x^{8} + 46881 x^{7} - 49477 x^{6} + 177589 x^{5} + 2194168 x^{4} - 9206881 x^{3} + 4572271 x^{2} + 8322007 x - 263899$ |
$16$ |
[8,4] |
$5^{12}\cdot 31^{4}\cdot 859^{4}$ |
$3$ |
$42.7136040684$ |
$6970.174429381283$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$11943059.9357$ |
| 16.0.971...000.1 |
$x^{16} - 2 x^{15} + 52 x^{14} - 107 x^{13} + 1290 x^{12} - 2290 x^{11} + 18491 x^{10} - 26109 x^{9} + 169521 x^{8} - 176611 x^{7} + 1019176 x^{6} - 698966 x^{5} + 3965073 x^{4} - 1463547 x^{3} + 9216181 x^{2} - 997033 x + 10180861$ |
$16$ |
[0,8] |
$2^{12}\cdot 5^{12}\cdot 9929^{4}$ |
$3$ |
$56.1340500687$ |
$12199.383335223294$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2, 2]$ |
$2$ |
$7$ |
$3287689.12716$ |
| 16.8.971...000.1 |
$x^{16} - 5 x^{15} - 34 x^{14} + 246 x^{13} - 116 x^{12} - 3193 x^{11} + 11638 x^{10} + 489 x^{9} - 96243 x^{8} + 197723 x^{7} - 100986 x^{6} - 193583 x^{5} + 2062068 x^{4} - 3089100 x^{3} - 5371768 x^{2} + 5532183 x + 4156921$ |
$16$ |
[8,4] |
$2^{12}\cdot 5^{12}\cdot 9929^{4}$ |
$3$ |
$56.1340500687$ |
$12199.383335223294$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$97798292.3718$ |
| 16.0.128...000.1 |
$x^{16} + 70 x^{14} + 1783 x^{12} + 22049 x^{10} + 229588 x^{8} + 3837981 x^{6} + 48944102 x^{4} + 303996664 x^{2} + 709103641$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{4}$ |
$4$ |
$57.1286172227$ |
|
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2, 2]$ |
$2$ |
$7$ |
$3903627.77831$ |
| 16.8.128...000.1 |
$x^{16} - 25 x^{14} - 508 x^{12} + 9740 x^{10} + 144774 x^{8} - 1237785 x^{6} - 17521882 x^{4} + 47000185 x^{2} + 709103641$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{4}$ |
$4$ |
$57.1286172227$ |
|
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$123081571.116$ |
| 16.8.503...625.1 |
$x^{16} - 3 x^{15} - 68 x^{14} + 377 x^{13} - 208 x^{12} - 5997 x^{11} + 35742 x^{10} + 10218 x^{9} - 477001 x^{8} + 417900 x^{7} + 2297256 x^{6} - 3629051 x^{5} - 2500217 x^{4} + 4705425 x^{3} - 24665835 x^{2} + 37541221 x + 130562021$ |
$16$ |
[8,4] |
$5^{12}\cdot 119851^{4}$ |
$2$ |
$62.2139704744$ |
$1157.5728555285998$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$196167511.55$ |
| 16.8.503...625.2 |
$x^{16} - x^{15} - 21 x^{14} + 19 x^{13} - 492 x^{12} - 232 x^{11} + 7044 x^{10} + 1997 x^{9} + 33241 x^{8} + 58997 x^{7} - 106311 x^{6} - 1472230 x^{5} + 1366325 x^{4} - 3682039 x^{3} - 36603102 x^{2} + 74157764 x + 69533551$ |
$16$ |
[8,4] |
$5^{12}\cdot 119851^{4}$ |
$2$ |
$62.213970474428955$ |
$1157.5728555285998$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$174681240.79300246$ |
| 16.8.490...625.1 |
$x^{16} - 5 x^{15} - 40 x^{14} + 307 x^{13} - 966 x^{12} - 1659 x^{11} + 40346 x^{10} - 135524 x^{9} - 23894 x^{8} + 1946502 x^{7} - 5668399 x^{6} + 3245050 x^{5} + 23736488 x^{4} - 77068202 x^{3} + 112248421 x^{2} - 90190604 x + 32715509$ |
$16$ |
[8,4] |
$5^{8}\cdot 439^{4}\cdot 2411^{4}$ |
$3$ |
$71.7216768543$ |
$73787.24581064368$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$578154887.404$ |
| 16.8.490...625.2 |
$x^{16} - 7 x^{15} - 10 x^{14} - 49 x^{13} - 486 x^{12} + 4169 x^{11} + 24032 x^{10} + 82573 x^{9} + 113753 x^{8} - 328690 x^{7} - 2162497 x^{6} - 5295348 x^{5} - 3651274 x^{4} + 13271587 x^{3} + 41038390 x^{2} + 48594476 x + 21906751$ |
$16$ |
[8,4] |
$5^{8}\cdot 439^{4}\cdot 2411^{4}$ |
$3$ |
$71.7216768543$ |
$73787.24581064368$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$11$ |
$638378353.767$ |
| 16.0.190...000.1 |
$x^{16} + 536 x^{14} + 111100 x^{12} + 11304513 x^{10} + 596833141 x^{8} + 16129436971 x^{6} + 215761836571 x^{4} + 1286266114845 x^{2} + 2729569883881$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 1652141^{4}$ |
$3$ |
$160.334423679$ |
|
✓ |
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2, 2, 2328432]$ |
$2$ |
$7$ |
$6960.86418224$ |
| 16.16.190...000.1 |
$x^{16} - 462 x^{14} + 89327 x^{12} - 9310893 x^{10} + 559562474 x^{8} - 19075067464 x^{6} + 331665376040 x^{4} - 2176436381363 x^{2} + 2729569883881$ |
$16$ |
[16,0] |
$2^{16}\cdot 5^{8}\cdot 1652141^{4}$ |
$3$ |
$160.334423679$ |
|
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$15$ |
$3173262068170$ |
| 16.0.190...000.2 |
$x^{16} + 496 x^{14} + 99711 x^{12} + 10503607 x^{10} + 620292337 x^{8} + 20131740705 x^{6} + 319403408552 x^{4} + 1786640146669 x^{2} + 2729569883881$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 1652141^{4}$ |
$3$ |
$160.334423679$ |
|
✓ |
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2, 2, 3714216]$ |
$2$ |
$7$ |
$6960.86418224$ |
| 16.16.190...000.2 |
$x^{16} - 496 x^{14} + 99711 x^{12} - 10503607 x^{10} + 620292337 x^{8} - 20131740705 x^{6} + 319403408552 x^{4} - 1786640146669 x^{2} + 2729569883881$ |
$16$ |
[16,0] |
$2^{16}\cdot 5^{8}\cdot 1652141^{4}$ |
$3$ |
$160.334423679$ |
|
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
trivial |
$2$ |
$15$ |
$3447259257570$ |
| 16.0.190...000.3 |
$x^{16} + 436 x^{14} + 74782 x^{12} + 6534529 x^{10} + 318454784 x^{8} + 8852113889 x^{6} + 136052191747 x^{4} + 1031216847970 x^{2} + 2729569883881$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 1652141^{4}$ |
$3$ |
$160.3344236785762$ |
|
✓ |
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1869) |
$[2, 2, 2044704]$ |
$2$ |
$7$ |
$6960.864182240299$ |
