| 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 $p$ |
| 16.0.232218265089212416.2 |
$x^{16} - 3 x^{14} + 4 x^{12} + 5 x^{10} - 7 x^{8} + 8 x^{6} + 8 x^{4} - 4 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{24}\cdot 7^{12}$ |
$2$ |
$12.1721844145$ |
$24.344368828919517$ |
|
|
? |
$C_4^2:D_4$ (as 16T410) |
trivial |
trivial |
$2$ |
$7$ |
$180.538289579$ |
$0$ |
$7$ |
| 16.0.743...312.2 |
$x^{16} + x^{14} + 2 x^{12} + 5 x^{10} + 21 x^{8} + 32 x^{6} + 22 x^{4} + 6 x^{2} + 2$ |
$16$ |
(0, 8) |
$2^{29}\cdot 7^{12}$ |
$2$ |
$15.1161223051$ |
$61.788489129137815$ |
|
|
|
$C_2^4.C_2\wr D_4$ (as 16T1452) |
trivial |
trivial |
$2$ |
$7$ |
$1692.6484736$ |
$0$ |
$7$ |
| 16.0.148...624.2 |
$x^{16} - 3 x^{14} + 11 x^{12} - 16 x^{10} + 7 x^{8} + x^{6} + x^{4} + 10 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{30}\cdot 7^{12}$ |
$2$ |
$15.7853702152$ |
$26.5477224547918$ |
|
|
|
$C_4^2:D_4$ (as 16T366) |
trivial |
trivial |
$2$ |
$7$ |
$1986.83288889$ |
$0$ |
$7$ |
| 16.0.354...625.2 |
$x^{16} - x^{15} + x^{13} - 2 x^{12} - 30 x^{11} + 50 x^{10} + 58 x^{9} - 87 x^{8} - 58 x^{7} + 50 x^{6} + 30 x^{5} - 2 x^{4} - x^{3} + x + 1$ |
$16$ |
(0, 8) |
$3^{8}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$16.6674499448$ |
$21.935597734512804$ |
|
|
|
$C_2^3.D_4$ (as 16T165) |
trivial |
trivial |
$2$ |
$7$ |
$1763.13414331$ |
$0$ |
$7$ |
| 16.0.413...625.1 |
$x^{16} - 5 x^{15} + 8 x^{14} - 3 x^{13} + 11 x^{12} - 61 x^{11} + 82 x^{10} + 30 x^{9} - 164 x^{8} + 114 x^{7} + 91 x^{6} - 287 x^{5} + 383 x^{4} - 330 x^{3} + 191 x^{2} - 85 x + 25$ |
$16$ |
(0, 8) |
$3^{14}\cdot 5^{4}\cdot 7^{12}$ |
$3$ |
$16.828566722$ |
$25.16457673743996$ |
|
|
? |
$C_2^2:\SD_{16}$ (as 16T155) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1066.18204964$ |
$0$ |
$7$ |
| 16.4.413...625.1 |
$x^{16} - 6 x^{15} + 10 x^{14} + 3 x^{13} - 35 x^{12} + 54 x^{11} - 20 x^{10} - 15 x^{9} + 13 x^{8} + 15 x^{7} - 20 x^{6} - 54 x^{5} - 35 x^{4} - 3 x^{3} + 10 x^{2} + 6 x + 1$ |
$16$ |
(4, 6) |
$3^{14}\cdot 5^{4}\cdot 7^{12}$ |
$3$ |
$16.828566722$ |
$25.16457673743996$ |
|
|
? |
$C_2^2:\SD_{16}$ (as 16T155) |
trivial |
$[2]$ |
$2$ |
$9$ |
$6886.20795798$ |
$3$ |
$7$ |
| 16.0.413...625.2 |
$x^{16} - 3 x^{15} + x^{14} + 3 x^{13} + 22 x^{12} - 84 x^{11} + 103 x^{10} - 12 x^{9} - 83 x^{8} + 51 x^{7} + 64 x^{6} - 120 x^{5} + 85 x^{4} - 18 x^{3} - 2 x^{2} + 1$ |
$16$ |
(0, 8) |
$3^{14}\cdot 5^{4}\cdot 7^{12}$ |
$3$ |
$16.828566722$ |
$25.16457673743996$ |
|
|
? |
$C_2^2:\SD_{16}$ (as 16T155) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$2318.84721988$ |
$0$ |
$7$ |
| 16.4.413...625.2 |
$x^{16} - 6 x^{15} + 11 x^{14} + 12 x^{13} - 101 x^{12} + 228 x^{11} - 253 x^{10} + 57 x^{9} + 271 x^{8} - 480 x^{7} + 434 x^{6} - 255 x^{5} + 121 x^{4} - 63 x^{3} + 32 x^{2} - 9 x + 1$ |
$16$ |
(4, 6) |
$3^{14}\cdot 5^{4}\cdot 7^{12}$ |
$3$ |
$16.828566722$ |
$25.16457673743996$ |
|
|
? |
$C_2^2:\SD_{16}$ (as 16T155) |
trivial |
$[2]$ |
$2$ |
$9$ |
$3166.20743789$ |
$3$ |
$7$ |
| 16.4.594...496.2 |
$x^{16} - 6 x^{14} - 4 x^{13} + 32 x^{11} - 8 x^{10} - 32 x^{9} - 32 x^{8} + 56 x^{7} + 36 x^{6} - 68 x^{5} + 39 x^{4} - 28 x^{3} + 14 x^{2} - 4 x + 1$ |
$16$ |
(4, 6) |
$2^{32}\cdot 7^{12}$ |
$2$ |
$17.2140682826$ |
$24.344368828919517$ |
|
|
? |
$C_4^2:D_4$ (as 16T399) |
trivial |
$[2]$ |
$2$ |
$9$ |
$6845.75719852$ |
$3$ |
$7$ |
| 16.4.114...625.1 |
$x^{16} - 4 x^{15} + 4 x^{14} + 4 x^{13} - 16 x^{12} + 32 x^{11} - 40 x^{10} + 10 x^{9} + 25 x^{8} - 8 x^{7} - 10 x^{6} - 16 x^{5} + 23 x^{4} + 4 x^{3} - 11 x^{2} + 2 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{6}\cdot 7^{12}$ |
$3$ |
$17.9381736005$ |
$21.935597734512804$ |
|
|
|
$C_2^3.D_4$ (as 16T146) |
trivial |
$[2]$ |
$2$ |
$9$ |
$5389.48480451$ |
$3$ |
$7$ |
| 16.0.237...984.2 |
$x^{16} + 10 x^{14} + 51 x^{12} + 162 x^{10} + 282 x^{8} + 230 x^{6} + 107 x^{4} + 18 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{34}\cdot 7^{12}$ |
$2$ |
$18.7720745728$ |
$61.788489129137815$ |
|
|
|
$C_2^4.C_2\wr D_4$ (as 16T1456) |
trivial |
trivial |
$2$ |
$7$ |
$12081.9124415$ |
$0$ |
$7$ |
| 16.0.237...984.4 |
$x^{16} - 3 x^{14} - 3 x^{12} + 5 x^{10} + 35 x^{8} + 43 x^{6} + 43 x^{4} + 3 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{34}\cdot 7^{12}$ |
$2$ |
$18.7720745728$ |
$61.788489129137815$ |
|
|
|
$C_2^4.C_2\wr D_4$ (as 16T1473) |
trivial |
trivial |
$2$ |
$7$ |
$43733.9435117$ |
$0$ |
$7$ |
| 16.0.319...625.1 |
$x^{16} - 7 x^{15} + 25 x^{14} - 50 x^{13} + 66 x^{12} - 59 x^{11} + 33 x^{10} - 20 x^{9} + 25 x^{8} - 11 x^{7} - 17 x^{6} + 4 x^{5} + 32 x^{4} - 28 x^{3} + 6 x + 1$ |
$16$ |
(0, 8) |
$3^{10}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$19.1209434194$ |
$21.935597734512804$ |
|
|
|
$C_2^3.D_4$ (as 16T177) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$2639.49988243$ |
$0$ |
$7$ |
| 16.0.759...736.1 |
$x^{16} - x^{15} - x^{14} - 3 x^{13} - 16 x^{12} + 2 x^{11} + 20 x^{10} + 64 x^{9} + 160 x^{8} + 100 x^{7} + 186 x^{6} + 4 x^{5} + 83 x^{4} - 41 x^{3} + 35 x^{2} - 5 x + 4$ |
$16$ |
(0, 8) |
$2^{8}\cdot 7^{12}\cdot 11^{8}$ |
$3$ |
$20.1852842909$ |
$41.26242117154535$ |
|
|
|
$C_2^4:D_{12}$ (as 16T742) |
trivial |
trivial |
$2$ |
$7$ |
$108962.93172$ |
$0$ |
$11$ |
| 16.0.120...544.1 |
$x^{16} - 3 x^{14} + 9 x^{12} - 15 x^{10} + 16 x^{8} + 15 x^{6} + 9 x^{4} + 3 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{30}\cdot 3^{4}\cdot 7^{12}$ |
$3$ |
$20.774715525$ |
$57.10311102741276$ |
|
|
|
$D_4^2:D_4$ (as 16T843) |
trivial |
trivial |
$2$ |
$7$ |
$23853.1884206$ |
$0$ |
$7$ |
| 16.8.287...625.2 |
$x^{16} - 8 x^{15} + 28 x^{14} - 56 x^{13} + 53 x^{12} + 46 x^{11} - 227 x^{10} + 332 x^{9} - 206 x^{8} - 90 x^{7} + 271 x^{6} - 192 x^{5} + 31 x^{4} + 34 x^{3} - 17 x^{2} + 1$ |
$16$ |
(8, 4) |
$3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$21.9355977345$ |
$21.935597734512804$ |
|
|
|
$C_2^3.D_4$ (as 16T177) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$125457.503679$ |
$6$ |
$7$ |
| 16.0.287...625.4 |
$x^{16} - 4 x^{15} + 6 x^{14} - 6 x^{13} - 13 x^{12} + 54 x^{11} - 46 x^{10} + 5 x^{9} + 102 x^{8} - 218 x^{7} + 125 x^{6} - 114 x^{5} + 137 x^{4} - 33 x^{3} + 48 x^{2} - 44 x + 16$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$21.9355977345$ |
$21.935597734512804$ |
|
|
|
$C_2^3.D_4$ (as 16T165) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$56032.3711527$ |
$0$ |
$7$ |
| 16.0.287...625.8 |
$x^{16} - x^{15} + 3 x^{14} - 3 x^{13} + 35 x^{12} - 33 x^{11} + 29 x^{10} + 29 x^{9} + 27 x^{8} - 29 x^{7} + 29 x^{6} + 33 x^{5} + 35 x^{4} + 3 x^{3} + 3 x^{2} + x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$21.9355977345$ |
$32.801369337662685$ |
|
|
? |
$C_4^2.D_4$ (as 16T380) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$8673.01420676$ |
$0$ |
$7$ |
| 16.0.287...625.9 |
$x^{16} - 5 x^{15} + 19 x^{14} - 58 x^{13} + 140 x^{12} - 284 x^{11} + 482 x^{10} - 655 x^{9} + 748 x^{8} - 736 x^{7} + 632 x^{6} - 503 x^{5} + 386 x^{4} - 235 x^{3} + 160 x^{2} - 50 x + 25$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$21.9355977345$ |
$32.801369337662685$ |
|
|
? |
$C_4^2.D_4$ (as 16T380) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$7059.85401527$ |
$0$ |
$7$ |
| 16.4.433...184.2 |
$x^{16} - 5 x^{14} + x^{12} + 19 x^{10} + 7 x^{8} - 47 x^{6} - 20 x^{4} - 2 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{16}\cdot 3^{14}\cdot 7^{12}$ |
$3$ |
$22.507881684$ |
$43.1072426842905$ |
|
|
? |
$C_2^5:\SD_{16}$ (as 16T993) |
trivial |
$[2]$ |
$2$ |
$9$ |
$88519.4412599$ |
$3$ |
$7$ |
| 16.0.609...504.1 |
$x^{16} - 8 x^{15} + 31 x^{14} - 70 x^{13} + 114 x^{12} - 166 x^{11} + 262 x^{10} - 438 x^{9} + 771 x^{8} - 1188 x^{7} + 1292 x^{6} - 1000 x^{5} + 624 x^{4} - 304 x^{3} + 104 x^{2} - 32 x + 8$ |
$16$ |
(0, 8) |
$2^{26}\cdot 3^{8}\cdot 7^{12}$ |
$3$ |
$22.991002058468275$ |
$50.88745258779943$ |
|
|
|
$C_2^6.(C_2\times D_4)$ (as 16T1126) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$24866.219277278546$ |
$0$ |
$7$ |
| 16.0.152...976.1 |
$x^{16} - 2 x^{14} + x^{12} + 16 x^{10} + 28 x^{8} - 16 x^{6} + 8 x^{4} - 96 x^{2} + 64$ |
$16$ |
(0, 8) |
$2^{40}\cdot 7^{12}$ |
$2$ |
$24.3443688289$ |
$61.788489129137815$ |
|
|
|
$C_2^5.(C_2\times D_4)$ (as 16T1021) |
$[2]$ |
$[2]$ |
$4$ |
$7$ |
$190432.972366$ |
$0$ |
$7$ |
| 16.0.152...976.2 |
$x^{16} - 4 x^{14} + 25 x^{12} - 82 x^{10} + 126 x^{8} - 64 x^{6} - 6 x^{4} + 4 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{40}\cdot 7^{12}$ |
$2$ |
$24.3443688289$ |
$61.788489129137815$ |
|
|
|
$C_2^5.(C_2\times D_4)$ (as 16T1021) |
$[2]$ |
$[2]$ |
$4$ |
$7$ |
$141688.338654$ |
$0$ |
$7$ |
| 16.0.608...904.1 |
$x^{16} - 13 x^{14} + 57 x^{12} - 78 x^{10} + 67 x^{8} - 45 x^{6} + 23 x^{4} - 8 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{42}\cdot 7^{12}$ |
$2$ |
$26.5477224548$ |
$61.788489129137815$ |
|
|
? |
$C_2^4.(C_4\times D_4)$ (as 16T867) |
trivial |
trivial |
$2$ |
$7$ |
$241130.962586$ |
$0$ |
$7$ |
| 16.0.608...904.2 |
$x^{16} - 2 x^{14} + 8 x^{12} + 30 x^{10} + 14 x^{8} - 30 x^{6} + 8 x^{4} + 2 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{42}\cdot 7^{12}$ |
$2$ |
$26.5477224548$ |
$61.788489129137815$ |
|
|
? |
$C_2^4.(C_4\times D_4)$ (as 16T867) |
trivial |
trivial |
$2$ |
$7$ |
$197486.239313$ |
$0$ |
$7$ |
| 16.0.608...904.3 |
$x^{16} - 4 x^{14} + 25 x^{12} - 68 x^{10} + 175 x^{8} - 260 x^{6} + 211 x^{4} - 52 x^{2} + 4$ |
$16$ |
(0, 8) |
$2^{42}\cdot 7^{12}$ |
$2$ |
$26.5477224548$ |
$61.788489129137815$ |
|
|
? |
$C_2^5.(C_2\times D_4)$ (as 16T983) |
trivial |
trivial |
$2$ |
$7$ |
$259563.640132$ |
$0$ |
$7$ |
| 16.0.608...904.4 |
$x^{16} - 3 x^{14} + 2 x^{12} + 13 x^{10} + 2 x^{8} - 13 x^{6} + 2 x^{4} + 3 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{42}\cdot 7^{12}$ |
$2$ |
$26.5477224548$ |
$61.788489129137815$ |
|
|
? |
$C_2^5.(C_2\times D_4)$ (as 16T983) |
trivial |
trivial |
$2$ |
$7$ |
$193123.808805$ |
$0$ |
$7$ |
| 16.4.123...456.1 |
$x^{16} - 18 x^{14} - 34 x^{13} + 17 x^{12} + 144 x^{11} + 246 x^{10} - 78 x^{9} - 1107 x^{8} - 2110 x^{7} - 1974 x^{6} - 810 x^{5} + 153 x^{4} + 316 x^{3} + 132 x^{2} + 22 x + 1$ |
$16$ |
(4, 6) |
$2^{24}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$27.746580271315977$ |
$32.99643067564309$ |
|
|
? |
$C_2^3.D_4$ (as 16T146) |
$[2]$ |
$[2, 4]$ |
$2$ |
$9$ |
$65390.40406088645$ |
$2$ |
$7$ |
| 16.0.123...456.1 |
$x^{16} + 10 x^{14} + 39 x^{12} + 16 x^{10} - 371 x^{8} - 372 x^{6} + 1863 x^{4} + 1026 x^{2} + 81$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$27.7465802713$ |
$32.99643067564309$ |
|
|
? |
$C_2^4:D_4$ (as 16T350) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$38651.5164377$ |
$0$ |
$7$ |
| 16.8.123...456.1 |
$x^{16} - 10 x^{14} + 39 x^{12} - 16 x^{10} - 371 x^{8} + 372 x^{6} + 1863 x^{4} - 1026 x^{2} + 81$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$27.7465802713$ |
$32.99643067564309$ |
|
|
? |
$C_2^4:D_4$ (as 16T350) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$801915.681135$ |
$6$ |
$7$ |
| 16.4.123...456.2 |
$x^{16} - 2 x^{14} - 3 x^{12} + 64 x^{10} - 398 x^{8} + 390 x^{6} + 408 x^{4} - 936 x^{2} + 9$ |
$16$ |
(4, 6) |
$2^{24}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$27.746580271315977$ |
$32.99643067564309$ |
|
|
? |
$C_2^4:D_4$ (as 16T350) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$87764.36404942715$ |
$3$ |
$7$ |
| 16.0.310...776.1 |
$x^{16} - 8 x^{15} + 46 x^{14} - 164 x^{13} + 478 x^{12} - 1092 x^{11} + 2350 x^{10} - 5072 x^{9} + 10630 x^{8} - 20008 x^{7} + 30858 x^{6} - 41828 x^{5} + 53390 x^{4} - 68396 x^{3} + 95514 x^{2} - 95592 x + 39629$ |
$16$ |
(0, 8) |
$2^{28}\cdot 7^{12}\cdot 17^{4}$ |
$3$ |
$29.3926168068$ |
$84.40447656622003$ |
|
|
|
$C_4.D_4^2$ (as 16T538) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$169090.096995$ |
$0$ |
$17$ |
| 16.0.310...776.2 |
$x^{16} - 6 x^{15} + 3 x^{14} + 68 x^{13} - 147 x^{12} - 372 x^{11} + 1882 x^{10} - 2060 x^{9} - 2277 x^{8} + 7790 x^{7} - 9337 x^{6} + 8276 x^{5} + 4271 x^{4} - 28156 x^{3} + 27130 x^{2} - 13784 x + 14156$ |
$16$ |
(0, 8) |
$2^{28}\cdot 7^{12}\cdot 17^{4}$ |
$3$ |
$29.3926168068$ |
$84.40447656622003$ |
|
|
|
$C_4.D_4^2$ (as 16T538) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$118245.439386$ |
$0$ |
$17$ |
| 16.16.179...625.1 |
$x^{16} - 5 x^{15} - 23 x^{14} + 142 x^{13} + 122 x^{12} - 1367 x^{11} + 169 x^{10} + 6206 x^{9} - 3110 x^{8} - 14796 x^{7} + 9442 x^{6} + 19146 x^{5} - 12353 x^{4} - 12782 x^{3} + 7192 x^{2} + 3456 x - 1424$ |
$16$ |
(16, 0) |
$3^{12}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
|
✓ |
|
$C_4:C_4$ (as 16T8) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$7752916.72291$ |
$13$ |
$7$ |
| 16.0.179...625.2 |
$x^{16} - 5 x^{15} + 21 x^{14} - 30 x^{13} + 50 x^{12} + 75 x^{11} + 674 x^{10} + 700 x^{9} + 1239 x^{8} - 700 x^{7} + 674 x^{6} - 75 x^{5} + 50 x^{4} + 30 x^{3} + 21 x^{2} + 5 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
✓ |
✓ |
|
$C_4:C_4$ (as 16T8) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$10$ |
$7$ |
$120012.452011$ |
$0$ |
$7$ |
| 16.0.179...625.3 |
$x^{16} - 5 x^{15} + 27 x^{14} - 114 x^{13} + 254 x^{12} - 531 x^{11} + 1034 x^{10} - 878 x^{9} + 2007 x^{8} - 1492 x^{7} + 944 x^{6} - 3627 x^{5} + 1796 x^{4} - 4920 x^{3} + 10695 x^{2} - 8425 x + 7795$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
✓ |
✓ |
|
$C_4:C_4$ (as 16T8) |
$[4, 8]$ |
$[4, 8]$ |
$2$ |
$7$ |
$14409.2792961$ |
$0$ |
$7$ |
| 16.0.179...625.4 |
$x^{16} - x^{15} - 2 x^{14} + x^{13} - 7 x^{12} - 61 x^{11} + 110 x^{10} + 85 x^{9} - 59 x^{8} + 340 x^{7} + 1760 x^{6} - 3904 x^{5} - 1792 x^{4} + 1024 x^{3} - 8192 x^{2} - 16384 x + 65536$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
✓ |
✓ |
|
$C_4:C_4$ (as 16T8) |
$[4, 8]$ |
$[4, 8]$ |
$10$ |
$7$ |
$103783.231276$ |
$0$ |
$7$ |
| 16.8.389...856.1 |
$x^{16} - 12 x^{14} + 46 x^{12} - 92 x^{10} + 141 x^{8} - 124 x^{6} + 72 x^{4} - 44 x^{2} + 9$ |
$16$ |
(8, 4) |
$2^{48}\cdot 7^{12}$ |
$2$ |
$34.4281365653$ |
$48.688737657839035$ |
|
|
? |
$D_4^2:D_4$ (as 16T987) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$7335119.8822$ |
$6$ |
$7$ |
| 16.0.389...856.1 |
$x^{16} + 12 x^{14} + 50 x^{12} + 128 x^{10} + 245 x^{8} + 264 x^{6} + 120 x^{4} + 16 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{48}\cdot 7^{12}$ |
$2$ |
$34.4281365653$ |
$48.688737657839035$ |
|
|
? |
$D_4^2:D_4$ (as 16T987) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$321274.815689$ |
$0$ |
$7$ |
| 16.8.389...856.2 |
$x^{16} - 12 x^{14} + 50 x^{12} - 128 x^{10} + 245 x^{8} - 264 x^{6} + 120 x^{4} - 16 x^{2} + 1$ |
$16$ |
(8, 4) |
$2^{48}\cdot 7^{12}$ |
$2$ |
$34.4281365653$ |
$48.688737657839035$ |
|
|
? |
$D_4^2:D_4$ (as 16T987) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$7335119.8822$ |
$6$ |
$7$ |
| 16.0.389...856.2 |
$x^{16} + 12 x^{14} + 46 x^{12} + 92 x^{10} + 141 x^{8} + 124 x^{6} + 72 x^{4} + 44 x^{2} + 9$ |
$16$ |
(0, 8) |
$2^{48}\cdot 7^{12}$ |
$2$ |
$34.4281365653$ |
$48.688737657839035$ |
|
|
? |
$D_4^2:D_4$ (as 16T987) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$321274.815689$ |
$0$ |
$7$ |
| 16.8.857...000.1 |
$x^{16} - 8 x^{15} + 14 x^{14} + 42 x^{13} - 276 x^{12} + 746 x^{11} - 1074 x^{10} + 486 x^{9} + 1222 x^{8} - 3030 x^{7} + 3470 x^{6} - 2348 x^{5} + 871 x^{4} - 64 x^{3} - 66 x^{2} + 14 x + 1$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12}$ |
$4$ |
$36.1669435903$ |
$62.04323962981709$ |
|
|
? |
$C_2^3.D_4$ (as 16T177) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$1553525.30571$ |
$6$ |
$7$ |
| 16.8.857...000.2 |
$x^{16} - 4 x^{15} + 16 x^{13} - 75 x^{12} + 120 x^{11} + 128 x^{10} - 546 x^{9} + 1274 x^{8} + 154 x^{7} - 1984 x^{6} + 2120 x^{5} - 2624 x^{4} - 1964 x^{3} - 1274 x^{2} + 1850 x + 625$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12}$ |
$4$ |
$36.1669435903$ |
$62.04323962981709$ |
|
|
? |
$C_2^3.D_4$ (as 16T177) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$1968247.46283$ |
$6$ |
$7$ |
| 16.8.857...000.3 |
$x^{16} - 2 x^{15} - 8 x^{14} + 12 x^{13} + 26 x^{12} + 64 x^{11} - 240 x^{10} - 296 x^{9} + 1136 x^{8} - 872 x^{7} - 816 x^{6} + 3088 x^{5} - 2680 x^{4} - 96 x^{3} + 832 x^{2} - 224 x + 16$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 7^{12}$ |
$4$ |
$36.1669435903$ |
$62.04323962981709$ |
|
|
|
$C_2^4:D_4$ (as 16T329) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$5109761.88958$ |
$5$ |
$7$ |
| 16.8.117...000.1 |
$x^{16} - 5 x^{14} - 52 x^{12} + 55 x^{10} + 484 x^{8} - 145 x^{6} - 733 x^{4} - 100 x^{2} + 16$ |
$16$ |
(8, 4) |
$2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$4$ |
$36.8911310028$ |
$62.04323962981709$ |
|
|
|
$C_2^4:D_4$ (as 16T329) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$4948356.49425$ |
$6$ |
$7$ |
| 16.0.117...000.1 |
$x^{16} + 20 x^{14} + 170 x^{12} + 590 x^{10} + 868 x^{8} + 10 x^{6} + 365 x^{4} - 20 x^{2} + 16$ |
$16$ |
(0, 8) |
$2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$4$ |
$36.8911310028$ |
$62.04323962981709$ |
|
|
|
$C_2^3.D_4$ (as 16T177) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$7$ |
$341187.135738$ |
$0$ |
$7$ |
| 16.0.117...000.2 |
$x^{16} - 20 x^{14} + 170 x^{12} - 590 x^{10} + 868 x^{8} - 10 x^{6} + 365 x^{4} + 20 x^{2} + 16$ |
$16$ |
(0, 8) |
$2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$4$ |
$36.8911310028$ |
$62.04323962981709$ |
|
|
|
$C_2^3.D_4$ (as 16T177) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$7$ |
$432268.925263$ |
$0$ |
$7$ |
| 16.4.155...424.1 |
$x^{16} - 8 x^{14} - 20 x^{12} - 20 x^{10} + 32 x^{8} + 24 x^{6} - 40 x^{4} + 8 x^{2} + 4$ |
$16$ |
(4, 6) |
$2^{50}\cdot 7^{12}$ |
$2$ |
$37.5441491457$ |
|
|
|
? |
$C_2^5.C_2\wr C_2^2$ (as 16T1408) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$2247158.41183$ |
$2$ |
$7$ |
| 16.4.155...424.2 |
$x^{16} + 8 x^{14} - 20 x^{12} + 20 x^{10} + 32 x^{8} - 24 x^{6} - 40 x^{4} - 8 x^{2} + 4$ |
$16$ |
(4, 6) |
$2^{50}\cdot 7^{12}$ |
$2$ |
$37.5441491457$ |
|
|
|
|
$C_2^5.C_2\wr C_2^2$ (as 16T1408) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$9624211.84744$ |
$2$ |
$7$ |
| 16.0.623...696.1 |
$x^{16} + 8 x^{14} + 30 x^{12} + 68 x^{10} + 98 x^{8} + 88 x^{6} + 50 x^{4} + 20 x^{2} + 9$ |
$16$ |
(0, 8) |
$2^{52}\cdot 7^{12}$ |
$2$ |
$40.9421849597$ |
|
|
|
|
$C_2^5.C_2\wr C_2^2$ (as 16T1408) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$4171194.60081$ |
$0$ |
$7$ |
