| 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 |
| 12.0.164...352.1 |
$x^{12} - 4 x^{11} - 62 x^{10} + 232 x^{9} + 1679 x^{8} - 5668 x^{7} - 20398 x^{6} + 62556 x^{5} + 37242 x^{4} - 194132 x^{3} + 1081520 x^{2} - 893952 x + 689057$ |
$12$ |
[0,6] |
$2^{33}\cdot 61^{8}$ |
$2$ |
$104.244314566$ |
$104.24431456608558$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[349]$ |
$2$ |
$5$ |
$27056.6931186$ |
| 12.12.164...352.1 |
$x^{12} - 4 x^{11} - 86 x^{10} + 312 x^{9} + 2535 x^{8} - 8164 x^{7} - 30878 x^{6} + 85260 x^{5} + 155506 x^{4} - 338228 x^{3} - 289984 x^{2} + 370384 x + 136193$ |
$12$ |
[12,0] |
$2^{33}\cdot 61^{8}$ |
$2$ |
$104.244314566$ |
$104.24431456608558$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$93449375.2856$ |
| 12.0.199...192.1 |
$x^{12} - 4 x^{11} + 36 x^{10} - 176 x^{9} + 438 x^{8} - 2328 x^{7} + 7312 x^{6} - 2828 x^{5} - 3243 x^{4} - 44992 x^{3} + 124344 x^{2} - 309384 x + 444727$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{4}\cdot 17^{3}\cdot 61^{8}$ |
$4$ |
$128.35640121478377$ |
$313.0040605056856$ |
✓ |
|
? |
$D_4\times A_4$ (as 12T51) |
$[2, 870]$ |
$2$ |
$5$ |
$27056.69311857099$ |
| 12.12.227...657.1 |
$x^{12} - x^{11} - 100 x^{10} + 99 x^{9} + 3340 x^{8} - 2877 x^{7} - 46644 x^{6} + 33812 x^{5} + 266073 x^{4} - 180321 x^{3} - 517506 x^{2} + 369428 x + 16999$ |
$12$ |
[12,0] |
$17^{9}\cdot 61^{8}$ |
$2$ |
$129.734828196$ |
$129.73482819609035$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$319721807.832$ |
| 12.0.120...608.1 |
$x^{12} - 4 x^{11} - 38 x^{10} + 152 x^{9} + 1255 x^{8} - 4324 x^{7} - 13694 x^{6} + 49196 x^{5} - 96158 x^{4} - 49332 x^{3} + 4802880 x^{2} - 4481424 x + 9228321$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{6}\cdot 61^{8}$ |
$3$ |
$180.556449229$ |
$180.55644922865258$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2, 5378]$ |
$2$ |
$5$ |
$27056.69311857099$ |
| 12.12.120...608.1 |
$x^{12} - 4 x^{11} - 110 x^{10} + 392 x^{9} + 3823 x^{8} - 11812 x^{7} - 50510 x^{6} + 128060 x^{5} + 280906 x^{4} - 512340 x^{3} - 591888 x^{2} + 559584 x + 518337$ |
$12$ |
[12,0] |
$2^{33}\cdot 3^{6}\cdot 61^{8}$ |
$3$ |
$180.556449229$ |
$180.55644922865258$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$2$ |
$11$ |
$1310663235.9642558$ |
| 16.8.916...289.1 |
$x^{16} - 4 x^{15} + 5 x^{14} - 3 x^{13} + 5 x^{12} + 46 x^{11} - 212 x^{10} + 219 x^{9} + 256 x^{8} - 711 x^{7} + 436 x^{6} + 137 x^{5} - 253 x^{4} + 66 x^{3} + 23 x^{2} - 11 x + 1$ |
$16$ |
[8,4] |
$3^{14}\cdot 61^{8}$ |
$2$ |
$20.4242451861$ |
$40.52294385736571$ |
|
|
|
$C_2^4.\SL(2,3)$ (as 16T728) |
trivial |
$2$ |
$11$ |
$46987.9329971$ |
| 16.4.146...624.1 |
$x^{16} - 4 x^{15} + 14 x^{14} - 27 x^{13} + 29 x^{12} - 53 x^{11} - 56 x^{10} + 51 x^{9} - 62 x^{8} + 189 x^{7} - 377 x^{6} + 269 x^{5} - 28 x^{4} - 57 x^{3} + 17 x^{2} + 10 x + 1$ |
$16$ |
[4,6] |
$2^{4}\cdot 3^{14}\cdot 61^{8}$ |
$3$ |
$24.2886576939$ |
$81.04588771473142$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T732) |
trivial |
$2$ |
$9$ |
$47988.7675232$ |
| 16.6.173...160.1 |
$x^{16} - 8 x^{15} + 36 x^{14} - 112 x^{13} + 265 x^{12} - 498 x^{11} + 763 x^{10} - 966 x^{9} + 1007 x^{8} - 850 x^{7} + 543 x^{6} - 218 x^{5} + 5 x^{4} + 60 x^{3} - 28 x^{2} + 1$ |
$16$ |
[6,5] |
$-\,2^{6}\cdot 3^{8}\cdot 5\cdot 43\cdot 61^{8}$ |
$5$ |
$24.540827174$ |
$1113.1270607407046$ |
|
|
? |
$C_4^4.C_2\wr A_4$ (as 16T1845) |
trivial |
$2$ |
$10$ |
$218886.822294$ |
| 16.0.410...561.1 |
$x^{16} - 2 x^{15} + 9 x^{14} - 25 x^{13} + 55 x^{12} - 118 x^{11} + 150 x^{10} - 57 x^{9} + 224 x^{8} + 235 x^{7} + 370 x^{6} + 214 x^{5} + 227 x^{4} + 178 x^{3} + 119 x^{2} + 70 x + 25$ |
$16$ |
[0,8] |
$11^{8}\cdot 61^{8}$ |
$2$ |
$25.903667693977237$ |
$51.3944511582871$ |
|
|
? |
$\SL(2,3):C_2$ (as 16T60) |
$[2]$ |
$2$ |
$7$ |
$37053.591595285565$ |
| 16.12.417...416.1 |
$x^{16} - 12 x^{14} + 37 x^{12} + 12 x^{10} - 183 x^{8} + 129 x^{6} + 157 x^{4} - 108 x^{2} + 16$ |
$16$ |
[12,2] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.9418310372$ |
$135.30269517237056$ |
|
|
|
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$13$ |
$3284543.63955$ |
| 16.4.417...416.1 |
$x^{16} + 9 x^{14} + 9 x^{12} - 108 x^{10} - 252 x^{8} + 189 x^{6} + 810 x^{4} + 486 x^{2} + 81$ |
$16$ |
[4,6] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.9418310372$ |
$129.5663047844211$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$9$ |
$575416.944369$ |
| 16.8.417...416.1 |
$x^{16} - 4 x^{14} - 32 x^{12} + 41 x^{10} + 214 x^{8} - 52 x^{6} - 131 x^{4} + 20 x^{2} + 16$ |
$16$ |
[8,4] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.941831037173447$ |
$129.5663047844211$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$11$ |
$746109.5950902541$ |
| 16.12.417...416.2 |
$x^{16} - 15 x^{14} + 64 x^{12} - 42 x^{10} - 222 x^{8} + 336 x^{6} - 2 x^{4} - 162 x^{2} + 49$ |
$16$ |
[12,2] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.9418310372$ |
$129.5663047844211$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$13$ |
$2727878.0184$ |
| 16.12.417...416.3 |
$x^{16} - 11 x^{14} + 38 x^{12} - 44 x^{10} - 14 x^{8} + 56 x^{6} - 22 x^{4} - 4 x^{2} + 1$ |
$16$ |
[12,2] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.941831037173447$ |
$135.30269517237056$ |
|
|
|
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$13$ |
$2219287.583170383$ |
| 16.4.417...416.3 |
$x^{16} + 2 x^{14} - 28 x^{12} - 127 x^{10} - 176 x^{8} - 44 x^{6} + 59 x^{4} + 19 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.941831037173447$ |
$135.30269517237056$ |
|
|
|
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$9$ |
$384631.33056536416$ |
| 16.4.417...416.4 |
$x^{16} + 14 x^{14} + 67 x^{12} + 83 x^{10} - 332 x^{8} - 1297 x^{6} - 1655 x^{4} - 706 x^{2} + 49$ |
$16$ |
[4,6] |
$2^{12}\cdot 3^{12}\cdot 61^{8}$ |
$3$ |
$29.941831037173447$ |
$135.30269517237056$ |
|
|
|
$C_2^7:\SL(2,3)$ (as 16T1542) |
trivial |
$2$ |
$9$ |
$688804.6955226554$ |
| 16.2.465...800.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 13 x^{13} - x^{12} - 46 x^{11} + 145 x^{10} - 390 x^{9} + 602 x^{8} - 517 x^{7} + 493 x^{6} - 185 x^{5} + 192 x^{4} - 27 x^{3} + 21 x^{2} + 1$ |
$16$ |
[2,7] |
$-\,2^{3}\cdot 3^{8}\cdot 5^{2}\cdot 43^{2}\cdot 61^{8}$ |
$5$ |
$30.1455683697$ |
$1113.1270607407046$ |
|
|
? |
$C_4^4.C_2\wr A_4$ (as 16T1845) |
trivial |
$2$ |
$8$ |
$1373019.99242$ |
| 16.6.257...000.1 |
$x^{16} - 8 x^{12} + 17 x^{8} - 7 x^{4} - 5$ |
$16$ |
[6,5] |
$-\,2^{14}\cdot 3^{8}\cdot 5^{3}\cdot 61^{8}$ |
$4$ |
$33.5493157404$ |
$358.97814740415384$ |
|
|
|
$C_4^4:(C_2\times A_4)$ (as 16T1657) |
trivial |
$2$ |
$10$ |
$3885982.65956$ |
| 16.16.292...912.1 |
$x^{16} - 20 x^{14} + 164 x^{12} - 713 x^{10} + 1774 x^{8} - 2542 x^{6} + 2003 x^{4} - 772 x^{2} + 112$ |
$16$ |
[16,0] |
$2^{12}\cdot 3^{12}\cdot 7\cdot 61^{8}$ |
$4$ |
$33.8140338278$ |
$365.81596492664835$ |
|
|
? |
$C_2\wr \SL(2,3)$ (as 16T1670) |
trivial |
$2$ |
$15$ |
$12115649.4701$ |
| 16.8.296...736.1 |
$x^{16} - 22 x^{14} + 179 x^{12} - 818 x^{10} + 2503 x^{8} - 5358 x^{6} + 7746 x^{4} - 6768 x^{2} + 2601$ |
$16$ |
[8,4] |
$2^{18}\cdot 3^{10}\cdot 61^{8}$ |
$3$ |
$33.8473324298$ |
$135.30269517237056$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1546) |
trivial |
$2$ |
$11$ |
$10283956.393$ |
| 16.0.296...736.1 |
$x^{16} + 7 x^{14} + 6 x^{12} - 8 x^{10} + 79 x^{8} + 717 x^{6} + 1683 x^{4} + 1215 x^{2} + 144$ |
$16$ |
[0,8] |
$2^{18}\cdot 3^{10}\cdot 61^{8}$ |
$3$ |
$33.8473324298$ |
$135.30269517237056$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1546) |
$[2]$ |
$2$ |
$7$ |
$1388481.40394$ |
| 16.0.296...736.2 |
$x^{16} + 4 x^{14} - 70 x^{12} - 238 x^{10} + 751 x^{8} + 6642 x^{6} + 14715 x^{4} + 7290 x^{2} + 729$ |
$16$ |
[0,8] |
$2^{18}\cdot 3^{10}\cdot 61^{8}$ |
$3$ |
$33.8473324298$ |
$135.30269517237056$ |
|
|
? |
$C_2^7:\SL(2,3)$ (as 16T1546) |
$[2]$ |
$2$ |
$7$ |
$891171.532006$ |
| 16.8.341...369.1 |
$x^{16} - 2 x^{15} - x^{14} - 6 x^{13} - 133 x^{12} + 215 x^{11} + 76 x^{10} - 78 x^{9} + 427 x^{8} - 96 x^{7} - 248 x^{6} - 167 x^{5} - 187 x^{4} - 138 x^{3} - 19 x^{2} + 20 x + 4$ |
$16$ |
[8,4] |
$3^{14}\cdot 61^{10}$ |
$2$ |
$34.1438307341$ |
$80.3999836421474$ |
|
|
|
$C_2^5.\SL(2,3)$ (as 16T1040) |
trivial |
$2$ |
$11$ |
$3368903.28481$ |
| 16.0.432...025.1 |
$x^{16} - 5 x^{15} + 13 x^{14} + 23 x^{13} - 97 x^{12} - 28 x^{11} + 190 x^{10} + 115 x^{9} + 86 x^{8} - 403 x^{7} - 747 x^{6} + 610 x^{5} + 542 x^{4} - 108 x^{3} + 699 x^{2} - 927 x + 268$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$34.6552099382$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
$[2]$ |
$2$ |
$7$ |
$1316818.0363$ |
| 16.8.432...025.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 21 x^{13} - x^{12} - 53 x^{11} - 256 x^{10} - 69 x^{9} + 620 x^{8} + 1118 x^{7} + 28 x^{6} - 2172 x^{5} - 834 x^{4} + 1183 x^{3} + 497 x^{2} - 57 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$34.6552099382$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$11$ |
$4042747.07842$ |
| 16.4.432...025.1 |
$x^{16} - x^{15} - 11 x^{14} - 16 x^{13} + 48 x^{12} + 201 x^{11} + 131 x^{10} - 559 x^{9} - 1368 x^{8} - 566 x^{7} + 2053 x^{6} + 2863 x^{5} - 148 x^{4} - 2613 x^{3} - 1096 x^{2} + 775 x + 442$ |
$16$ |
[4,6] |
$3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$34.6552099382$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$9$ |
$5549131.71368$ |
| 16.4.432...025.2 |
$x^{16} - 4 x^{15} + 10 x^{14} - 11 x^{13} + 11 x^{12} - 147 x^{11} + 205 x^{10} - 188 x^{8} - 988 x^{7} + 729 x^{6} + 1598 x^{5} - 1876 x^{4} + 302 x^{3} + 325 x^{2} - 126 x + 7$ |
$16$ |
[4,6] |
$3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$34.6552099382$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$9$ |
$2759124.66733$ |
| 16.0.565...400.1 |
$x^{16} - 8 x^{15} + 30 x^{14} - 67 x^{13} + 125 x^{12} - 208 x^{11} + 342 x^{10} - 481 x^{9} + 593 x^{8} - 628 x^{7} + 340 x^{6} - 697 x^{5} + 500 x^{4} + 450 x^{3} + 1000 x^{2} + 511 x + 523$ |
$16$ |
[0,8] |
$2^{6}\cdot 3^{8}\cdot 5^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$35.2385092495$ |
$1235.8007311683866$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
$[2]$ |
$2$ |
$7$ |
$645901.460708$ |
| 16.4.565...400.1 |
$x^{16} - 4 x^{15} + 12 x^{14} - 24 x^{13} + 17 x^{12} + 40 x^{11} - 226 x^{10} + 168 x^{9} - 62 x^{8} + 1226 x^{7} - 3163 x^{6} + 3929 x^{5} + 7591 x^{4} - 15998 x^{3} + 2514 x^{2} - 5762 x - 278$ |
$16$ |
[4,6] |
$2^{6}\cdot 3^{8}\cdot 5^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$35.2385092495$ |
$1235.8007311683866$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$9$ |
$2176746.45731$ |
| 16.8.565...400.1 |
$x^{16} - 3 x^{15} + 6 x^{14} - 23 x^{13} + 2 x^{12} + 83 x^{11} - 143 x^{10} + 435 x^{9} - 617 x^{8} + 1163 x^{7} - 4465 x^{6} + 8028 x^{5} - 8579 x^{4} + 6803 x^{3} - 3218 x^{2} + 722 x - 59$ |
$16$ |
[8,4] |
$2^{6}\cdot 3^{8}\cdot 5^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$35.2385092495$ |
$1235.8007311683866$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$11$ |
$8929620.28223$ |
| 16.4.565...400.2 |
$x^{16} - 3 x^{15} + 5 x^{14} - 4 x^{13} + 45 x^{12} - 154 x^{11} + 308 x^{10} - 489 x^{9} + 1520 x^{8} - 3609 x^{7} + 4541 x^{6} + 231 x^{5} - 6795 x^{4} + 7060 x^{3} - 1986 x^{2} - 308 x + 49$ |
$16$ |
[4,6] |
$2^{6}\cdot 3^{8}\cdot 5^{2}\cdot 53^{2}\cdot 61^{8}$ |
$5$ |
$35.2385092495$ |
$1235.8007311683866$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$9$ |
$1874993.48696$ |
| 16.6.105...728.1 |
$x^{16} - x^{12} - 10 x^{8} + 19 x^{4} - 8$ |
$16$ |
[6,5] |
$-\,2^{23}\cdot 3^{8}\cdot 61^{8}$ |
$3$ |
$36.6400589417$ |
|
|
|
? |
$C_4^4:(C_2\times A_4)$ (as 16T1657) |
trivial |
$2$ |
$10$ |
$4493737.34256$ |
| 16.0.150...961.1 |
$x^{16} - x^{15} - x^{14} - 4 x^{13} - 32 x^{12} - x^{11} + 203 x^{10} + 223 x^{9} - 766 x^{8} - 1476 x^{7} + 3631 x^{6} + 8628 x^{5} - 9053 x^{4} - 31868 x^{3} - 3791 x^{2} + 43654 x + 31772$ |
$16$ |
[0,8] |
$23^{8}\cdot 61^{8}$ |
$2$ |
$37.456641600656084$ |
$74.31625359160908$ |
|
|
|
$\SL(2,3):C_2$ (as 16T60) |
$[12]$ |
$2$ |
$7$ |
$144826.71779034333$ |
| 16.0.467...592.1 |
$x^{16} + 20 x^{14} + 164 x^{12} + 713 x^{10} + 1774 x^{8} + 2542 x^{6} + 2003 x^{4} + 772 x^{2} + 112$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{12}\cdot 7\cdot 61^{8}$ |
$4$ |
$40.211889615$ |
$365.81596492664835$ |
✓ |
|
? |
$C_2\wr \SL(2,3)$ (as 16T1670) |
$[2, 20]$ |
$2$ |
$7$ |
$31577.6139578$ |
| 16.8.600...904.1 |
$x^{16} - 6 x^{14} - 66 x^{12} + 24 x^{10} + 144 x^{8} - 36 x^{6} - 72 x^{4} + 9 x^{2} + 9$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{14}\cdot 61^{8}$ |
$3$ |
$40.8484903722$ |
$148.638813439041$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T728) |
trivial |
$2$ |
$11$ |
$13653173.2732$ |
| 16.0.600...904.1 |
$x^{16} + 21 x^{14} + 162 x^{12} + 579 x^{10} + 1044 x^{8} + 972 x^{6} + 468 x^{4} + 108 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{14}\cdot 61^{8}$ |
$3$ |
$40.8484903722$ |
$148.638813439041$ |
✓ |
|
? |
$C_2^4.\SL(2,3)$ (as 16T728) |
$[4, 16]$ |
$2$ |
$7$ |
$31577.6139578$ |
| 16.16.600...904.1 |
$x^{16} - 21 x^{14} + 162 x^{12} - 579 x^{10} + 1044 x^{8} - 972 x^{6} + 468 x^{4} - 108 x^{2} + 9$ |
$16$ |
[16,0] |
$2^{16}\cdot 3^{14}\cdot 61^{8}$ |
$3$ |
$40.8484903722$ |
$148.638813439041$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T728) |
trivial |
$2$ |
$15$ |
$76577829.7713$ |
| 16.8.600...904.2 |
$x^{16} - 9 x^{14} - 15 x^{12} + 210 x^{10} - 270 x^{8} - 189 x^{6} + 144 x^{4} + 90 x^{2} + 9$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{14}\cdot 61^{8}$ |
$3$ |
$40.8484903722$ |
$148.638813439041$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T728) |
trivial |
$2$ |
$11$ |
$12494490.5724$ |
| 16.8.131...681.1 |
$x^{16} - 3 x^{15} - 14 x^{14} + 9 x^{13} + 128 x^{12} + 20 x^{11} - 709 x^{10} + 310 x^{9} + 1422 x^{8} - 1175 x^{7} - 289 x^{6} + 66 x^{5} + 109 x^{4} + 428 x^{3} + 12 x^{2} - 63 x + 4$ |
$16$ |
[8,4] |
$3^{8}\cdot 53^{2}\cdot 61^{8}\cdot 193^{2}$ |
$4$ |
$42.8997431711$ |
$2714.5453822931822$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$11$ |
$64113447.9954$ |
| 16.0.131...681.1 |
$x^{16} - x^{15} + 15 x^{14} - 4 x^{13} - 59 x^{12} - 49 x^{11} + 299 x^{10} + 111 x^{9} - 240 x^{8} - 144 x^{7} + 420 x^{6} - 81 x^{5} + 145 x^{4} - 166 x^{3} + 274 x^{2} - 251 x + 85$ |
$16$ |
[0,8] |
$3^{8}\cdot 53^{2}\cdot 61^{8}\cdot 193^{2}$ |
$4$ |
$42.8997431711$ |
$2714.5453822931822$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
$[2]$ |
$2$ |
$7$ |
$3038959.24669$ |
| 16.8.131...681.2 |
$x^{16} - 3 x^{15} - 2 x^{14} - 12 x^{13} + 40 x^{12} + 86 x^{11} - 76 x^{10} - 220 x^{9} - 501 x^{8} + 935 x^{7} + 1100 x^{6} - 772 x^{5} - 2866 x^{4} + 2964 x^{3} - 597 x^{2} - 110 x + 25$ |
$16$ |
[8,4] |
$3^{8}\cdot 53^{2}\cdot 61^{8}\cdot 193^{2}$ |
$4$ |
$42.8997431711$ |
$2714.5453822931822$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
trivial |
$2$ |
$11$ |
$65766096.7382$ |
| 16.0.131...681.2 |
$x^{16} - 3 x^{15} + 11 x^{14} - x^{13} + 15 x^{12} - 37 x^{11} + 104 x^{10} + 27 x^{9} - 61 x^{8} - 39 x^{7} + 452 x^{6} - 414 x^{5} + 60 x^{4} + 121 x^{3} + 57 x^{2} + 10 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 53^{2}\cdot 61^{8}\cdot 193^{2}$ |
$4$ |
$42.8997431711$ |
$2714.5453822931822$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1811) |
$[2]$ |
$2$ |
$7$ |
$1074717.97021$ |
| 16.16.145...064.1 |
$x^{16} - x^{15} - 25 x^{14} + 3 x^{13} + 190 x^{12} + 51 x^{11} - 571 x^{10} - 193 x^{9} + 802 x^{8} + 193 x^{7} - 571 x^{6} - 51 x^{5} + 190 x^{4} - 3 x^{3} - 25 x^{2} + x + 1$ |
$16$ |
[16,0] |
$2^{18}\cdot 3^{10}\cdot 7^{2}\cdot 61^{8}$ |
$4$ |
$43.1679775199$ |
$365.81596492664835$ |
|
|
? |
$C_2\wr \SL(2,3)$ (as 16T1669) |
trivial |
$2$ |
$15$ |
$120670916.616$ |
| 16.10.347...235.1 |
$x^{16} - 2 x^{15} - 28 x^{14} + 15 x^{13} + 246 x^{12} - 120 x^{11} - 1379 x^{10} + 516 x^{9} + 5443 x^{8} + 256 x^{7} - 11538 x^{6} - 4560 x^{5} + 9704 x^{4} + 5897 x^{3} - 1345 x^{2} - 1450 x - 236$ |
$16$ |
[10,3] |
$-\,3^{8}\cdot 5\cdot 7\cdot 53^{4}\cdot 61^{8}$ |
$5$ |
$45.5825655349$ |
$1155.985733589208$ |
|
|
|
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$12$ |
$76856580.4751$ |
| 16.6.347...235.1 |
$x^{16} - x^{15} + x^{14} + 16 x^{13} - 105 x^{12} + 175 x^{11} - 173 x^{10} - 1484 x^{9} + 1688 x^{8} + 6296 x^{7} + 129 x^{6} - 10408 x^{5} - 5378 x^{4} + 3686 x^{3} + 4020 x^{2} - 560 x - 875$ |
$16$ |
[6,5] |
$-\,3^{8}\cdot 5\cdot 7\cdot 53^{4}\cdot 61^{8}$ |
$5$ |
$45.5825655349$ |
$1155.985733589208$ |
|
|
|
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$10$ |
$36476384.631$ |
| 16.6.347...235.2 |
$x^{16} - 4 x^{15} + 6 x^{14} - 4 x^{13} - 142 x^{12} + 445 x^{11} - 651 x^{10} + 1183 x^{9} - 155 x^{8} + 2389 x^{7} + 318 x^{6} + 6787 x^{5} + 1064 x^{4} + 10946 x^{3} - 10080 x^{2} + 1253 x + 49$ |
$16$ |
[6,5] |
$-\,3^{8}\cdot 5\cdot 7\cdot 53^{4}\cdot 61^{8}$ |
$5$ |
$45.5825655349$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$10$ |
$44301934.0863$ |
| 16.10.347...235.2 |
$x^{16} - x^{15} - 21 x^{14} - 40 x^{13} + 39 x^{12} + 413 x^{11} + 843 x^{10} - 526 x^{9} - 4274 x^{8} - 4279 x^{7} + 4370 x^{6} + 11923 x^{5} + 6608 x^{4} - 4564 x^{3} - 8055 x^{2} - 4249 x - 833$ |
$16$ |
[10,3] |
$-\,3^{8}\cdot 5\cdot 7\cdot 53^{4}\cdot 61^{8}$ |
$5$ |
$45.5825655349$ |
$1155.985733589208$ |
|
|
? |
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$12$ |
$64912440.0636$ |
| 16.10.585...939.1 |
$x^{16} - 2 x^{15} - 5 x^{14} - 9 x^{13} + 184 x^{11} + 45 x^{10} - 672 x^{9} - 806 x^{8} + 175 x^{7} + 3733 x^{6} + 2765 x^{5} - 5283 x^{4} - 3384 x^{3} + 1259 x^{2} + 154 x + 4$ |
$16$ |
[10,3] |
$-\,3^{8}\cdot 53^{4}\cdot 59\cdot 61^{8}$ |
$4$ |
$47.0947789732$ |
$1500.8747731091928$ |
|
|
|
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$12$ |
$80745298.2032$ |
| 16.6.585...939.1 |
$x^{16} - 4 x^{15} - 6 x^{14} + 30 x^{13} - 113 x^{12} + 305 x^{11} - 450 x^{10} + 749 x^{9} - 763 x^{8} + 543 x^{7} - 1051 x^{6} + 2032 x^{5} - 4035 x^{4} + 5922 x^{3} - 3666 x^{2} + 503 x + 103$ |
$16$ |
[6,5] |
$-\,3^{8}\cdot 53^{4}\cdot 59\cdot 61^{8}$ |
$4$ |
$47.0947789732$ |
$1500.8747731091928$ |
|
|
|
$C_2\wr Q_8.A_4$ (as 16T1810) |
trivial |
$2$ |
$10$ |
$92669127.6657$ |
