| 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 |
| 10.2.116...000.1 |
$x^{10} - 4 x^{9} - 152 x^{8} + 1668 x^{7} - 10768 x^{6} + 218998 x^{5} - 3701688 x^{4} + 31675372 x^{3} - 143249842 x^{2} + 331145280 x - 309744081$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{6}\cdot 197^{8}$ |
$3$ |
$508.74479273330377$ |
$647.6576171727737$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
trivial |
$2$ |
$5$ |
$7046191053.030855$ |
| 10.2.336...000.1 |
$x^{10} - 4 x^{9} - 941 x^{8} + 25784 x^{7} - 265610 x^{6} + 101740 x^{5} + 7847806 x^{4} + 178396256 x^{3} - 1296471695 x^{2} - 18321482368 x + 143601975799$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{6}\cdot 13^{5}\cdot 197^{8}$ |
$4$ |
$1129.1474451500058$ |
$1437.4612855171638$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
trivial |
$2$ |
$5$ |
$389979031921.8397$ |
| 10.2.772...125.1 |
$x^{10} - 5 x^{9} + 5 x^{8} + 10 x^{7} - 15 x^{6} + 32907263 x^{5} - 82268170 x^{4} + 493609120 x^{3} - 658145485 x^{2} + 575877290 x + 270721989537761$ |
$10$ |
[2,4] |
$5^{11}\cdot 17^{8}\cdot 197^{8}$ |
$3$ |
$3879.7087365995644$ |
$4204.822069725841$ |
|
|
? |
$F_5$ (as 10T4) |
$[2, 2, 10, 10]$ |
$[2, 2, 10, 10]$ |
$2$ |
$5$ |
$331491628403.7845$ |
| 12.4.110...125.2 |
$x^{12} - 45 x^{10} + 1050 x^{8} - 13530 x^{6} + 99685 x^{4} - 328905 x^{2} + 317520$ |
$12$ |
[4,4] |
$5^{11}\cdot 197^{8}$ |
$2$ |
$148.03576582619178$ |
|
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$851508807.1406436$ |
| 20.0.565...000.2 |
$x^{20} + 884 x^{18} - 120 x^{17} + 320632 x^{16} - 47040 x^{15} + 62498912 x^{14} - 845280 x^{13} + 7170696115 x^{12} + 2029080960 x^{11} + 497966799168 x^{10} + 363381965160 x^{9} + 20788727497872 x^{8} + 25825943410560 x^{7} + 504577565508196 x^{6} + 823130089914720 x^{5} + 6675937179144981 x^{4} + 10233463840763040 x^{3} + 40465493406379000 x^{2} + 32655100199688840 x + 23192516886401110$ |
$20$ |
[0,10] |
$2^{55}\cdot 5^{15}\cdot 197^{16}$ |
$3$ |
$1540.39809286$ |
$1540.3980928551418$ |
|
|
? |
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$2$ |
$9$ |
|
| 20.4.565...000.2 |
$x^{20} + 684 x^{18} - 120 x^{17} + 210872 x^{16} - 27840 x^{15} + 37744672 x^{14} + 2898720 x^{13} + 4248246835 x^{12} + 2111045760 x^{11} + 310035466968 x^{10} + 366294835560 x^{9} + 14179985825472 x^{8} + 26313627836160 x^{7} + 288546146778916 x^{6} + 569323661850720 x^{5} - 4104002620116539 x^{4} - 1025151183166560 x^{3} - 197619730538519440 x^{2} + 186630461902181640 x + 61046467660180710$ |
$20$ |
[4,8] |
$2^{55}\cdot 5^{15}\cdot 197^{16}$ |
$3$ |
$1540.39809286$ |
$1540.3980928551418$ |
|
|
|
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$2$ |
$11$ |
|
| 20.4.526...000.1 |
$x^{20} - x^{19} - 253 x^{18} - 24544 x^{17} + 398685 x^{16} + 8721545 x^{15} - 70361823 x^{14} - 3938000908 x^{13} - 11285455377 x^{12} + 2955494285207 x^{11} - 38784617114891 x^{10} - 385201843870298 x^{9} + 14936778594591960 x^{8} - 124575614095119552 x^{7} - 656667047355929392 x^{6} + 20992220260103943024 x^{5} - 141973587074569077668 x^{4} - 247833350982037177072 x^{3} + 9459373257275866071148 x^{2} - 56140694999572599084636 x + 117438049640833114893196$ |
$20$ |
[4,8] |
$2^{16}\cdot 5^{15}\cdot 13^{15}\cdot 197^{16}$ |
$4$ |
$2729.49306336$ |
$2729.493063361952$ |
|
|
|
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$2$ |
$11$ |
|
| 24.4.613...125.2 |
$x^{24} - 35 x^{22} - 55 x^{21} + 955 x^{20} + 505 x^{19} - 13360 x^{18} - 20130 x^{17} + 209535 x^{16} + 359985 x^{15} - 3499870 x^{14} + 3872145 x^{13} + 4149075 x^{12} + 14576245 x^{11} - 73943310 x^{10} - 41050830 x^{9} + 549395715 x^{8} - 939702525 x^{7} + 1082823105 x^{6} - 269406495 x^{5} - 9880462205 x^{4} + 31459457800 x^{3} - 44701823080 x^{2} + 26766458640 x - 4828553680$ |
$24$ |
[4,10] |
$5^{23}\cdot 197^{16}$ |
$2$ |
$158.30345915995787$ |
$320.19845723009803$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[4]$ |
$2$ |
$13$ |
$591498666797754600$ |
