| 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 $p$ |
| 24.4.270...125.2 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} - 1304 x^{20} + 2465 x^{19} + 2465 x^{18} - 1885 x^{17} - 599575 x^{16} + 5496080 x^{15} + 20488210 x^{14} - 25107040 x^{13} - 597431900 x^{12} - 567629035 x^{11} + 3603058165 x^{10} + 9448143015 x^{9} - 17099510555 x^{8} + 16736471880 x^{7} + 402014550880 x^{6} + 156208942105 x^{5} - 3470676872911 x^{4} - 7274032113936 x^{3} + 8069786480454 x^{2} + 22227043889439 x - 6585670043891$ |
$24$ |
(4, 10) |
$5^{39}\cdot 29^{22}$ |
$2$ |
$299.4730564861151$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2, 2]$ |
$2$ |
$13$ |
$81380503790989600000$ |
$3$ |
$29$ |
| 24.4.270...125.6 |
$x^{24} - 6 x^{23} + 47 x^{22} + 257 x^{21} + 4820 x^{20} + 13841 x^{19} - 139051 x^{18} + 300092 x^{17} + 4529857 x^{16} + 12951695 x^{15} - 40857249 x^{14} - 321520216 x^{13} + 288484927 x^{12} + 9616225897 x^{11} + 53296332145 x^{10} + 177543971151 x^{9} + 414475529204 x^{8} + 716490646492 x^{7} + 917999196792 x^{6} + 890153835770 x^{5} + 721074386011 x^{4} + 717193087189 x^{3} + 654364923577 x^{2} - 372292473393 x + 31122013545$ |
$24$ |
(4, 10) |
$5^{39}\cdot 29^{22}$ |
$2$ |
$299.4730564861151$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4, 2]$ |
$2$ |
$13$ |
$257526267927115430000$ |
$3$ |
$29$ |
| 24.4.270...125.8 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} - 2174 x^{20} + 2465 x^{19} + 15515 x^{18} + 81490 x^{17} + 1583400 x^{16} + 173855 x^{15} - 10638940 x^{14} + 82989010 x^{13} + 625240725 x^{12} + 868904090 x^{11} - 5226790060 x^{10} - 19884822660 x^{9} - 42563392655 x^{8} - 77668721620 x^{7} - 6224510120 x^{6} + 97457228755 x^{5} + 56974469259 x^{4} + 287183270484 x^{3} - 277834934826 x^{2} - 687175108716 x + 338358763849$ |
$24$ |
(4, 10) |
$5^{39}\cdot 29^{22}$ |
$2$ |
$299.4730564861151$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2, 2]$ |
$2$ |
$13$ |
$109965381349596890000$ |
$3$ |
$29$ |
| 24.4.270...125.9 |
$x^{24} - 7 x^{23} - 6 x^{22} - 88 x^{21} + 800 x^{20} + 33972 x^{19} - 33044 x^{18} - 679237 x^{17} - 7247986 x^{16} - 18808685 x^{15} + 240393964 x^{14} + 1548866817 x^{13} - 1226398054 x^{12} - 64602797057 x^{11} - 428838287440 x^{10} - 1562629162232 x^{9} - 3495074371706 x^{8} - 4678953132493 x^{7} - 4731483065509 x^{6} - 12469668216145 x^{5} - 33540673060979 x^{4} - 37892792137502 x^{3} - 4499980454036 x^{2} + 18569747459402 x + 8710672685155$ |
$24$ |
(4, 10) |
$5^{39}\cdot 29^{22}$ |
$2$ |
$299.4730564861151$ |
$565.287791942645$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4, 2]$ |
$2$ |
$13$ |
$1278504647863611700000$ |
$3$ |
$29$ |
| 24.4.676...125.1 |
$x^{24} - 4 x^{23} - 46 x^{22} - 480 x^{21} + 5830 x^{20} - 25870 x^{19} + 206480 x^{18} - 191630 x^{17} - 4281025 x^{16} + 28414975 x^{15} - 195744705 x^{14} + 208438870 x^{13} + 1179057105 x^{12} - 6862168300 x^{11} + 66919163400 x^{10} - 36121402305 x^{9} - 363153392130 x^{8} + 823833868955 x^{7} - 9862870228300 x^{6} + 10526861697400 x^{5} + 52566236252030 x^{4} - 75005259428795 x^{3} - 303707165704555 x^{2} - 333094778067275 x - 142134894616225$ |
$24$ |
(4, 10) |
$5^{41}\cdot 29^{22}$ |
$2$ |
$342.4563751948184$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$29$ |
| 24.4.676...125.3 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} - 1305 x^{19} - 10005 x^{18} + 60320 x^{17} - 237655 x^{16} + 297395 x^{15} + 227650 x^{14} + 48632275 x^{13} - 58519100 x^{12} - 162429725 x^{11} - 1167334100 x^{10} + 1650665500 x^{9} - 3500169500 x^{8} + 30497763000 x^{7} + 43848203000 x^{6} - 146123238875 x^{5} - 523765574375 x^{4} + 1137682488125 x^{3} - 286773405625 x^{2} - 99248258750 x + 56010581875$ |
$24$ |
(4, 10) |
$5^{41}\cdot 29^{22}$ |
$2$ |
$342.4563751948184$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4, 4]$ |
$[2, 2, 4, 8]$ |
$2$ |
$13$ |
$35389578082944830000$ |
$2$ |
$29$ |
| 24.4.676...125.5 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} - 1305 x^{19} - 10005 x^{18} - 30305 x^{17} - 52780 x^{16} + 1127520 x^{15} + 2873900 x^{14} + 19324150 x^{13} + 65927150 x^{12} + 57825275 x^{11} - 1875785975 x^{10} - 3653343875 x^{9} + 4226336750 x^{8} + 31324081750 x^{7} - 91930159500 x^{6} - 128610048250 x^{5} + 436357363125 x^{4} + 79569910000 x^{3} - 882473280625 x^{2} + 125130178750 x + 751938081875$ |
$24$ |
(4, 10) |
$5^{41}\cdot 29^{22}$ |
$2$ |
$342.4563751948184$ |
$565.287791942645$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4, 20]$ |
$[40, 4, 2, 2]$ |
$2$ |
$13$ |
$8743760410650709000$ |
$2$ |
$29$ |
| 24.4.676...125.7 |
$x^{24} - 2 x^{23} + 29 x^{22} + 67 x^{21} - 1759 x^{20} + 20223 x^{19} - 168196 x^{18} + 859042 x^{17} - 5474434 x^{16} - 7907232 x^{15} + 105814264 x^{14} - 2189868478 x^{13} + 11394285106 x^{12} - 86360583312 x^{11} + 306625002524 x^{10} - 1291349956173 x^{9} + 4488374944421 x^{8} - 12556632345742 x^{7} + 26369655366134 x^{6} - 75512246952018 x^{5} + 178557365193021 x^{4} - 355090002574042 x^{3} + 402065305569184 x^{2} - 234817172836068 x + 88163445447261$ |
$24$ |
(4, 10) |
$5^{41}\cdot 29^{22}$ |
$2$ |
$342.4563751948184$ |
$565.287791942645$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2, 2]$ |
$2$ |
$13$ |
$758655361253825000000$ |
$3$ |
$29$ |
