| 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 |
| 12.0.686...125.1 |
$x^{12} - x^{11} + 13 x^{10} - 36 x^{9} + 203 x^{8} + 718 x^{7} + 2114 x^{6} + 4269 x^{5} + 13201 x^{4} + 14773 x^{3} + 16093 x^{2} + 15972 x + 14641$ |
$12$ |
[0,6] |
$5^{9}\cdot 37^{8}$ |
$2$ |
$37.1274668761$ |
$37.12746687605088$ |
✓ |
✓ |
|
$C_{12}$ (as 12T1) |
$[7, 7]$ |
$10$ |
$5$ |
$5133.82158211$ |
| 12.12.500...125.1 |
$x^{12} - x^{11} - 62 x^{10} - 14 x^{9} + 1329 x^{8} + 1402 x^{7} - 11278 x^{6} - 17844 x^{5} + 32825 x^{4} + 67959 x^{3} - 2310 x^{2} - 38017 x - 7919$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{9}\cdot 37^{8}$ |
$3$ |
$64.3066589857$ |
$64.30665898565067$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$9734294.63743$ |
| 12.12.280...000.1 |
$x^{12} - 4 x^{11} - 57 x^{10} + 146 x^{9} + 1238 x^{8} - 1388 x^{7} - 11111 x^{6} + 2146 x^{5} + 36221 x^{4} + 11712 x^{3} - 19262 x^{2} - 5282 x + 101$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{9}\cdot 37^{8}$ |
$3$ |
$74.2549337521$ |
$74.25493375210176$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$10882467.7706$ |
| 12.0.301...232.1 |
$x^{12} - 4 x^{11} - 30 x^{10} + 56 x^{9} + 671 x^{8} + 364 x^{7} - 7214 x^{6} - 19844 x^{5} + 10058 x^{4} + 155196 x^{3} + 361120 x^{2} + 384832 x + 174833$ |
$12$ |
[0,6] |
$2^{33}\cdot 37^{8}$ |
$2$ |
$74.696508815$ |
$74.69650881502758$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[13, 13]$ |
$2$ |
$5$ |
$8961.68747011$ |
| 12.12.301...232.1 |
$x^{12} - 4 x^{11} - 54 x^{10} + 136 x^{9} + 1143 x^{8} - 1108 x^{7} - 10526 x^{6} - 1940 x^{5} + 34370 x^{4} + 30556 x^{3} - 10064 x^{2} - 13104 x - 2543$ |
$12$ |
[12,0] |
$2^{33}\cdot 37^{8}$ |
$2$ |
$74.696508815$ |
$74.69650881502758$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$23555582.4933$ |
| 12.0.372...533.1 |
$x^{12} - x^{11} - 44 x^{10} - 38 x^{9} + 855 x^{8} + 1626 x^{7} - 7196 x^{6} - 23416 x^{5} + 21953 x^{4} + 169301 x^{3} + 261476 x^{2} + 175353 x + 54317$ |
$12$ |
[0,6] |
$13^{9}\cdot 37^{8}$ |
$2$ |
$76.0195562699$ |
$76.01955626985882$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[73]$ |
$2$ |
$5$ |
$17287.4310274$ |
| 12.12.416...737.1 |
$x^{12} - x^{11} - 68 x^{10} + 3 x^{9} + 1528 x^{8} + 1135 x^{7} - 12600 x^{6} - 17100 x^{5} + 25453 x^{4} + 41563 x^{3} - 10018 x^{2} - 22360 x - 2789$ |
$12$ |
[12,0] |
$17^{9}\cdot 37^{8}$ |
$2$ |
$92.9617963176$ |
$92.96179631764876$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$65606044.7889$ |
| 12.12.807...125.1 |
$x^{12} - x^{11} - 77 x^{10} - 9 x^{9} + 1939 x^{8} + 1192 x^{7} - 18668 x^{6} - 8224 x^{5} + 78090 x^{4} + 3434 x^{3} - 110290 x^{2} + 15653 x + 23111$ |
$12$ |
[12,0] |
$5^{9}\cdot 7^{6}\cdot 37^{8}$ |
$3$ |
$98.2300441638$ |
$98.23004416381879$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$167516541.331$ |
| 12.0.179...000.1 |
$x^{12} - 4 x^{11} - 12 x^{10} - 4 x^{9} + 623 x^{8} + 652 x^{7} - 4226 x^{6} - 27584 x^{5} + 4436 x^{4} + 283092 x^{3} + 1152868 x^{2} + 1882348 x + 1804241$ |
$12$ |
[0,6] |
$2^{18}\cdot 5^{9}\cdot 37^{8}$ |
$3$ |
$105.012334385$ |
$105.01233438533802$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2474]$ |
$2$ |
$5$ |
$5133.82158211$ |
| 12.12.179...000.1 |
$x^{12} - 4 x^{11} - 72 x^{10} + 196 x^{9} + 1803 x^{8} - 3028 x^{7} - 16346 x^{6} + 24856 x^{5} + 46976 x^{4} - 89468 x^{3} + 16588 x^{2} + 22788 x - 7799$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{9}\cdot 37^{8}$ |
$3$ |
$105.012334385$ |
$105.01233438533802$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$389073567.435$ |
| 12.12.121...125.1 |
$x^{12} - x^{11} - 92 x^{10} - 4 x^{9} + 2729 x^{8} + 1012 x^{7} - 30478 x^{6} + 3506 x^{5} + 139735 x^{4} - 113051 x^{3} - 119910 x^{2} + 120373 x + 2101$ |
$12$ |
[12,0] |
$5^{9}\cdot 11^{6}\cdot 37^{8}$ |
$3$ |
$123.137877044$ |
$123.13787704420932$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 2]$ |
$2$ |
$11$ |
$201110977.318$ |
| 12.0.204...000.1 |
$x^{12} - 4 x^{11} + 3 x^{10} - 54 x^{9} + 778 x^{8} + 372 x^{7} + 629 x^{6} - 35694 x^{5} + 33501 x^{4} + 423832 x^{3} + 2496638 x^{2} + 4550838 x + 6393601$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 37^{8}$ |
$4$ |
$128.613317971$ |
$128.61331797130134$ |
✓ |
✓ |
|
$C_{12}$ (as 12T1) |
$[2, 9074]$ |
$2$ |
$5$ |
$5133.82158211$ |
| 12.0.219...128.1 |
$x^{12} - 4 x^{11} - 6 x^{10} - 24 x^{9} + 631 x^{8} + 684 x^{7} - 4606 x^{6} - 34548 x^{5} - 18126 x^{4} + 341212 x^{3} + 1521584 x^{2} + 2516208 x + 2118577$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{6}\cdot 37^{8}$ |
$3$ |
$129.378148416$ |
$129.3781484156443$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[6602]$ |
$2$ |
$5$ |
$8961.68747011$ |
| 12.12.219...128.1 |
$x^{12} - 4 x^{11} - 78 x^{10} + 216 x^{9} + 2047 x^{8} - 3732 x^{7} - 19918 x^{6} + 29916 x^{5} + 64794 x^{4} - 100292 x^{3} - 24352 x^{2} + 60576 x - 9071$ |
$12$ |
[12,0] |
$2^{33}\cdot 3^{6}\cdot 37^{8}$ |
$3$ |
$129.378148416$ |
$129.3781484156443$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$565004627.561$ |
| 12.12.271...557.1 |
$x^{12} - x^{11} - 83 x^{10} + 53 x^{9} + 2129 x^{8} - 194 x^{7} - 16608 x^{6} - 12548 x^{5} + 13750 x^{4} + 7204 x^{3} - 3308 x^{2} - 745 x + 211$ |
$12$ |
[12,0] |
$3^{6}\cdot 13^{9}\cdot 37^{8}$ |
$3$ |
$131.669733828$ |
$131.66973382823667$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$640446361.126$ |
| 12.0.331...125.1 |
$x^{12} - x^{11} - 2 x^{10} - 34 x^{9} + 689 x^{8} + 2542 x^{7} + 7082 x^{6} - 20224 x^{5} - 8435 x^{4} + 292459 x^{3} + 2868210 x^{2} + 7346803 x + 12193561$ |
$12$ |
[0,6] |
$5^{9}\cdot 13^{6}\cdot 37^{8}$ |
$3$ |
$133.86498555$ |
$133.86498554969228$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[5594]$ |
$2$ |
$5$ |
$5133.82158211$ |
| 12.0.509...349.1 |
$x^{12} - x^{11} - 38 x^{10} + 26 x^{9} + 731 x^{8} + 2134 x^{7} + 2176 x^{6} - 18276 x^{5} - 71867 x^{4} - 81519 x^{3} + 65946 x^{2} + 943921 x + 1870007$ |
$12$ |
[0,6] |
$29^{9}\cdot 37^{8}$ |
$2$ |
$138.760646459$ |
$138.76064645906234$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[4, 1492]$ |
$2$ |
$5$ |
$9408.21364884$ |
| 12.12.131...000.1 |
$x^{12} - 4 x^{11} - 132 x^{10} + 396 x^{9} + 5863 x^{8} - 14388 x^{7} - 95986 x^{6} + 267696 x^{5} + 422796 x^{4} - 1899788 x^{3} + 1680788 x^{2} - 74532 x - 251999$ |
$12$ |
[12,0] |
$2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 37^{8}$ |
$4$ |
$181.886698577$ |
$181.88669857681768$ |
|
✓ |
|
$C_{12}$ (as 12T1) |
$[2]$ |
$2$ |
$11$ |
$4690661300.109102$ |
| 12.0.131...000.1 |
$x^{12} - 4 x^{11} + 48 x^{10} - 204 x^{9} + 2323 x^{8} - 3348 x^{7} + 45974 x^{6} - 100824 x^{5} + 707976 x^{4} + 849892 x^{3} + 16302428 x^{2} + 25990548 x + 84787321$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 37^{8}$ |
$4$ |
$181.886698577$ |
$181.88669857681768$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[2, 15482]$ |
$2$ |
$5$ |
$5133.821582106669$ |
| 16.0.275...801.1 |
$x^{16} - 5 x^{14} + 46 x^{12} - 144 x^{10} + 575 x^{8} - 1079 x^{6} + 2391 x^{4} - 2217 x^{2} + 2704$ |
$16$ |
[0,8] |
$23^{8}\cdot 37^{8}$ |
$2$ |
$29.171904291629644$ |
$53.25148632433377$ |
|
|
|
$\SL(2,3):C_2$ (as 16T60) |
$[3]$ |
$2$ |
$7$ |
$716382.0233516465$ |
| 16.0.175...081.1 |
$x^{16} - x^{15} + 13 x^{14} - 9 x^{13} + 72 x^{12} + 9 x^{11} + 238 x^{10} + 353 x^{9} + 512 x^{8} + 970 x^{7} + 228 x^{6} - 309 x^{5} - 453 x^{4} - 624 x^{3} + 687 x^{2} - 157 x + 13$ |
$16$ |
[0,8] |
$29^{8}\cdot 37^{8}$ |
$2$ |
$32.7566787083$ |
$59.79526776272607$ |
✓ |
|
? |
$\SL(2,3):C_2$ (as 16T60) |
trivial |
$2$ |
$7$ |
$310200.468169$ |
| 16.0.299...161.1 |
$x^{16} - 4 x^{15} + 10 x^{14} - 19 x^{13} + 62 x^{12} - 115 x^{11} + 331 x^{10} - 769 x^{9} + 1546 x^{8} - 1742 x^{7} + 3761 x^{6} - 5848 x^{5} + 4933 x^{4} - 2439 x^{3} + 4388 x^{2} + 96 x + 1024$ |
$16$ |
[0,8] |
$31^{8}\cdot 37^{8}$ |
$2$ |
$33.8673884437522$ |
$61.822798900065244$ |
|
|
|
$\SL(2,3):C_2$ (as 16T60) |
$[3]$ |
$2$ |
$7$ |
$2210225.488219896$ |
| 16.0.410...521.1 |
$x^{16} - 8 x^{15} + 26 x^{14} - 42 x^{13} + 114 x^{12} - 502 x^{11} + 1223 x^{10} - 1561 x^{9} + 1583 x^{8} - 2488 x^{7} + 4167 x^{6} - 4809 x^{5} + 6107 x^{4} - 6752 x^{3} + 5310 x^{2} - 2369 x + 529$ |
$16$ |
[0,8] |
$37^{8}\cdot 43^{8}$ |
$2$ |
$39.88734135035826$ |
$72.81184632989822$ |
|
|
? |
$\SL(2,3):C_2$ (as 16T60) |
trivial |
$2$ |
$7$ |
$1362800.3056570473$ |
| 16.16.244...056.1 |
$x^{16} - 31 x^{14} + 396 x^{12} - 2708 x^{10} + 10731 x^{8} - 24827 x^{6} + 32001 x^{4} - 20380 x^{2} + 4624$ |
$16$ |
[16,0] |
$2^{12}\cdot 19^{8}\cdot 37^{8}$ |
$3$ |
$44.5913026127$ |
$223.6223515990486$ |
|
|
? |
$C_2^3.\SL(2,3)$ (as 16T439) |
trivial |
$2$ |
$15$ |
$90647999.7719$ |
| 16.16.344...536.1 |
$x^{16} - x^{15} - 37 x^{14} + 40 x^{13} + 511 x^{12} - 513 x^{11} - 3415 x^{10} + 2714 x^{9} + 11778 x^{8} - 5509 x^{7} - 20521 x^{6} + 1733 x^{5} + 15885 x^{4} + 4005 x^{3} - 3895 x^{2} - 2165 x - 307$ |
$16$ |
[16,0] |
$2^{4}\cdot 19^{10}\cdot 37^{8}$ |
$3$ |
$45.559543257$ |
$258.3008364266063$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T732) |
trivial |
$2$ |
$15$ |
$164419529.044$ |
| 16.0.344...536.1 |
$x^{16} - x^{15} + 4 x^{14} + 17 x^{13} - 17 x^{12} + 147 x^{11} + 25 x^{10} - 18 x^{9} + 1017 x^{8} - 375 x^{7} + 1273 x^{6} - 985 x^{5} + 2347 x^{4} + 2727 x^{3} + 4562 x^{2} + 2596 x + 949$ |
$16$ |
[0,8] |
$2^{4}\cdot 19^{10}\cdot 37^{8}$ |
$3$ |
$45.559543257$ |
$258.3008364266063$ |
✓ |
|
? |
$C_2^4.\SL(2,3)$ (as 16T732) |
$[2, 10]$ |
$2$ |
$7$ |
$168824.791868$ |
| 16.0.390...896.1 |
$x^{16} + 31 x^{14} + 396 x^{12} + 2708 x^{10} + 10731 x^{8} + 24827 x^{6} + 32001 x^{4} + 20380 x^{2} + 4624$ |
$16$ |
[0,8] |
$2^{16}\cdot 19^{8}\cdot 37^{8}$ |
$3$ |
$53.0282943343$ |
$265.93329159522875$ |
✓ |
|
? |
$C_2^3.\SL(2,3)$ (as 16T439) |
$[2, 130]$ |
$2$ |
$7$ |
$84412.3959339$ |
| 16.12.108...661.1 |
$x^{16} - 8 x^{15} + 19 x^{14} + 7 x^{13} - 95 x^{12} + 115 x^{11} + 63 x^{10} - 249 x^{9} + 154 x^{8} + 141 x^{7} - 234 x^{6} + 18 x^{5} + 110 x^{4} - 28 x^{3} - 18 x^{2} + 4 x + 1$ |
$16$ |
[12,2] |
$7\cdot 29^{8}\cdot 37^{8}\cdot 883$ |
$4$ |
$56.5250600581$ |
$4701.06425007895$ |
|
|
✓ |
$C_2\wr C_2^3:C_3$ (as 16T1658) |
trivial |
$2$ |
$13$ |
$347789470.981$ |
| 16.0.444...281.1 |
$x^{16} + 9 x^{14} + 105 x^{12} + 361 x^{10} + 1405 x^{8} - 1371 x^{6} + 8165 x^{4} + 19820 x^{2} + 10816$ |
$16$ |
[0,8] |
$37^{8}\cdot 103^{8}$ |
$2$ |
$61.73329733620261$ |
$112.69027232473408$ |
|
|
|
$\SL(2,3):C_2$ (as 16T60) |
$[5]$ |
$2$ |
$7$ |
$227218172.6701016$ |
| 16.0.882...216.1 |
$x^{16} - 7 x^{15} + 38 x^{14} - 176 x^{13} + 702 x^{12} - 2227 x^{11} + 6112 x^{10} - 13083 x^{9} + 31473 x^{8} - 49147 x^{7} + 80892 x^{6} - 136431 x^{5} + 303508 x^{4} - 105096 x^{3} + 396174 x^{2} - 515639 x + 160747$ |
$16$ |
[0,8] |
$2^{12}\cdot 19^{10}\cdot 37^{8}$ |
$3$ |
$64.4309239696$ |
$258.3008364266063$ |
✓ |
|
? |
$C_2^4.\SL(2,3)$ (as 16T732) |
$[2, 170]$ |
$2$ |
$7$ |
$168824.791868$ |
| 16.16.882...216.1 |
$x^{16} - 49 x^{14} + 942 x^{12} - 9367 x^{10} + 52478 x^{8} - 166706 x^{6} + 282663 x^{4} - 219488 x^{2} + 61009$ |
$16$ |
[16,0] |
$2^{12}\cdot 19^{10}\cdot 37^{8}$ |
$3$ |
$64.4309239696$ |
$258.3008364266063$ |
|
|
? |
$C_2^4.\SL(2,3)$ (as 16T732) |
trivial |
$2$ |
$15$ |
$2881793519.03$ |
| 16.8.671...641.1 |
$x^{16} - 22 x^{14} + 135 x^{12} - 213 x^{10} + 551 x^{8} - 797 x^{6} + 443 x^{4} - 86 x^{2} + 1$ |
$16$ |
[8,4] |
$7^{2}\cdot 29^{8}\cdot 37^{8}\cdot 883^{2}$ |
$4$ |
$97.5398770744$ |
$4701.06425007895$ |
|
|
? |
$C_2\wr C_2^3:C_3$ (as 16T1656) |
$[2]$ |
$2$ |
$11$ |
$7030073415.12$ |
| 24.0.250...625.1 |
$x^{24} - x^{23} - 12 x^{22} + 59 x^{21} - 70 x^{20} + 656 x^{19} + 3603 x^{18} - 23821 x^{17} + 17836 x^{16} + 310712 x^{15} + 581972 x^{14} - 450391 x^{13} - 2503560 x^{12} - 7942312 x^{11} - 13371150 x^{10} + 9746067 x^{9} + 97143531 x^{8} + 101893385 x^{7} - 484484 x^{6} - 121448426 x^{5} - 170245548 x^{4} - 175545590 x^{3} + 19487171 x^{2} + 233846052 x + 214358881$ |
$24$ |
[0,12] |
$3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$64.3066589857$ |
$64.30665898565067$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[7, 7, 21]$ |
$30$ |
$11$ |
$9967917708.730377$ |
| 24.0.789...000.1 |
$x^{24} - 25 x^{22} + 503 x^{20} - 9646 x^{18} + 182809 x^{16} - 1055086 x^{14} + 5241618 x^{12} - 24439847 x^{10} + 99184185 x^{8} - 132179069 x^{6} + 173627619 x^{4} - 216130442 x^{2} + 214358881$ |
$24$ |
[0,12] |
$2^{24}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$74.2549337521$ |
$74.25493375210176$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[7, 273]$ |
$20$ |
$11$ |
$11143646997.107319$ |
| 24.0.582...736.1 |
$x^{24} + 127493 x^{16} + 66883114 x^{8} + 214358881$ |
$24$ |
[0,12] |
$2^{72}\cdot 37^{16}$ |
$2$ |
$88.8296197487$ |
$88.82961974869428$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[13, 273]$ |
$16$ |
$11$ |
$48241832946.27025$ |
| 24.0.323...000.1 |
$x^{24} - 8 x^{23} - 74 x^{22} + 572 x^{21} + 3016 x^{20} - 17760 x^{19} - 85518 x^{18} + 285704 x^{17} + 1661305 x^{16} - 1906632 x^{15} - 20467124 x^{14} - 10151352 x^{13} + 139734456 x^{12} + 275550256 x^{11} - 290937638 x^{10} - 1685333160 x^{9} - 1899102168 x^{8} + 1612921144 x^{7} + 7900602944 x^{6} + 12266775908 x^{5} + 11114510270 x^{4} + 6111392440 x^{3} + 2347621720 x^{2} + 1082467988 x + 466788641$ |
$24$ |
[0,12] |
$2^{36}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$105.012334385$ |
$105.01233438533802$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[7, 7, 273]$ |
$10$ |
$11$ |
$398411333053.5562$ |
| 24.0.323...000.2 |
$x^{24} - 8 x^{23} - 62 x^{22} + 484 x^{21} + 2436 x^{20} - 13248 x^{19} - 70450 x^{18} + 179416 x^{17} + 1399257 x^{16} - 378792 x^{15} - 17124156 x^{14} - 25959832 x^{13} + 101802748 x^{12} + 390836320 x^{11} + 116024630 x^{10} - 1958107528 x^{9} - 4696824292 x^{8} - 1953979976 x^{7} + 12773845768 x^{6} + 35911367324 x^{5} + 52719242130 x^{4} + 51730545864 x^{3} + 36485133200 x^{2} + 18160149436 x + 5290407641$ |
$24$ |
[0,12] |
$2^{36}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$105.012334385$ |
$105.01233438533802$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[7, 25977]$ |
$10$ |
$11$ |
$6725277456.98278$ |
| 24.24.419...000.1 |
$x^{24} - 8 x^{23} - 89 x^{22} + 682 x^{21} + 3906 x^{20} - 24500 x^{19} - 110918 x^{18} + 465104 x^{17} + 2123965 x^{16} - 4632212 x^{15} - 26339374 x^{14} + 16492238 x^{13} + 195692836 x^{12} + 97964556 x^{11} - 749173448 x^{10} - 1078182300 x^{9} + 852063037 x^{8} + 2904335054 x^{7} + 1643983249 x^{6} - 1029742132 x^{5} - 1466625360 x^{4} - 423087310 x^{3} + 80882765 x^{2} + 54298258 x + 6170341$ |
$24$ |
[24,0] |
$2^{24}\cdot 3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$4$ |
$128.613317971$ |
$128.61331797130134$ |
|
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$300740116611316740$ |
| 24.0.419...000.1 |
$x^{24} + 125 x^{22} + 6474 x^{20} + 184744 x^{18} + 3233931 x^{16} + 36381162 x^{14} + 266574130 x^{12} + 1255588572 x^{10} + 3640456743 x^{8} + 5948206913 x^{6} + 4652648356 x^{4} + 1408706509 x^{2} + 62710561$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$4$ |
$128.613317971$ |
$128.61331797130134$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[13, 27222]$ |
$4$ |
$11$ |
$19935835417.460754$ |
| 24.0.419...000.2 |
$x^{24} - 8 x^{23} - 59 x^{22} + 462 x^{21} + 2321 x^{20} - 12320 x^{19} - 67133 x^{18} + 159434 x^{17} + 1330945 x^{16} - 134992 x^{15} - 16036704 x^{14} - 27485662 x^{13} + 91132236 x^{12} + 394884996 x^{11} + 212538172 x^{10} - 1824506750 x^{9} - 4975740968 x^{8} - 2814599106 x^{7} + 13726720304 x^{6} + 44169518338 x^{5} + 74094490570 x^{4} + 87039245120 x^{3} + 82997825665 x^{2} + 57644499198 x + 27519581881$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$4$ |
$128.613317971$ |
$128.61331797130134$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[7, 63518]$ |
$10$ |
$11$ |
$149648037300.06693$ |
| 24.0.419...000.3 |
$x^{24} - 4 x^{23} + 73 x^{22} - 64 x^{21} + 2595 x^{20} + 194 x^{19} + 64108 x^{18} + 69106 x^{17} + 1048576 x^{16} + 1235438 x^{15} + 11305562 x^{14} + 14569876 x^{13} + 83892415 x^{12} + 87789942 x^{11} + 376397320 x^{10} + 358161378 x^{9} + 1087344601 x^{8} + 565440970 x^{7} + 843950596 x^{6} + 157258846 x^{5} + 429229107 x^{4} + 99376060 x^{3} + 29844986 x^{2} - 533482 x + 10201$ |
$24$ |
[0,12] |
$2^{24}\cdot 3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$4$ |
$128.613317971$ |
$128.61331797130134$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[190554]$ |
$6$ |
$11$ |
$22287293994.214638$ |
| 24.0.483...384.1 |
$x^{24} - 8 x^{23} - 80 x^{22} + 616 x^{21} + 3372 x^{20} - 20456 x^{19} - 94784 x^{18} + 356984 x^{17} + 1794427 x^{16} - 3047840 x^{15} - 21605812 x^{14} + 3304760 x^{13} + 150284026 x^{12} + 156661920 x^{11} - 464783780 x^{10} - 1155870120 x^{9} - 350268644 x^{8} + 1982745608 x^{7} + 4075466908 x^{6} + 5299688864 x^{5} + 6390494712 x^{4} + 6839288144 x^{3} + 5187598340 x^{2} + 2285047168 x + 468801937$ |
$24$ |
[0,12] |
$2^{66}\cdot 3^{12}\cdot 37^{16}$ |
$3$ |
$129.378148416$ |
$129.3781484156443$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[65, 195]$ |
$6$ |
$11$ |
$578564738622.0123$ |
| 24.0.483...384.2 |
$x^{24} - 8 x^{23} - 56 x^{22} + 440 x^{21} + 2212 x^{20} - 11432 x^{19} - 64120 x^{18} + 141240 x^{17} + 1256811 x^{16} + 68448 x^{15} - 14905092 x^{14} - 28429992 x^{13} + 79047378 x^{12} + 390023872 x^{11} + 290365908 x^{10} - 1788382920 x^{9} - 5888745820 x^{8} - 5580135032 x^{7} + 12389609260 x^{6} + 55784544784 x^{5} + 108393707744 x^{4} + 131971429616 x^{3} + 104062581524 x^{2} + 49472019600 x + 11097198433$ |
$24$ |
[0,12] |
$2^{66}\cdot 3^{12}\cdot 37^{16}$ |
$3$ |
$129.378148416$ |
$129.3781484156443$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[5, 49515]$ |
$6$ |
$11$ |
$48241832946.27025$ |
| 24.24.132...000.1 |
$x^{24} - 8 x^{23} - 92 x^{22} + 704 x^{21} + 4111 x^{20} - 26028 x^{19} - 117090 x^{18} + 509816 x^{17} + 2231002 x^{16} - 5367792 x^{15} - 27523076 x^{14} + 24287088 x^{13} + 205463193 x^{12} + 41747800 x^{11} - 825295310 x^{10} - 836059888 x^{9} + 1317870833 x^{8} + 2577895764 x^{7} + 362957148 x^{6} - 1766856056 x^{5} - 1049216470 x^{4} + 156169824 x^{3} + 275479570 x^{2} + 74671276 x + 6310201$ |
$24$ |
[24,0] |
$2^{48}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$148.509867504$ |
$148.50986750420353$ |
|
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[3]$ |
$2$ |
$23$ |
$540203986139263400$ |
| 24.0.132...000.1 |
$x^{24} + 100 x^{22} - 20 x^{21} + 4283 x^{20} + 800 x^{19} + 100534 x^{18} + 104780 x^{17} + 1411714 x^{16} + 3216200 x^{15} + 14103044 x^{14} + 45119040 x^{13} + 128250693 x^{12} + 368563800 x^{11} + 958839258 x^{10} + 2225567320 x^{9} + 4890015045 x^{8} + 9909590960 x^{7} + 17733794116 x^{6} + 28210650640 x^{5} + 40261970054 x^{4} + 49556581960 x^{3} + 45869948198 x^{2} + 25925858480 x + 6509677241$ |
$24$ |
[0,12] |
$2^{48}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$148.509867504$ |
$148.50986750420353$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[96486]$ |
$4$ |
$11$ |
$398411333053.5562$ |
| 24.0.132...000.2 |
$x^{24} - 8 x^{23} - 44 x^{22} + 352 x^{21} + 1791 x^{20} - 7980 x^{19} - 54538 x^{18} + 70984 x^{17} + 1106130 x^{16} + 1116688 x^{15} - 12963524 x^{14} - 42646992 x^{13} + 44169161 x^{12} + 524355736 x^{11} + 893174282 x^{10} - 1865519120 x^{9} - 10923568263 x^{8} - 16882482156 x^{7} + 13646410924 x^{6} + 113134875128 x^{5} + 251119945850 x^{4} + 323605399520 x^{3} + 260370792930 x^{2} + 122749357868 x + 26178734321$ |
$24$ |
[0,12] |
$2^{48}\cdot 5^{18}\cdot 37^{16}$ |
$3$ |
$148.509867504$ |
$148.50986750420353$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[675402]$ |
$2$ |
$11$ |
$11143646997.107319$ |
| 24.24.309...576.1 |
$x^{24} - 8 x^{23} - 92 x^{22} + 704 x^{21} + 4114 x^{20} - 26048 x^{19} - 117136 x^{18} + 510888 x^{17} + 2226132 x^{16} - 5400240 x^{15} - 27340740 x^{14} + 24986280 x^{13} + 203157462 x^{12} + 33109840 x^{11} - 814255980 x^{10} - 784744176 x^{9} + 1300194263 x^{8} + 2418787456 x^{7} + 330759964 x^{6} - 1501084256 x^{5} - 818273848 x^{4} + 118554056 x^{3} + 142936700 x^{2} + 13353000 x - 1326863$ |
$24$ |
[24,0] |
$2^{72}\cdot 3^{12}\cdot 37^{16}$ |
$3$ |
$153.857414622$ |
$153.85741462176222$ |
|
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
trivial |
$2$ |
$23$ |
$6133024406480763000$ |
| 24.0.309...576.1 |
$x^{24} + 100 x^{22} + 4238 x^{20} - 72 x^{19} + 99584 x^{18} + 18000 x^{17} + 1431472 x^{16} + 706896 x^{15} + 13128836 x^{14} + 11429712 x^{13} + 81954702 x^{12} + 95671584 x^{11} + 357149324 x^{10} + 439125480 x^{9} + 1165132963 x^{8} + 1442564784 x^{7} + 1847097084 x^{6} + 1388445552 x^{5} - 3772546652 x^{4} - 1837560960 x^{3} + 16709249612 x^{2} - 16338012912 x + 6468904129$ |
$24$ |
[0,12] |
$2^{72}\cdot 3^{12}\cdot 37^{16}$ |
$3$ |
$153.857414622$ |
$153.85741462176222$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[138642]$ |
$8$ |
$11$ |
$578564738622.0123$ |
| 24.0.309...576.2 |
$x^{24} - 8 x^{23} - 44 x^{22} + 352 x^{21} + 1794 x^{20} - 8000 x^{19} - 54464 x^{18} + 71336 x^{17} + 1102708 x^{16} + 1101136 x^{15} - 12896068 x^{14} - 42193048 x^{13} + 44025094 x^{12} + 517633680 x^{11} + 877800100 x^{10} - 1842113328 x^{9} - 10757887577 x^{8} - 16643852416 x^{7} + 13516041484 x^{6} + 112825019552 x^{5} + 253449955224 x^{4} + 332536241096 x^{3} + 274273108220 x^{2} + 133356132040 x + 29426629249$ |
$24$ |
[0,12] |
$2^{72}\cdot 3^{12}\cdot 37^{16}$ |
$3$ |
$153.857414622$ |
$153.85741462176222$ |
✓ |
✓ |
|
$C_2\times C_{12}$ (as 24T2) |
$[13, 85826]$ |
$2$ |
$11$ |
$37009091870.61969$ |
| 24.0.171...000.1 |
$x^{24} - 2 x^{23} + 45 x^{22} - 146 x^{21} + 1823 x^{20} + 3466 x^{19} + 52848 x^{18} + 106546 x^{17} + 1613689 x^{16} + 983218 x^{15} + 13553270 x^{14} + 8602138 x^{13} + 100321032 x^{12} - 322514132 x^{11} + 970930263 x^{10} - 1734879882 x^{9} + 4625489997 x^{8} - 6177840944 x^{7} + 7421648527 x^{6} - 7673706640 x^{5} + 8002793493 x^{4} - 2094657766 x^{3} + 543440762 x^{2} - 135377916 x + 28398241$ |
$24$ |
[0,12] |
$2^{36}\cdot 3^{12}\cdot 5^{18}\cdot 37^{16}$ |
$4$ |
$181.886698577$ |
$181.88669857681768$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
$[7, 325122]$ |
$10$ |
$11$ |
$231885256438.8789$ |
