| 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 $p$ |
| 24.4.793...125.2 |
$x^{24} + 20 x^{22} - 770 x^{21} + 2855 x^{20} - 11069 x^{19} + 273960 x^{18} - 1345895 x^{17} + 3677590 x^{16} - 39532205 x^{15} + 159141211 x^{14} - 528125245 x^{13} + 570475560 x^{12} + 5623078910 x^{11} - 3925207595 x^{10} + 103271298968 x^{9} - 512909269785 x^{8} + 3869705236240 x^{7} - 105064387120 x^{6} - 34558314470915 x^{5} + 95827936729908 x^{4} - 712984185306885 x^{3} - 1346688814473495 x^{2} + 780128272073630 x - 6337468007467195$ |
$24$ |
(4, 10) |
$5^{23}\cdot 109^{22}$ |
$2$ |
$344.73645439025245$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[4]$ |
$2$ |
$13$ |
$597424944738845700000$ |
$3$ |
$109$ |
| 24.4.793...125.4 |
$x^{24} + 20 x^{22} - 1315 x^{21} - 3685 x^{20} - 14339 x^{19} + 508310 x^{18} + 2497445 x^{17} + 4113590 x^{16} - 94050735 x^{15} - 538779467 x^{14} - 495962615 x^{13} + 9738875945 x^{12} + 44133619845 x^{11} - 462411120 x^{10} - 452561639545 x^{9} - 1192569241005 x^{8} + 2003237849695 x^{7} + 5832061129295 x^{6} + 7715558314060 x^{5} - 16830828175137 x^{4} + 31329819743690 x^{3} + 47890297341585 x^{2} - 1213528339980 x - 10083908316745$ |
$24$ |
(4, 10) |
$5^{23}\cdot 109^{22}$ |
$2$ |
$344.73645439025245$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.198...125.2 |
$x^{24} - 7 x^{23} + 79 x^{22} + 2192 x^{21} + 951 x^{20} - 73971 x^{19} + 296142 x^{18} - 437269 x^{17} - 25447367 x^{16} + 14663949 x^{15} + 52734132 x^{14} - 3204051604 x^{13} + 4777981043 x^{12} + 9870669284 x^{11} - 211830781428 x^{10} + 733189509211 x^{9} - 1606421115812 x^{8} + 1489603487719 x^{7} - 748708367693 x^{6} + 3220945135531 x^{5} + 218009196916 x^{4} - 10733024542362 x^{3} + 11561408149679 x^{2} - 23098194194718 x + 33099651501611$ |
$24$ |
(4, 10) |
$5^{25}\cdot 109^{22}$ |
$2$ |
$394.21642118069246$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.198...125.3 |
$x^{24} - 11 x^{23} - 184 x^{22} + 414 x^{21} + 21156 x^{20} + 130369 x^{19} - 573629 x^{18} - 10374491 x^{17} - 40499259 x^{16} + 63137869 x^{15} + 1516158650 x^{14} + 6207297595 x^{13} - 8972648265 x^{12} - 155537370310 x^{11} - 591535003705 x^{10} - 539118862913 x^{9} + 8814575385238 x^{8} + 46548505864162 x^{7} + 116472545683493 x^{6} + 183167523246822 x^{5} - 766471544135556 x^{4} - 2811711625025504 x^{3} + 3148197504380324 x^{2} + 8743879197452896 x + 3885657514846319$ |
$24$ |
(4, 10) |
$5^{25}\cdot 109^{22}$ |
$2$ |
$394.21642118069246$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2]$ |
$[4, 2]$ |
$2$ |
$13$ |
$2508520167871778000000$ |
$3$ |
$109$ |
| 24.4.310...125.4 |
$x^{24} - 4 x^{23} - 19 x^{22} + 41 x^{21} - 924 x^{20} - 2134 x^{19} - 15054 x^{18} + 226096 x^{17} - 1772774 x^{16} + 9270216 x^{15} - 34152511 x^{14} + 118387559 x^{13} - 308674586 x^{12} + 831523599 x^{11} - 2017425401 x^{10} + 3623391931 x^{9} - 6516060799 x^{8} - 11893729764 x^{7} + 12456453991 x^{6} - 275609583184 x^{5} + 493099765449 x^{4} - 2240219740086 x^{3} + 1425020058379 x^{2} - 4413544397286 x + 3678733317739$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{22}$ |
$2$ |
$589.4910449499399$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.310...125.5 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} + 2834 x^{19} - 44036 x^{18} - 57661 x^{17} - 1415256 x^{16} + 694439 x^{15} + 44391122 x^{14} + 102502292 x^{13} + 1292830797 x^{12} - 1442356888 x^{11} - 18720445563 x^{10} - 34726833200 x^{9} - 349146185635 x^{8} + 369607531020 x^{7} + 3238944370185 x^{6} + 3835239205565 x^{5} - 3277895022818 x^{4} - 69088721991113 x^{3} + 133886710418672 x^{2} - 139979798740848 x + 106137646790617$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{22}$ |
$2$ |
$589.4910449499399$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.310...125.7 |
$x^{24} - 4 x^{23} - 254 x^{22} + 1056 x^{21} + 27841 x^{20} - 221482 x^{19} - 1416357 x^{18} + 30612418 x^{17} + 23191823 x^{16} - 2679515947 x^{15} + 1385130935 x^{14} + 157807069445 x^{13} - 150192235150 x^{12} - 6651257008750 x^{11} + 6853213072800 x^{10} + 213155822679025 x^{9} - 156572287101475 x^{8} - 4864158248362525 x^{7} + 9059477468600 x^{6} + 69921581379951850 x^{5} + 57022652089776375 x^{4} - 458071166589338375 x^{3} - 719948292858093375 x^{2} + 138789505998367875 x + 133083518085041625$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{22}$ |
$2$ |
$589.4910449499399$ |
$1044.6208257588585$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.310...125.8 |
$x^{24} - 4 x^{23} + 51 x^{22} - 834 x^{21} + 6701 x^{20} - 108758 x^{19} + 197967 x^{18} + 3807747 x^{17} + 11180972 x^{16} - 146458883 x^{15} - 5491915820 x^{14} + 48483697370 x^{13} + 8713810310 x^{12} - 971289401695 x^{11} + 555093214845 x^{10} + 22740273179999 x^{9} - 111750667493131 x^{8} - 54842928320401 x^{7} + 2658080811861514 x^{6} - 7377216896445326 x^{5} - 10684046040392870 x^{4} + 60438421112331585 x^{3} + 28867203933674245 x^{2} - 350119631147849655 x + 369584965499972445$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{22}$ |
$2$ |
$589.4910449499399$ |
$1044.6208257588585$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.775...125.3 |
$x^{24} - 4 x^{23} - 19 x^{22} + 41 x^{21} - 924 x^{20} + 46 x^{19} - 60289 x^{18} + 299671 x^{17} - 1402719 x^{16} + 3676336 x^{15} - 17127583 x^{14} + 78640927 x^{13} - 283033208 x^{12} + 1036235627 x^{11} - 3016695763 x^{10} + 4516164279 x^{9} + 7279927719 x^{8} - 62974976156 x^{7} + 195866588229 x^{6} - 613584529186 x^{5} + 1546716777856 x^{4} - 2758884582209 x^{3} + 3661328690256 x^{2} - 3554144626374 x + 1679053237231$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{22}$ |
$2$ |
$674.1005980039541$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.775...125.4 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} + 2834 x^{19} + 21364 x^{18} + 25179 x^{17} - 2030016 x^{16} + 5145999 x^{15} + 28786682 x^{14} + 187221452 x^{13} - 1746756283 x^{12} - 82132808 x^{11} - 2678039203 x^{10} + 132310175816 x^{9} - 317634875979 x^{8} - 295298304404 x^{7} - 4043012653999 x^{6} + 15662270208221 x^{5} + 8144327200966 x^{4} - 63811669760569 x^{3} - 36108548401904 x^{2} + 68690326579856 x + 40172649399481$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{22}$ |
$2$ |
$674.1005980039541$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.775...125.6 |
$x^{24} - 4 x^{23} - 254 x^{22} - 34 x^{21} + 44191 x^{20} + 59738 x^{19} - 4567547 x^{18} - 12747237 x^{17} + 352770763 x^{16} + 1099813803 x^{15} - 19470208684 x^{14} - 69599286224 x^{13} + 816502818381 x^{12} + 2813707725246 x^{11} - 23388131852634 x^{10} - 64623218341975 x^{9} + 462052443063430 x^{8} + 622755148663240 x^{7} - 6626595760461020 x^{6} + 13733348902559870 x^{5} - 35450491104409705 x^{4} + 51320672491566220 x^{3} + 37492714241491370 x^{2} - 93098546371164205 x + 49562702395245145$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{22}$ |
$2$ |
$674.1005980039541$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.775...125.7 |
$x^{24} - 4 x^{23} + 51 x^{22} - 834 x^{21} - 9104 x^{20} + 62372 x^{19} + 161452 x^{18} - 764803 x^{17} - 14449833 x^{16} + 217426717 x^{15} - 1292393141 x^{14} + 4109239399 x^{13} + 90145874859 x^{12} - 992466787046 x^{11} + 4023297239359 x^{10} + 8894630580293 x^{9} - 156600476080492 x^{8} + 794614142006668 x^{7} - 754599389819107 x^{6} - 12008278306761262 x^{5} + 81776623934051886 x^{4} - 211255622115673764 x^{3} + 100982869294007736 x^{2} + 188879364095653431 x + 175235378465931541$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{22}$ |
$2$ |
$674.1005980039541$ |
$1044.6208257588585$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.121...125.1 |
$x^{24} - 8 x^{23} + 154 x^{22} - 2707 x^{21} + 4801 x^{20} - 69635 x^{19} - 669315 x^{18} - 13683405 x^{17} + 114638895 x^{16} + 1808310660 x^{15} - 11311191112 x^{14} + 335494519121 x^{13} - 3490147078653 x^{12} + 22812030919934 x^{11} - 85911975273342 x^{10} + 2833157536888679 x^{9} - 57548843451380927 x^{8} + 296266516829606741 x^{7} + 682632537714409397 x^{6} - 27618808199421429361 x^{5} + 157779271878133046685 x^{4} - 40648493488719725080 x^{3} - 4744869948320367492210 x^{2} + 28448164756412907037605 x - 37204042319301327453990$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{22}$ |
$2$ |
$1008.0155076457088$ |
$1988.5965494204843$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.121...125.2 |
$x^{24} - 8 x^{23} + 154 x^{22} - 1617 x^{21} + 14066 x^{20} - 276735 x^{19} - 3342540 x^{18} - 21512330 x^{17} - 1755877405 x^{16} - 21187795390 x^{15} - 255621036137 x^{14} - 3121642209904 x^{13} - 29238748653878 x^{12} - 262716539298871 x^{11} - 1965551508513022 x^{10} - 14376741241006801 x^{9} - 98274057255541012 x^{8} - 613355146733064554 x^{7} - 3189349509611219883 x^{6} - 13615928189441410406 x^{5} - 46276232999031353400 x^{4} - 186055656832220432600 x^{3} - 772617599027555200800 x^{2} - 1689115992995651605600 x - 1294413232648709515200$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{22}$ |
$2$ |
$1008.0155076457088$ |
$1988.5965494204843$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.121...125.3 |
$x^{24} - 2 x^{23} - 136 x^{22} - 338 x^{21} - 19184 x^{20} - 253276 x^{19} - 2856593 x^{18} - 22707494 x^{17} - 205480687 x^{16} - 1977358756 x^{15} - 12464475083 x^{14} - 77045381004 x^{13} - 371007400142 x^{12} - 3193260659621 x^{11} - 11041048635093 x^{10} - 3541195569763 x^{9} - 182216760040454 x^{8} - 613393728666227 x^{7} - 5811475554253906 x^{6} + 58760846944419757 x^{5} - 299378691519131075 x^{4} - 160314615016659925 x^{3} + 1977636447446727525 x^{2} - 12087343785942853800 x - 17598696334516968025$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{22}$ |
$2$ |
$1008.0155076457088$ |
$1988.5965494204843$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.121...125.4 |
$x^{24} - 2 x^{23} - 136 x^{22} + 2387 x^{21} - 16459 x^{20} + 46474 x^{19} - 1979143 x^{18} + 52938506 x^{17} - 713919362 x^{16} + 5311705594 x^{15} - 14190792558 x^{14} - 123739637579 x^{13} + 1123468252058 x^{12} - 433168638271 x^{11} - 31188597974893 x^{10} + 203109122842887 x^{9} - 745111168944179 x^{8} + 2040975476184348 x^{7} - 5738841525557156 x^{6} + 8957351103058307 x^{5} + 5972498324491150 x^{4} - 65865200424776400 x^{3} + 65642002233910200 x^{2} + 74684401650398100 x - 291419430721549325$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{22}$ |
$2$ |
$1008.0155076457088$ |
$1988.5965494204843$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.302...125.1 |
$x^{24} - 4 x^{23} - 249 x^{22} + 2406 x^{21} + 16451 x^{20} - 1421880 x^{19} - 19175035 x^{18} + 136739130 x^{17} + 4849518290 x^{16} + 30901965070 x^{15} - 18020757283 x^{14} + 241196461862 x^{13} + 11373610485762 x^{12} + 90341224477912 x^{11} + 604325520813907 x^{10} + 25260330923619720 x^{9} + 273395189856775365 x^{8} + 528702687957780280 x^{7} - 4306879117351701960 x^{6} - 25281953051698633480 x^{5} - 59156085060161136454 x^{4} - 79254023566786210304 x^{3} - 67793119439608014759 x^{2} - 32734721665600018164 x - 4141397209946656064$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{22}$ |
$2$ |
$1152.695808227139$ |
$1988.5965494204843$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.302...125.3 |
$x^{24} - 7085 x^{21} + 124805 x^{20} - 1239875 x^{19} + 25873875 x^{18} - 135963875 x^{17} - 800610450 x^{16} + 16090348375 x^{15} - 323323923225 x^{14} + 1088984310750 x^{13} + 18595413502375 x^{12} - 104404514097375 x^{11} - 12620129122625 x^{10} + 753886706963000 x^{9} - 604942490649375 x^{8} + 148897228988750 x^{7} + 257560591195125 x^{6} - 8015451702350000 x^{5} - 6395158336038650 x^{4} + 9449867030676875 x^{3} + 29105963848770625 x^{2} - 23963733028120375 x + 122841398038322375$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{22}$ |
$2$ |
$1152.695808227139$ |
$1988.5965494204843$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.302...125.7 |
$x^{24} - 9 x^{23} - 104 x^{22} + 136 x^{21} + 12171 x^{20} + 560623 x^{19} + 13095268 x^{18} + 229123383 x^{17} + 1521063553 x^{16} + 23575861108 x^{15} + 137925977616 x^{14} + 276085471556 x^{13} - 1921885566539 x^{12} - 1995650055774 x^{11} - 598601308226864 x^{10} - 6397385453136595 x^{9} - 11338230078986370 x^{8} + 96600397797232305 x^{7} + 105133710355336905 x^{6} - 2122063962805158820 x^{5} - 3484803654287678245 x^{4} + 29096301621681229455 x^{3} + 9307938316042254355 x^{2} - 265415529687088074920 x + 184066805325042817805$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{22}$ |
$2$ |
$1152.695808227139$ |
$1988.5965494204843$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.302...125.8 |
$x^{24} - 10 x^{23} - 130 x^{22} - 1375 x^{21} - 43055 x^{20} + 1059675 x^{19} + 17388720 x^{18} + 65666475 x^{17} - 1315524440 x^{16} - 31674793650 x^{15} - 6112459713 x^{14} + 2676301999705 x^{13} + 9263260871155 x^{12} - 85840773503625 x^{11} - 1133634344074955 x^{10} - 6946019093197625 x^{9} + 12878448845602620 x^{8} + 419908171660742200 x^{7} + 1789935095621701185 x^{6} + 3052719313910443450 x^{5} - 8090207241242840334 x^{4} - 225191825419500631285 x^{3} - 655033240953937142740 x^{2} + 2027391335915690045825 x + 6077636038895103413275$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{22}$ |
$2$ |
$1152.695808227139$ |
$1988.5965494204843$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
