| 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 $p$ |
| 10.2.339...125.1 |
$x^{10} - x^{9} - 5 x^{8} + 74 x^{7} + 374 x^{6} - 1318 x^{5} - 417 x^{4} + 3135 x^{3} + 2478 x^{2} - 4277 x - 3285$ |
$10$ |
(2, 4) |
$5^{6}\cdot 109^{9}$ |
$2$ |
$179.0877378726282$ |
$227.98766539169696$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[5]$ |
$[5]$ |
$2$ |
$5$ |
$19401037.764147706$ |
$2$ |
$109$ |
| 12.4.115...125.1 |
$x^{12} - 5 x^{11} + 93 x^{10} - 5 x^{9} - 1455 x^{8} + 20968 x^{7} - 11615 x^{6} - 421646 x^{5} + 2761180 x^{4} - 4062065 x^{3} - 32443744 x^{2} + 89620825 x - 59181367$ |
$12$ |
(4, 4) |
$5^{11}\cdot 109^{10}$ |
$2$ |
$218.06095960653687$ |
$434.0096172015417$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1589299194.2133982$ |
$4$ |
$109$ |
| 12.4.115...125.2 |
$x^{12} - 4 x^{11} - 21 x^{10} + 170 x^{9} - 2310 x^{8} + 16438 x^{7} - 53897 x^{6} - 188978 x^{5} + 18090 x^{4} - 4234555 x^{3} - 4768827 x^{2} - 57999097 x - 42550583$ |
$12$ |
(4, 4) |
$5^{11}\cdot 109^{10}$ |
$2$ |
$218.06095960653687$ |
$434.0096172015417$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1589299194.2133982$ |
$4$ |
$109$ |
| 12.4.722...125.1 |
$x^{12} - 5 x^{11} + 24 x^{10} - 860 x^{9} - 8270 x^{8} + 83805 x^{7} + 710315 x^{6} - 4502690 x^{5} - 7395625 x^{4} + 29122225 x^{3} + 61248605 x^{2} - 18023325 x - 46008855$ |
$12$ |
(4, 4) |
$5^{15}\cdot 109^{10}$ |
$2$ |
$372.87899583641683$ |
$826.2041172262856$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$7$ |
$64145990801.86358$ |
$3$ |
$109$ |
| 12.4.722...125.2 |
$x^{12} - 2 x^{11} + 26 x^{10} - 1105 x^{9} - 6870 x^{8} + 114542 x^{7} - 373969 x^{6} + 875782 x^{5} - 1819110 x^{4} + 1119855 x^{3} - 2077480 x^{2} - 3162190 x - 2138055$ |
$12$ |
(4, 4) |
$5^{15}\cdot 109^{10}$ |
$2$ |
$372.87899583641683$ |
$826.2041172262856$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$7$ |
$64145990801.86358$ |
$3$ |
$109$ |
| 12.4.722...125.3 |
$x^{12} - 4 x^{11} + 4 x^{10} + 109 x^{7} - 436 x^{6} + 436 x^{5} + 545 x^{4} - 1635 x^{3} + 1526 x^{2} - 654 x + 109$ |
$12$ |
(4, 4) |
$5^{15}\cdot 109^{10}$ |
$2$ |
$372.87899583641683$ |
$826.2041172262856$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$26401356000.73621$ |
$3$ |
$109$ |
| 12.4.722...125.4 |
$x^{12} - 4 x^{11} + 4 x^{10} + 1199 x^{7} - 8611 x^{6} + 20601 x^{5} + 13625 x^{4} - 204375 x^{3} + 533119 x^{2} - 693131 x + 411911$ |
$12$ |
(4, 4) |
$5^{15}\cdot 109^{10}$ |
$2$ |
$372.87899583641683$ |
$826.2041172262856$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$26401356000.73621$ |
$3$ |
$109$ |
| 12.4.451...125.1 |
$x^{12} - 3 x^{11} - 243 x^{10} + 275 x^{9} + 50475 x^{8} - 561115 x^{7} + 482295 x^{6} + 31275395 x^{5} - 157603075 x^{4} - 382175675 x^{3} + 3729559570 x^{2} - 2633397460 x - 11874466360$ |
$12$ |
(4, 4) |
$5^{19}\cdot 109^{10}$ |
$2$ |
$637.614113901233$ |
$1572.8067219410939$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$23368078776871.11$ |
$3$ |
$109$ |
| 12.4.451...125.2 |
$x^{12} - 4 x^{11} + 4 x^{10} - 13625 x^{7} + 54500 x^{6} - 54500 x^{5} - 68125 x^{4} + 204375 x^{3} - 190750 x^{2} + 81750 x - 13625$ |
$12$ |
(4, 4) |
$5^{19}\cdot 109^{10}$ |
$2$ |
$637.614113901233$ |
$1572.8067219410939$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[38]$ |
$[76]$ |
$2$ |
$7$ |
$69749364709.71965$ |
$3$ |
$109$ |
| 12.4.451...125.3 |
$x^{12} - x^{11} - 211 x^{10} + 3640 x^{9} - 32855 x^{8} + 84678 x^{7} + 780522 x^{6} - 11370208 x^{5} + 64723275 x^{4} - 145405600 x^{3} + 315519360 x^{2} - 1860663560 x + 3672402240$ |
$12$ |
(4, 4) |
$5^{19}\cdot 109^{10}$ |
$2$ |
$637.614113901233$ |
$1572.8067219410939$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$23368078776871.11$ |
$3$ |
$109$ |
| 12.4.451...125.4 |
$x^{12} - 6 x^{11} - 256 x^{10} + 1335 x^{9} + 22955 x^{8} - 99896 x^{7} - 1171974 x^{6} + 3871231 x^{5} + 36514425 x^{4} - 79600150 x^{3} - 660495202 x^{2} + 700957537 x + 5554650727$ |
$12$ |
(4, 4) |
$5^{19}\cdot 109^{10}$ |
$2$ |
$637.614113901233$ |
$1572.8067219410939$ |
|
|
? |
$A_5:C_4$ (as 12T124) |
$[38]$ |
$[76]$ |
$2$ |
$7$ |
$69749364709.71965$ |
$3$ |
$109$ |
| 15.3.340...000.1 |
$x^{15} - 560 x^{13} - 2190 x^{12} + 125440 x^{11} + 972291 x^{10} - 12130840 x^{9} - 169772400 x^{8} + 26150780 x^{7} + 10728552720 x^{6} + 52431723875 x^{5} - 191252303940 x^{4} - 2815241122800 x^{3} - 11072628168660 x^{2} - 14178242096280 x - 1815927247359$ |
$15$ |
(3, 6) |
$2^{10}\cdot 3^{12}\cdot 5^{9}\cdot 109^{13}\cdot 1009^{5}$ |
$5$ |
$5872.62618348$ |
$27684.74974421603$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$8$ |
|
|
$1009$ |
| 24.4.668...125.2 |
$x^{24} - 6 x^{23} - 14 x^{22} + 4 x^{21} + 891 x^{20} + 679 x^{19} - 7754 x^{18} - 38791 x^{17} - 410569 x^{16} + 2197544 x^{15} + 4505432 x^{14} - 20051017 x^{13} + 51216357 x^{12} - 358585487 x^{11} - 197064438 x^{10} + 4455403034 x^{9} - 13671872789 x^{8} + 30735470159 x^{7} + 116020550491 x^{6} - 555964077696 x^{5} + 235800719192 x^{4} + 1870121364843 x^{3} - 4237950373788 x^{2} - 1908275386172 x + 48779090077$ |
$24$ |
(4, 10) |
$5^{23}\cdot 109^{20}$ |
$2$ |
$233.18556850635812$ |
$434.0096172015417$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[2]$ |
$2$ |
$13$ |
$5661406329937305000$ |
$4$ |
$109$ |
| 24.4.167...125.1 |
$x^{24} - 4 x^{23} + 6 x^{22} + 691 x^{21} - 2804 x^{20} + 5062 x^{19} + 118342 x^{18} - 656543 x^{17} + 887527 x^{16} + 2847272 x^{15} - 85307922 x^{14} + 23832968 x^{13} + 632095218 x^{12} - 14242270787 x^{11} + 105554781933 x^{10} - 621100643243 x^{9} + 2763877959872 x^{8} - 8326674326343 x^{7} + 21115192091982 x^{6} - 51938854126098 x^{5} + 92867988021196 x^{4} - 96821353358334 x^{3} + 69441593331651 x^{2} + 21073336950101 x - 126261698575159$ |
$24$ |
(4, 10) |
$5^{25}\cdot 109^{20}$ |
$2$ |
$266.65465493097827$ |
$434.0096172015417$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$22795504820669985000$ |
$4$ |
$109$ |
| 24.4.260...125.1 |
$x^{24} - 2 x^{23} + 44 x^{22} - 403 x^{21} + 5621 x^{20} - 37769 x^{19} + 29433 x^{18} + 351959 x^{17} - 9540948 x^{16} + 108499856 x^{15} - 1344989119 x^{14} + 13670629513 x^{13} - 103119485161 x^{12} + 625136052987 x^{11} - 3058638612364 x^{10} + 12530279566856 x^{9} - 42642952834802 x^{8} + 123920973278314 x^{7} - 297165513885173 x^{6} + 604246439081846 x^{5} - 1070010058529220 x^{4} + 1572342507140645 x^{3} - 2223963960094270 x^{2} + 2361316394599040 x - 1293708172492605$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{20}$ |
$2$ |
$398.7417132580035$ |
$826.2041172262856$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$13$ |
$13903702787515465000000$ |
$4$ |
$109$ |
| 24.4.260...125.3 |
$x^{24} - 12 x^{23} + 69 x^{22} - 253 x^{21} - 494 x^{20} + 10253 x^{19} - 43711 x^{18} + 79557 x^{17} + 345646 x^{16} - 3113022 x^{15} + 5729844 x^{14} + 13381022 x^{13} - 69853884 x^{12} + 108569768 x^{11} + 130505069 x^{10} - 972533578 x^{9} + 900263181 x^{8} + 2240971933 x^{7} - 6516278311 x^{6} + 7679982492 x^{5} + 28375454008 x^{4} - 65028050436 x^{3} + 49336663252 x^{2} - 16202082394 x + 1976938513$ |
$24$ |
(4, 10) |
$5^{31}\cdot 109^{20}$ |
$2$ |
$398.7417132580035$ |
$826.2041172262856$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$1615696551407683000000$ |
$4$ |
$109$ |
| 24.4.652...125.1 |
$x^{24} - 10 x^{23} + 90 x^{22} + 65 x^{21} + 2585 x^{20} + 12487 x^{19} - 31595 x^{18} + 1065040 x^{17} + 1487835 x^{16} + 39815140 x^{15} + 48930207 x^{14} + 770341145 x^{13} - 2812174280 x^{12} + 8319390985 x^{11} - 88441401425 x^{10} + 312720018411 x^{9} - 4471113746970 x^{8} - 22247254886875 x^{7} - 148087811356945 x^{6} - 314346239120095 x^{5} - 157141129816556 x^{4} + 117814841944730 x^{3} + 221934780650850 x^{2} + 5609833434160 x - 61923160875005$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{20}$ |
$2$ |
$455.97304600134754$ |
$826.2041172262856$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.652...125.2 |
$x^{24} - 12 x^{23} + 69 x^{22} - 253 x^{21} - 1039 x^{20} + 15703 x^{19} - 49161 x^{18} - 26718 x^{17} + 340741 x^{16} + 39258 x^{15} - 3213606 x^{14} + 8868422 x^{13} - 13786464 x^{12} + 19304218 x^{11} - 46531641 x^{10} + 123461422 x^{9} - 181055514 x^{8} + 94978843 x^{7} - 713283991 x^{6} + 2215951467 x^{5} - 147758424 x^{4} - 3478940212 x^{3} - 797103256 x^{2} + 2918790147 x + 1727919511$ |
$24$ |
(4, 10) |
$5^{33}\cdot 109^{20}$ |
$2$ |
$455.97304600134754$ |
$826.2041172262856$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2, 10]$ |
$[10, 2, 2]$ |
$2$ |
$13$ |
$964588964336068000000$ |
$4$ |
$109$ |
| 24.4.101...125.1 |
$x^{24} - 8 x^{23} - 21 x^{22} + 158 x^{21} + 17521 x^{20} - 499300 x^{19} + 7173920 x^{18} - 63345565 x^{17} + 346054745 x^{16} - 474913965 x^{15} - 11392772688 x^{14} + 133851864844 x^{13} - 813550367597 x^{12} + 2981645001266 x^{11} - 2435024842828 x^{10} - 51869655906253 x^{9} + 399685506697014 x^{8} - 1670810908125977 x^{7} + 4035292992241761 x^{6} - 4632849417077168 x^{5} - 76712305186208660 x^{4} + 443232896601290480 x^{3} - 1000552945836705040 x^{2} - 3796076275541047680 x - 3357445932365498560$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{20}$ |
$2$ |
$681.8387386078426$ |
$1572.8067219410939$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$684088143414136900000000000$ |
$3$ |
$109$ |
| 24.4.101...125.2 |
$x^{24} - 4 x^{23} - 4 x^{22} + 581 x^{21} + 531 x^{20} - 13220 x^{19} - 9125 x^{18} - 6785 x^{17} - 143800 x^{16} - 143695 x^{15} + 1468682 x^{14} + 1458152 x^{13} + 1252517 x^{12} + 1458152 x^{11} + 1468682 x^{10} - 143695 x^{9} - 143800 x^{8} - 6785 x^{7} - 9125 x^{6} - 13220 x^{5} + 531 x^{4} + 581 x^{3} - 4 x^{2} - 4 x + 1$ |
$24$ |
(4, 10) |
$5^{39}\cdot 109^{20}$ |
$2$ |
$681.8387386078426$ |
$1572.8067219410939$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.254...125.2 |
$x^{24} - 4 x^{23} - 4 x^{22} + 2216 x^{21} + 10341 x^{20} - 91700 x^{19} - 668575 x^{18} - 2910000 x^{17} + 2316875 x^{16} - 43923000 x^{15} + 153499375 x^{14} + 1171962500 x^{13} + 2902106250 x^{12} - 13544400000 x^{11} - 8326087500 x^{10} - 67951250000 x^{9} - 33988515625 x^{8} + 796137109375 x^{7} + 849390625000 x^{6} + 5429137109375 x^{5} + 4696414062500 x^{4} + 11438583984375 x^{3} + 8942119140625 x^{2} + 17486484375000 x + 15517685546875$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{20}$ |
$2$ |
$779.7029409952114$ |
$1572.8067219410939$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
| 24.4.254...125.4 |
$x^{24} - 6 x^{23} - 134 x^{22} + 119 x^{21} + 2471 x^{20} + 27879 x^{19} + 702381 x^{18} + 2468279 x^{17} - 28706799 x^{16} - 237309426 x^{15} - 873257956 x^{14} - 1904585179 x^{13} + 15774702309 x^{12} + 81389877486 x^{11} - 90203841721 x^{10} - 118529390120 x^{9} - 2654693444055 x^{8} - 14494016214720 x^{7} - 35887806058555 x^{6} + 62679813222305 x^{5} + 1141104649642605 x^{4} - 575301586811980 x^{3} + 3520236106609955 x^{2} - 16597493673018930 x + 73789890406714980$ |
$24$ |
(4, 10) |
$5^{41}\cdot 109^{20}$ |
$2$ |
$779.7029409952114$ |
$1572.8067219410939$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$109$ |
