| 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 |
| 10.0.223...000.1 |
$x^{10} + 47 x^{8} + 1034 x^{6} + 14758 x^{4} + 99781 x^{2} + 235$ |
$10$ |
(0, 5) |
$-\,2^{8}\cdot 5^{7}\cdot 47^{9}$ |
$3$ |
$171.78730705$ |
$186.18280624232975$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$6695399.644993812$ |
$0$ |
| 15.1.498...000.1 |
$x^{15} - 5 x^{14} + 85 x^{13} - 565 x^{12} + 3725 x^{11} - 12460 x^{10} + 75435 x^{9} - 1318620 x^{8} + 20208195 x^{7} - 30765645 x^{6} + 36275958 x^{5} + 1137496230 x^{4} - 4949835075 x^{3} - 11624518980 x^{2} + 49088726460 x + 100311205788$ |
$15$ |
(1, 7) |
$-\,2^{10}\cdot 3^{13}\cdot 5^{9}\cdot 31^{5}\cdot 47^{13}$ |
$5$ |
$954.653557507$ |
$2540.3421566472416$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
trivial |
$2$ |
$7$ |
$134468600548977250$ |
$1$ |
| 15.1.656...000.1 |
$x^{15} - 5 x^{14} + 245 x^{13} - 715 x^{12} + 22565 x^{11} - 21480 x^{10} + 992875 x^{9} + 1050450 x^{8} + 22166375 x^{7} + 73659575 x^{6} + 276602050 x^{5} + 1171874500 x^{4} + 1993898625 x^{3} + 3823779000 x^{2} - 1444686000 x + 13303150250$ |
$15$ |
(1, 7) |
$-\,2^{10}\cdot 5^{17}\cdot 47^{13}\cdot 109^{5}$ |
$4$ |
$1321.74084679$ |
$3559.61058896397$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$7$ |
|
|
| 15.1.212...000.1 |
$x^{15} - 5 x^{14} + 60 x^{13} - 140 x^{12} + 1025 x^{11} - 60893 x^{10} + 209370 x^{9} + 2663110 x^{8} + 23996600 x^{7} - 102355320 x^{6} + 1329796016 x^{5} - 3077398160 x^{4} - 76353619120 x^{3} + 288748984560 x^{2} + 221707794080 x - 8821936400416$ |
$15$ |
(1, 7) |
$-\,2^{23}\cdot 3^{12}\cdot 5^{15}\cdot 31^{5}\cdot 47^{13}$ |
$5$ |
$3079.77065296$ |
$10186.815010742723$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$7$ |
|
|
| 15.1.218...000.1 |
$x^{15} + 145 x^{13} - 130 x^{12} + 8410 x^{11} + 5401576 x^{10} + 250650 x^{9} - 786071100 x^{8} + 4229116205 x^{7} + 30356526600 x^{6} + 9759670847621 x^{5} + 605028612190 x^{4} - 1890020683173160 x^{3} - 2535367162720480 x^{2} + 27422952298756080 x + 5898464498853712720$ |
$15$ |
(1, 7) |
$-\,2^{23}\cdot 5^{15}\cdot 7^{13}\cdot 11^{5}\cdot 47^{13}$ |
$5$ |
$4889.33736067$ |
$14519.282237111507$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$7$ |
|
|
| 15.1.498...000.1 |
$x^{15} - 599532 x^{10} - 127262464 x^{5} - 9993586688$ |
$15$ |
(1, 7) |
$-\,2^{23}\cdot 5^{15}\cdot 41^{5}\cdot 47^{13}\cdot 79^{5}$ |
$5$ |
$6023.34571479$ |
$43238.04437403287$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$7$ |
|
|
| 15.1.216...000.1 |
$x^{15} - 128075 x^{10} + 89832421875 x^{5} + 238265673828125$ |
$15$ |
(1, 7) |
$-\,2^{10}\cdot 5^{28}\cdot 47^{13}\cdot 401^{5}$ |
$4$ |
$6641.97045799$ |
$23449.761536701648$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
not computed |
not computed |
$2$ |
$7$ |
|
|
| 20.0.195...625.2 |
$x^{20} - 7 x^{19} + 400 x^{18} - 879 x^{17} + 62865 x^{16} - 1013 x^{15} + 7876524 x^{14} + 23647717 x^{13} + 705136221 x^{12} + 2536463528 x^{11} + 44224034337 x^{10} + 197930226533 x^{9} + 2898973215498 x^{8} + 16970323008747 x^{7} + 174137838839419 x^{6} + 822361467194839 x^{5} + 5587467721135106 x^{4} + 16064752448986945 x^{3} + 82769084983009675 x^{2} + 104479620367122980 x + 455474139643311460$ |
$20$ |
(0, 10) |
$5^{15}\cdot 13^{15}\cdot 47^{18}$ |
$3$ |
$732.104522421$ |
$732.1045224212894$ |
|
|
|
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 24.4.125...125.1 |
$x^{24} - 6 x^{23} - 84 x^{22} + 819 x^{21} + 146 x^{20} - 24971 x^{19} + 56406 x^{18} - 239096 x^{17} + 7833701 x^{16} - 39428226 x^{15} - 114207986 x^{14} + 1847203976 x^{13} - 10394678596 x^{12} + 52141400916 x^{11} - 266216941826 x^{10} + 1172344966045 x^{9} - 4108679132270 x^{8} + 12381458573420 x^{7} - 36417154960545 x^{6} + 98472127101920 x^{5} - 209874826058225 x^{4} + 342775774421350 x^{3} - 451054931471600 x^{2} + 431211451077725 x - 199731406194850$ |
$24$ |
(4, 10) |
$5^{41}\cdot 47^{20}$ |
$2$ |
$386.801935908222$ |
$737.6996554169373$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$54272305965607250000000$ |
$3$ |
| 24.4.125...125.4 |
$x^{24} - 11 x^{23} - 189 x^{22} + 2629 x^{21} + 8301 x^{20} - 214582 x^{19} + 273882 x^{18} + 6663458 x^{17} - 21695303 x^{16} - 61508412 x^{15} + 156482096 x^{14} + 1265169289 x^{13} - 2547063354 x^{12} - 9564484591 x^{11} + 15005245701 x^{10} + 50249144910 x^{9} - 31642359160 x^{8} - 189869689365 x^{7} - 65983955810 x^{6} + 429052010110 x^{5} + 428477991710 x^{4} - 177545028085 x^{3} - 566187092240 x^{2} - 899806835585 x - 901777573915$ |
$24$ |
(4, 10) |
$5^{41}\cdot 47^{20}$ |
$2$ |
$386.801935908222$ |
$737.6996554169373$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$4842528128085221000000$ |
$3$ |
| 24.4.125...125.6 |
$x^{24} - 6 x^{23} - 84 x^{22} + 819 x^{21} + 7196 x^{20} - 53171 x^{19} - 139819 x^{18} + 2029829 x^{17} - 3949199 x^{16} - 51759851 x^{15} + 29060939 x^{14} + 1155848076 x^{13} - 13227291046 x^{12} + 1102816641 x^{11} + 209455877099 x^{10} - 225707541130 x^{9} + 5409964436480 x^{8} + 23024347091270 x^{7} - 213919276754120 x^{6} - 290082186169355 x^{5} + 3006231947654245 x^{4} + 802930022267255 x^{3} - 10849896275710280 x^{2} + 5838016528696855 x + 23363425119504095$ |
$24$ |
(4, 10) |
$5^{41}\cdot 47^{20}$ |
$2$ |
$386.801935908222$ |
$737.6996554169373$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$13$ |
$2380757142382192000000$ |
$2$ |
