| 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 $p$ |
| 15.3.114...000.1 |
$x^{15} - 5 x^{14} - 205 x^{13} + 485 x^{12} + 18665 x^{11} + 4191 x^{10} - 867445 x^{9} - 2845895 x^{8} + 13972715 x^{7} + 92089185 x^{6} + 35252577 x^{5} - 1319451745 x^{4} - 5926881845 x^{3} - 11283996635 x^{2} + 18937195585 x + 31450063523$ |
$15$ |
(3, 6) |
$2^{23}\cdot 5^{17}\cdot 149^{13}$ |
$3$ |
$1371.42932256$ |
$2264.3269651432283$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
$[40]$ |
$[40]$ |
$2$ |
$8$ |
$40150303614025224$ |
$3$ |
$149$ |
| 20.0.399...125.1 |
$x^{20} - 6 x^{19} + 30 x^{18} - 1060 x^{17} + 12221 x^{16} - 70190 x^{15} + 718724 x^{14} - 5034680 x^{13} + 43472431 x^{12} - 236282030 x^{11} + 1266915970 x^{10} - 6551196136 x^{9} + 26888672646 x^{8} - 82376920120 x^{7} + 232530371755 x^{6} - 563315121120 x^{5} + 1005027627810 x^{4} - 1199779764500 x^{3} + 1008354191025 x^{2} - 475118881950 x + 87368211275$ |
$20$ |
(0, 10) |
$5^{15}\cdot 149^{18}$ |
$2$ |
$302.061340104$ |
$302.0613401037295$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[5, 5, 50, 50]$ |
$[50, 50, 5, 5]$ |
$2$ |
$9$ |
$1675397299064.9917$ |
$0$ |
$149$ |
| 24.4.529...125.1 |
$x^{24} - 2 x^{23} + 32 x^{22} + 2424 x^{21} - 8391 x^{20} - 216487 x^{19} - 614796 x^{18} - 27850734 x^{17} - 376351093 x^{16} - 2729225003 x^{15} - 19081736696 x^{14} - 183509248078 x^{13} - 724791091972 x^{12} - 2551487110059 x^{11} + 7929973713741 x^{10} + 137534406718492 x^{9} + 2607823839824001 x^{8} + 6657109113531594 x^{7} + 107497115747347673 x^{6} + 168549865887958763 x^{5} + 1767412848634061926 x^{4} - 6066224588639277287 x^{3} - 6789835303748244318 x^{2} + 10366847196876110809 x - 22732430452102984076$ |
$24$ |
(4, 10) |
$5^{39}\cdot 149^{20}$ |
$2$ |
$884.7382713313174$ |
$2083.814952609198$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$149$ |
| 24.4.529...125.4 |
$x^{24} - 7 x^{23} + 103 x^{22} - 4684 x^{21} + 42792 x^{20} - 604234 x^{19} + 11225948 x^{18} - 78745502 x^{17} + 1051548701 x^{16} - 14383137583 x^{15} + 85657689791 x^{14} - 1003459690667 x^{13} + 8787147531598 x^{12} - 36282628808304 x^{11} + 256040228284787 x^{10} - 322407516412444 x^{9} + 1013019224328463 x^{8} + 66615430857564618 x^{7} - 632051043110538544 x^{6} - 5702081496796538363 x^{5} - 10851373311045042219 x^{4} + 92249536788217761648 x^{3} + 1122067748117692054268 x^{2} + 3802216454740899657001 x + 1175531490184802981207$ |
$24$ |
(4, 10) |
$5^{39}\cdot 149^{20}$ |
$2$ |
$884.7382713313174$ |
$2083.814952609198$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$149$ |
| 24.4.132...125.2 |
$x^{24} - 2 x^{23} + 32 x^{22} + 189 x^{21} + 5764 x^{20} - 89837 x^{19} - 1028271 x^{18} - 13274809 x^{17} - 93578148 x^{16} - 1722788113 x^{15} - 1340980921 x^{14} - 58014463703 x^{13} + 685859047428 x^{12} + 6400548586951 x^{11} - 6860181991789 x^{10} - 40156594860183 x^{9} + 3845269392021726 x^{8} - 18797644677486931 x^{7} - 31510553075715397 x^{6} + 695526930216912573 x^{5} - 432792589826176049 x^{4} - 14050215246264991187 x^{3} + 34739715477877596507 x^{2} + 69590173923840856824 x - 366698381038675868096$ |
$24$ |
(4, 10) |
$5^{41}\cdot 149^{20}$ |
$2$ |
$1011.7246103917876$ |
$2083.814952609198$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$149$ |
| 24.4.132...125.4 |
$x^{24} - 12 x^{23} + 271 x^{22} - 590 x^{21} + 40695 x^{20} + 904519 x^{19} + 1277447 x^{18} + 189095024 x^{17} + 1732749360 x^{16} + 16276158725 x^{15} + 207290443976 x^{14} + 1538479325013 x^{13} + 16255589971246 x^{12} + 102920474610045 x^{11} + 427374355794280 x^{10} + 2969086642896399 x^{9} + 5021056994043387 x^{8} + 317950721485879 x^{7} + 66052933181887775 x^{6} - 380604735230379460 x^{5} - 723106578278422559 x^{4} + 3951985230524279208 x^{3} - 6382631992225093239 x^{2} + 1126494081599767680 x + 7649352307379696165$ |
$24$ |
(4, 10) |
$5^{41}\cdot 149^{20}$ |
$2$ |
$1011.7246103917876$ |
$2083.814952609198$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$149$ |
