| 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 $p$ |
| 24.4.918...125.1 |
$x^{24} - 4 x^{23} + 6 x^{22} - 449 x^{21} + 4273 x^{20} + 5874 x^{19} + 40584 x^{18} - 1486656 x^{17} + 320934 x^{16} + 31758582 x^{15} + 203615891 x^{14} - 1041728624 x^{13} - 8957494979 x^{12} + 15522090746 x^{11} + 187723100658 x^{10} - 120260671411 x^{9} - 2012872155141 x^{8} + 555294801359 x^{7} + 10666291776869 x^{6} + 2324146207637 x^{5} - 37689124873554 x^{4} - 13595215964929 x^{3} + 96703661945176 x^{2} - 15091490947869 x - 91903199858837$ |
$24$ |
(4, 10) |
$5^{23}\cdot 89^{22}$ |
$2$ |
$286.27741933105136$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$89$ |
| 24.4.918...125.5 |
$x^{24} - 120 x^{22} - 10 x^{21} + 4680 x^{20} - 6321 x^{19} - 96055 x^{18} + 164600 x^{17} + 411200 x^{16} - 2202100 x^{15} - 1290046 x^{14} - 7372490 x^{13} + 128716760 x^{12} - 501217985 x^{11} - 2530983710 x^{10} + 7243837191 x^{9} + 9151935820 x^{8} + 46635223810 x^{7} - 233437373280 x^{6} + 654694955355 x^{5} + 1464409611225 x^{4} - 13972190531300 x^{3} + 16165180816000 x^{2} + 1967394528875 x + 2006228467125$ |
$24$ |
(4, 10) |
$5^{23}\cdot 89^{22}$ |
$2$ |
$286.27741933105136$ |
$452.62236684313837$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$13$ |
$68610484458411210000$ |
$4$ |
$89$ |
| 24.4.918...125.6 |
$x^{24} - 120 x^{22} - 10 x^{21} + 6905 x^{20} + 799 x^{19} - 278060 x^{18} + 173055 x^{17} + 7887200 x^{16} - 16327735 x^{15} - 133024731 x^{14} + 532379580 x^{13} + 1177337010 x^{12} - 9573340425 x^{11} - 2946551855 x^{10} + 125420329119 x^{9} - 144462051275 x^{8} - 959076041810 x^{7} + 2708721649225 x^{6} + 397551181590 x^{5} - 9951527396947 x^{4} + 12150299345835 x^{3} + 5468893445760 x^{2} - 21535626575215 x + 14471246844265$ |
$24$ |
(4, 10) |
$5^{23}\cdot 89^{22}$ |
$2$ |
$286.27741933105136$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$13$ |
$13752419633095248000$ |
$4$ |
$89$ |
| 24.4.918...125.7 |
$x^{24} - 2 x^{23} + 63 x^{22} - 827 x^{21} - 1196 x^{20} - 68669 x^{19} - 124547 x^{18} - 1743022 x^{17} - 3317052 x^{16} - 20887621 x^{15} - 93267574 x^{14} - 124652522 x^{13} + 2308036563 x^{12} + 27608980468 x^{11} + 216820490264 x^{10} + 1095953073726 x^{9} + 4305306446543 x^{8} + 13985340544188 x^{7} + 34336140894428 x^{6} + 56766412919919 x^{5} + 63217215313641 x^{4} + 58841762063278 x^{3} + 47391301297208 x^{2} + 32252356357608 x + 25979013994259$ |
$24$ |
(4, 10) |
$5^{23}\cdot 89^{22}$ |
$2$ |
$286.27741933105136$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4]$ |
$2$ |
$13$ |
$36799407855653930000$ |
$4$ |
$89$ |
| 24.4.229...125.2 |
$x^{24} - 11 x^{23} - 114 x^{22} + 824 x^{21} + 12301 x^{20} - 5277 x^{19} - 1149493 x^{18} - 598157 x^{17} + 62457032 x^{16} - 28337252 x^{15} - 1893188568 x^{14} + 3477178433 x^{13} + 30807485227 x^{12} - 143840039207 x^{11} - 97275021018 x^{10} + 3086068549814 x^{9} - 6286206651279 x^{8} - 28596060866796 x^{7} + 105662214126501 x^{6} + 51235342679184 x^{5} - 580910749748916 x^{4} + 441206727204676 x^{3} + 114072323164339 x^{2} + 541180287831136 x - 312927910098871$ |
$24$ |
(4, 10) |
$5^{25}\cdot 89^{22}$ |
$2$ |
$327.36677040187857$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 2, 4]$ |
$[2, 2, 2, 4]$ |
$2$ |
$13$ |
$39093008005448335000$ |
$4$ |
$89$ |
| 24.4.229...125.3 |
$x^{24} - 10 x^{23} + 25 x^{22} + 1935 x^{21} - 10030 x^{20} - 34087 x^{19} + 1112160 x^{18} - 935550 x^{17} - 34093635 x^{16} + 116653690 x^{15} + 491077287 x^{14} - 5462726085 x^{13} - 28707547175 x^{12} - 82118098860 x^{11} - 276744138650 x^{10} - 1068771666276 x^{9} - 4126385140520 x^{8} - 4539669066765 x^{7} + 4838910931635 x^{6} - 43374754905545 x^{5} + 11151366131449 x^{4} + 63283022914135 x^{3} - 94608154678215 x^{2} - 151975177287750 x - 119337300832275$ |
$24$ |
(4, 10) |
$5^{25}\cdot 89^{22}$ |
$2$ |
$327.36677040187857$ |
$452.62236684313837$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 2, 4]$ |
$[2, 2, 2, 4]$ |
$2$ |
$13$ |
$158466950947891900000$ |
$4$ |
$89$ |
| 24.4.229...125.4 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + 446 x^{20} + 12994 x^{19} + 25454 x^{18} + 45034 x^{17} - 18156 x^{16} - 12083886 x^{15} + 6061701 x^{14} + 665735486 x^{13} + 2209626941 x^{12} - 7709179644 x^{11} - 98459485684 x^{10} - 168718807126 x^{9} + 2406563134669 x^{8} + 13899669932829 x^{7} + 14257456475664 x^{6} - 90366861809451 x^{5} - 326471613749334 x^{4} - 443687608352359 x^{3} - 313677448742334 x^{2} - 119801317951219 x - 8058266421349$ |
$24$ |
(4, 10) |
$5^{25}\cdot 89^{22}$ |
$2$ |
$327.36677040187857$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$13$ |
$90673756995467580000$ |
$4$ |
$89$ |
| 24.4.229...125.8 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + 3116 x^{20} + 6764 x^{19} - 132076 x^{18} + 859384 x^{17} + 1275904 x^{16} + 9094554 x^{15} - 96062239 x^{14} + 148582296 x^{13} + 5667704141 x^{12} - 31114295514 x^{11} + 29403672616 x^{10} + 318568634184 x^{9} - 2635907116121 x^{8} + 5096904048179 x^{7} + 1399615659494 x^{6} - 31620921402991 x^{5} + 150857399860436 x^{4} + 46785615621511 x^{3} - 1121050409397834 x^{2} + 642150457868791 x + 3470991058617581$ |
$24$ |
(4, 10) |
$5^{25}\cdot 89^{22}$ |
$2$ |
$327.36677040187857$ |
$452.62236684313837$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$13$ |
$53912689245734216000$ |
$4$ |
$89$ |
| 24.4.358...125.2 |
$x^{24} - 8 x^{23} + 64 x^{22} - 902 x^{21} + 6316 x^{20} - 136934 x^{19} + 609372 x^{18} - 8671906 x^{17} + 30971223 x^{16} - 528120304 x^{15} + 2227739352 x^{14} - 27368555416 x^{13} + 84384989853 x^{12} - 980595596854 x^{11} + 3158183643447 x^{10} - 24849991956160 x^{9} + 74624141823520 x^{8} - 442422095928880 x^{7} + 765727826720400 x^{6} - 2316315944560320 x^{5} - 3888629115012928 x^{4} - 1094970506171776 x^{3} - 29289495523457792 x^{2} - 50029902292521984 x - 21580162302394368$ |
$24$ |
(4, 10) |
$5^{31}\cdot 89^{22}$ |
$2$ |
$489.52750113277625$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4]$ |
$2$ |
$13$ |
$792553891707177200000000$ |
$4$ |
$89$ |
| 24.4.358...125.3 |
$x^{24} - 2 x^{23} - 216 x^{22} - 133 x^{21} + 28961 x^{20} + 21124 x^{19} - 2254073 x^{18} - 3441264 x^{17} + 150508008 x^{16} + 97710399 x^{15} - 6202398534 x^{14} - 3438452642 x^{13} + 243319281339 x^{12} - 492175602363 x^{11} - 2322137868424 x^{10} + 9252856332343 x^{9} - 17379547551176 x^{8} + 137815195972027 x^{7} - 42589341925234 x^{6} - 1040206415032347 x^{5} + 6757569482264748 x^{4} - 4671372579250361 x^{3} + 3296208146361217 x^{2} + 293224286414451 x - 419768284696857$ |
$24$ |
(4, 10) |
$5^{31}\cdot 89^{22}$ |
$2$ |
$489.52750113277625$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2, 2]$ |
$2$ |
$13$ |
$133533741597405740000000$ |
$3$ |
$89$ |
| 24.4.358...125.4 |
$x^{24} - 9790 x^{20} - 699540 x^{18} - 14942655 x^{16} + 343628555 x^{14} + 25447488760 x^{12} + 490016745570 x^{10} + 2644385805340 x^{8} - 12477500025945 x^{6} - 95369414191688 x^{4} + 284275397082800 x^{2} + 18205372928000$ |
$24$ |
(4, 10) |
$5^{31}\cdot 89^{22}$ |
$2$ |
$489.52750113277625$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4]$ |
$2$ |
$13$ |
$1877883798506105000000000$ |
$4$ |
$89$ |
| 24.4.358...125.8 |
$x^{24} - 2 x^{23} - 191 x^{22} + 152 x^{21} + 20801 x^{20} + 145552 x^{19} - 1176554 x^{18} - 16138302 x^{17} + 15768809 x^{16} + 1059872352 x^{15} + 7747419046 x^{14} + 3640653858 x^{13} - 202726936711 x^{12} - 1134655611298 x^{11} - 2506437023344 x^{10} + 18528375557180 x^{9} + 138487686799265 x^{8} - 8715047372200 x^{7} - 866046602082015 x^{6} - 4747675198206540 x^{5} - 13439138362502051 x^{4} + 97786901456032952 x^{3} + 139064771037891016 x^{2} - 927383945402843232 x + 858450394618182224$ |
$24$ |
(4, 10) |
$5^{31}\cdot 89^{22}$ |
$2$ |
$489.52750113277625$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2, 2]$ |
$2$ |
$13$ |
$27022688166806175000000$ |
$3$ |
$89$ |
| 24.4.896...125.4 |
$x^{24} - 7120 x^{20} - 823250 x^{18} - 52100600 x^{16} - 1856885765 x^{14} - 36450450625 x^{12} - 431712720525 x^{10} - 3595814890500 x^{8} - 22064899402000 x^{6} - 71180667348800 x^{4} - 12699200672000 x^{2} + 5255995392000$ |
$24$ |
(4, 10) |
$5^{33}\cdot 89^{22}$ |
$2$ |
$559.7893031284452$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$89$ |
| 24.4.896...125.6 |
$x^{24} - 4 x^{23} - 99 x^{22} + 431 x^{21} - 14784 x^{20} - 3090 x^{19} + 940100 x^{18} - 2629940 x^{17} + 74365635 x^{16} + 214136855 x^{15} - 2267018532 x^{14} + 877025663 x^{13} - 159570300332 x^{12} - 33238859092 x^{11} + 1688439158893 x^{10} + 2467042788125 x^{9} + 87026862121385 x^{8} - 19654322538325 x^{7} + 696572665120450 x^{6} + 4771707259687380 x^{5} - 7522754457264744 x^{4} + 27858329958403216 x^{3} + 49846168997904256 x^{2} - 92937065600889664 x + 150093087495580416$ |
$24$ |
(4, 10) |
$5^{33}\cdot 89^{22}$ |
$2$ |
$559.7893031284452$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4, 4]$ |
$[4, 4, 2, 2]$ |
$2$ |
$13$ |
$1641545903294094000000000$ |
$3$ |
$89$ |
| 24.4.896...125.7 |
$x^{24} - 8 x^{23} + 64 x^{22} + 433 x^{21} - 12374 x^{20} + 111376 x^{19} - 796828 x^{18} + 342904 x^{17} + 33490368 x^{16} - 474785274 x^{15} + 4152261112 x^{14} - 24039246086 x^{13} + 143167194098 x^{12} - 631563143414 x^{11} + 3636688422802 x^{10} - 22886598332681 x^{9} + 117396649195528 x^{8} - 717771526707744 x^{7} + 2380263669327347 x^{6} - 8282002593358136 x^{5} + 21376347951105196 x^{4} + 23743341392067512 x^{3} + 17398950398107184 x^{2} + 516534814705031808 x + 525709300570411456$ |
$24$ |
(4, 10) |
$5^{33}\cdot 89^{22}$ |
$2$ |
$559.7893031284452$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4]$ |
$[4, 2]$ |
$2$ |
$13$ |
$268297290075719700000000$ |
$4$ |
$89$ |
| 24.4.896...125.8 |
$x^{24} - 9 x^{23} - 104 x^{22} + 476 x^{21} + 11696 x^{20} - 119376 x^{19} - 129406 x^{18} + 9366649 x^{17} - 113806816 x^{16} + 871740359 x^{15} - 531819484 x^{14} - 65395748189 x^{13} + 555095871071 x^{12} - 323147684679 x^{11} - 25936497075049 x^{10} + 219160819386589 x^{9} - 932052046902271 x^{8} + 1597327943149004 x^{7} + 12076497815529119 x^{6} - 163997645628589366 x^{5} + 1106353490183569846 x^{4} - 4803003296867383829 x^{3} + 13617369347618628836 x^{2} - 23231218386562315844 x + 19475512782813222496$ |
$24$ |
(4, 10) |
$5^{33}\cdot 89^{22}$ |
$2$ |
$559.7893031284452$ |
$861.6363513918435$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 4, 4]$ |
$[4, 4, 2, 2]$ |
$2$ |
$13$ |
$707391311051196900000000$ |
$3$ |
$89$ |
