| 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...125.1 |
$x^{24} - 3 x^{23} - 48 x^{22} + 1011 x^{21} - 4924 x^{20} - 50169 x^{19} + 595607 x^{18} - 1314528 x^{17} - 29238869 x^{16} + 146129816 x^{15} + 476072951 x^{14} - 5857285238 x^{13} + 4639762577 x^{12} + 136201021381 x^{11} - 199348343379 x^{10} - 1777336978324 x^{9} + 1067500702067 x^{8} + 43709580488417 x^{7} - 49731181757494 x^{6} - 1275716187976979 x^{5} + 3270771528761191 x^{4} + 10940492801655277 x^{3} - 46488436134411758 x^{2} + 26007923032387921 x - 28803949486872709$ |
$24$ |
(4, 10) |
$5^{23}\cdot 109^{22}$ |
$2$ |
$344.73645439025245$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[4]$ |
$2$ |
$13$ |
$423720467377299900000$ |
$3$ |
$109$ |
| 24.4.793...125.3 |
$x^{24} - 7 x^{23} - 10 x^{22} + 191 x^{21} + 5232 x^{20} - 50756 x^{19} - 103228 x^{18} + 4101970 x^{17} - 18135546 x^{16} - 44809022 x^{15} + 758033746 x^{14} - 561722527 x^{13} - 30035184260 x^{12} + 225699820351 x^{11} - 416576528428 x^{10} - 3526824626556 x^{9} + 16629918291242 x^{8} + 37908911704435 x^{7} - 464202423303746 x^{6} + 1369547075868283 x^{5} - 1624823723192944 x^{4} + 39193205099073 x^{3} + 1645956357578605 x^{2} - 884202385961979 x - 557334739690193$ |
$24$ |
(4, 10) |
$5^{23}\cdot 109^{22}$ |
$2$ |
$344.73645439025245$ |
$548.7451287829729$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[4]$ |
$2$ |
$13$ |
$597424944738845700000$ |
$3$ |
$109$ |
| 24.4.198...125.1 |
$x^{24} - 5 x^{23} + 209 x^{22} - 1880 x^{21} + 32594 x^{20} - 272065 x^{19} + 2635055 x^{18} - 19567110 x^{17} + 115591720 x^{16} - 636706975 x^{15} + 2075133195 x^{14} - 4971008140 x^{13} - 8141707720 x^{12} + 103071532200 x^{11} - 437711604180 x^{10} + 931546438375 x^{9} + 18717638250 x^{8} - 6598619973625 x^{7} + 15635409017400 x^{6} - 5700030099325 x^{5} - 24477246719700 x^{4} + 35395870489275 x^{3} - 37058252983075 x^{2} + 63713167016750 x - 43788301427225$ |
$24$ |
(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...125.4 |
$x^{24} - 4 x^{22} - 1720 x^{21} + 2534 x^{20} - 21919 x^{19} + 1017560 x^{18} - 726439 x^{17} + 27898590 x^{16} - 588128056 x^{15} + 1390598856 x^{14} - 887782745 x^{13} + 8589863531 x^{12} + 394516859000 x^{11} - 2881514159386 x^{10} + 12307692947266 x^{9} - 57112338853215 x^{8} + 136568401104246 x^{7} - 295898798851140 x^{6} + 664506903596229 x^{5} + 762235631605796 x^{4} + 1441034178181325 x^{3} + 10994425979664316 x^{2} + 1614204526794420 x + 25870416406358929$ |
$24$ |
(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...125.1 |
$x^{24} - 8 x^{23} - 129 x^{22} - 147 x^{21} + 3228 x^{20} + 158842 x^{19} + 1053984 x^{18} - 9808513 x^{17} - 76160579 x^{16} - 450020679 x^{15} - 2717296001 x^{14} + 52399337618 x^{13} + 328478108269 x^{12} - 353321674938 x^{11} + 1948975349062 x^{10} - 51292150331142 x^{9} - 618357410982019 x^{8} + 656059631472823 x^{7} + 6505464300663649 x^{6} - 31548707766373451 x^{5} + 128927288240805416 x^{4} + 1624646840245764032 x^{3} + 1807623391985900651 x^{2} - 7069968264645204397 x - 12243302508029584947$ |
$24$ |
(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...125.2 |
$x^{24} - 8 x^{23} - 248 x^{22} + 2570 x^{21} + 12895 x^{20} - 154273 x^{19} - 649511 x^{18} + 4410739 x^{17} + 80487860 x^{16} - 1237460435 x^{15} + 9115230369 x^{14} - 37029689892 x^{13} + 18570656718 x^{12} + 1233676621485 x^{11} - 10776819849125 x^{10} + 51960327427103 x^{9} - 85935470940599 x^{8} - 504355550480534 x^{7} + 4332524947644800 x^{6} - 14584396630946395 x^{5} + 23737920905602591 x^{4} + 220719460432342 x^{3} - 77837845170326738 x^{2} + 144706889504174735 x - 97343601424442475$ |
$24$ |
(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...125.3 |
$x^{24} - 6 x^{23} - 119 x^{22} + 854 x^{21} + 773 x^{20} + 2279 x^{19} - 116504 x^{18} + 131264 x^{17} + 1377786 x^{16} - 9016213 x^{15} + 54820101 x^{14} - 291002611 x^{13} + 1688745126 x^{12} - 6093135791 x^{11} + 946807313 x^{10} + 128787890109 x^{9} - 1042831991924 x^{8} + 6058909229774 x^{7} - 31152601913539 x^{6} + 132621568642227 x^{5} - 429046905921579 x^{4} + 1022073252974979 x^{3} - 1618865338234484 x^{2} + 1275542802740324 x - 138227932264867$ |
$24$ |
(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...125.6 |
$x^{24} - 4 x^{23} - 19 x^{22} + 41 x^{21} - 597 x^{20} + 13671 x^{19} + 24186 x^{18} - 1075364 x^{17} + 3255941 x^{16} + 32762768 x^{15} - 161302319 x^{14} - 279645234 x^{13} + 3702224901 x^{12} - 9890668734 x^{11} - 50043794302 x^{10} + 264536772046 x^{9} + 1061941855001 x^{8} - 951472296959 x^{7} - 12470926761144 x^{6} - 10830692287662 x^{5} - 34948090904564 x^{4} - 163900066389289 x^{3} - 773374619523099 x^{2} + 1128448284182756 x + 1539376879689673$ |
$24$ |
(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...125.1 |
$x^{24} - x^{23} + 26 x^{22} + 4324 x^{21} - 36164 x^{20} + 228200 x^{19} + 2423260 x^{18} - 52795400 x^{17} + 12191610 x^{16} + 389603410 x^{15} - 24980880090 x^{14} - 95001237860 x^{13} + 564886906010 x^{12} + 3257072992890 x^{11} - 325999515690 x^{10} - 80289385905850 x^{9} - 575516846950175 x^{8} - 2178231732896650 x^{7} - 5203181801343800 x^{6} - 10323209578181600 x^{5} - 12074325776481600 x^{4} - 14251912534362400 x^{3} - 7970914560545600 x^{2} - 7242594366566400 x - 526693993977600$ |
$24$ |
(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...125.2 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} + 2289 x^{19} - 36951 x^{18} - 257131 x^{17} - 2160816 x^{16} - 10570166 x^{15} - 58221914 x^{14} - 334047504 x^{13} - 2840137354 x^{12} - 17573498949 x^{11} - 53028192729 x^{10} + 9787960309 x^{9} + 303196438954 x^{8} - 2081058435416 x^{7} - 19502917205716 x^{6} - 58884808349206 x^{5} - 56632692617989 x^{4} + 70895246532636 x^{3} + 141232682009801 x^{2} - 147220000013204 x - 156414394013519$ |
$24$ |
(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...125.5 |
$x^{24} - 4 x^{23} + 6 x^{22} - 4 x^{21} + x^{20} + 2289 x^{19} - 36951 x^{18} + 764744 x^{17} - 6534441 x^{16} + 39556209 x^{15} - 225945664 x^{14} + 1274179371 x^{13} - 7905503604 x^{12} + 42847272051 x^{11} - 177590708604 x^{10} + 502337228434 x^{9} - 872862194796 x^{8} + 1090144100834 x^{7} - 2871158445966 x^{6} + 11095491646169 x^{5} + 7413167545761 x^{4} - 115542441171739 x^{3} + 81660544543551 x^{2} + 123118816711296 x + 128639378702231$ |
$24$ |
(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...125.8 |
$x^{24} - 11 x^{23} - 332 x^{22} + 3268 x^{21} + 43724 x^{20} - 551700 x^{19} - 3287795 x^{18} + 62282400 x^{17} + 361677480 x^{16} - 1787464860 x^{15} - 20115830640 x^{14} - 209785570025 x^{13} - 1888734115400 x^{12} - 4307072744615 x^{11} + 44959677718280 x^{10} + 462660530553940 x^{9} + 2730610794749210 x^{8} + 12436896913663470 x^{7} + 43107261720991995 x^{6} + 112913570686439785 x^{5} + 224526598105176305 x^{4} + 378979505633068470 x^{3} + 480945466938287990 x^{2} + 474137879628295090 x + 264495221253438445$ |
$24$ |
(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...125.5 |
$x^{24} + 16350 x^{20} - 1814850 x^{18} + 5986825 x^{16} + 3043866965 x^{14} - 37017062175 x^{12} - 1856266269475 x^{10} + 38406857938650 x^{8} + 183163137913575 x^{6} - 7199514724704670 x^{4} + 63149113723696375 x^{2} + 613116592600078125$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{22}$ |
$2$ |
$1008.0155076457088$ |
$1988.5965494204843$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[4]$ |
$[4, 2]$ |
$2$ |
$13$ |
$57801913481412370000000000000$ |
$3$ |
$109$ |
| 24.4.121...125.6 |
$x^{24} - 4 x^{23} - 539 x^{22} + 1086 x^{21} + 113470 x^{20} + 27250 x^{19} - 13123600 x^{18} - 31340225 x^{17} + 809984450 x^{16} + 4472357200 x^{15} - 16119328205 x^{14} - 309619963080 x^{13} - 2064320544855 x^{12} + 7393793313620 x^{11} + 151550967164950 x^{10} + 279974977306050 x^{9} - 2500699679307025 x^{8} - 10114745628055450 x^{7} - 8643679244966650 x^{6} + 34369213753089725 x^{5} + 274147047781904980 x^{4} + 711676780139306705 x^{3} + 650857501854281055 x^{2} + 827626342716637805 x + 1034553768331546475$ |
$24$ |
(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...125.7 |
$x^{24} - 10 x^{23} + 500 x^{22} - 2015 x^{21} + 104704 x^{20} - 92261 x^{19} + 4859175 x^{18} + 12487020 x^{17} - 510772970 x^{16} - 3314452609 x^{15} - 31140205664 x^{14} + 119927852710 x^{13} + 2472619323385 x^{12} + 3284311801605 x^{11} + 16789597854924 x^{10} + 232636356206209 x^{9} - 5382532219292770 x^{8} - 68216971899770040 x^{7} - 231843662150173315 x^{6} - 96335762207475134 x^{5} - 1641152941333342264 x^{4} - 16395190145863156920 x^{3} - 26759151775733541280 x^{2} + 29487604013892516000 x + 32717178984424509504$ |
$24$ |
(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...125.8 |
$x^{24} - 12 x^{23} - 40 x^{22} + 401 x^{21} - 930 x^{20} + 247873 x^{19} - 1200746 x^{18} - 6559960 x^{17} - 64580422 x^{16} - 2923221605 x^{15} - 12334220651 x^{14} - 93433926183 x^{13} - 127075389375 x^{12} + 9477419064504 x^{11} + 83412644565090 x^{10} + 530594726847237 x^{9} + 3434957990181416 x^{8} + 5105977496091715 x^{7} - 45579398797207878 x^{6} - 385128811285350640 x^{5} + 2216757763306056151 x^{4} - 22438363614405112672 x^{3} + 141472039110471732990 x^{2} - 220230876669439407034 x + 777019087232248674575$ |
$24$ |
(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...125.2 |
$x^{24} - 10900 x^{20} - 2616000 x^{18} - 68321200 x^{16} + 2810042345 x^{14} + 236206858600 x^{12} + 7233058852900 x^{10} + 122627097345300 x^{8} + 1145957171176100 x^{6} + 4520800192684405 x^{4} + 80286843623000 x^{2} + 2271403140498000$ |
$24$ |
(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...125.4 |
$x^{24} - 327 x^{22} + 80006 x^{20} - 689425 x^{19} - 10627500 x^{18} + 127486400 x^{17} + 983351675 x^{16} - 5622369875 x^{15} - 43113578235 x^{14} + 31076049875 x^{13} - 2491469565005 x^{12} - 20356427375050 x^{11} + 50536588219815 x^{10} + 45471115514965 x^{9} + 2047220323717975 x^{8} + 13391522375867970 x^{7} + 83856726566419600 x^{6} + 294114815359314515 x^{5} + 937304416391101555 x^{4} + 1910970795246895600 x^{3} + 2345716619408079065 x^{2} + 907059044865183450 x + 1178915603470686505$ |
$24$ |
(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...125.5 |
$x^{24} - 9 x^{23} - 186 x^{22} + 6125 x^{21} + 1890 x^{20} - 1553796 x^{19} + 144869 x^{18} + 206603326 x^{17} + 54280540 x^{16} - 22183903385 x^{15} - 30353054894 x^{14} + 2651575997586 x^{13} + 26822906943269 x^{12} + 103983139272220 x^{11} + 72891074608505 x^{10} - 980914470669021 x^{9} - 6138271022337721 x^{8} - 9977135306495559 x^{7} + 149502475065329320 x^{6} + 1003641385636169600 x^{5} + 1798798175900669701 x^{4} - 1934235095941169054 x^{3} - 7612128467148681691 x^{2} - 389400971404249110 x + 10069108374601211445$ |
$24$ |
(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...125.6 |
$x^{24} - 8 x^{23} - 338 x^{22} - 2914 x^{21} + 132859 x^{20} + 330222 x^{19} - 12895796 x^{18} - 57122136 x^{17} + 649290837 x^{16} + 8613838618 x^{15} - 18311679996 x^{14} - 1037927849712 x^{13} + 1318676901773 x^{12} + 46791472406149 x^{11} + 47307452100241 x^{10} - 946929364183972 x^{9} - 5008136828513789 x^{8} + 9886343624744886 x^{7} + 69931212171066273 x^{6} - 227488047481772008 x^{5} + 738562956788278941 x^{4} + 5030120600016639407 x^{3} - 19782820377631184533 x^{2} - 33978910528075722209 x + 102513143473323231709$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{22}$ |
$2$ |
$1152.695808227139$ |
$1988.5965494204843$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
