| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.11.350...609.1 |
$x^{15} - 3 x^{14} - 16 x^{13} + 49 x^{12} + 32 x^{11} - 38 x^{10} - 174 x^{9} - 390 x^{8} + 969 x^{7} + 348 x^{6} - 1173 x^{5} + 120 x^{4} + 333 x^{3} + 24 x^{2} - 88 x + 13$ |
$15$ |
[11,2] |
$7^{10}\cdot 2281^{2}\cdot 48859^{2}$ |
$3$ |
$43.2853906374$ |
$38630.79297259466$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$12$ |
$15546964.7594$ |
| 15.3.119...625.1 |
$x^{15} - 5 x^{13} - 10 x^{12} + 139 x^{10} + 50 x^{9} - 1670 x^{8} - 1950 x^{7} + 6980 x^{6} + 16836 x^{5} + 5450 x^{4} - 28890 x^{3} - 58420 x^{2} - 39745 x - 7279$ |
$15$ |
[3,6] |
$5^{18}\cdot 7^{10}\cdot 3331^{2}$ |
$3$ |
$74.4456482954$ |
|
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$8$ |
$191983513.22$ |
| 15.7.461...416.1 |
$x^{15} - 6 x^{14} - 15 x^{13} + 195 x^{12} - 177 x^{11} - 1944 x^{10} + 125 x^{9} + 17799 x^{8} + 6408 x^{7} - 65914 x^{6} - 5610 x^{5} + 101934 x^{4} - 28655 x^{3} - 49518 x^{2} + 36987 x - 10313$ |
$15$ |
[7,4] |
$2^{12}\cdot 3^{20}\cdot 17^{2}\cdot 3343733^{2}$ |
$4$ |
$81.4597496787$ |
$92267.1110657069$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$10$ |
$574507211.585$ |
| 15.3.555...504.1 |
$x^{15} - 5 x^{14} - 33 x^{13} + 233 x^{12} + 65 x^{11} - 2325 x^{10} + 815 x^{9} + 13241 x^{8} - 6709 x^{7} - 40119 x^{6} + 11733 x^{5} + 69219 x^{4} + 7603 x^{3} - 9583 x^{2} - 13475 x + 2107$ |
$15$ |
[3,6] |
$2^{12}\cdot 7^{10}\cdot 13^{2}\cdot 883^{2}\cdot 19081^{2}$ |
$5$ |
$82.4688708273$ |
$153177.95971385858$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$8$ |
$480573521.927$ |
| 15.11.226...000.1 |
$x^{15} - 5 x^{14} - 57 x^{13} + 289 x^{12} + 825 x^{11} - 4717 x^{10} - 3601 x^{9} + 31833 x^{8} + 1339 x^{7} - 83815 x^{6} + 2237 x^{5} + 55003 x^{4} + 36939 x^{3} + 1177 x^{2} - 4915 x + 235$ |
$15$ |
[11,2] |
$2^{12}\cdot 5^{8}\cdot 13^{10}\cdot 101323^{2}$ |
$4$ |
$105.600175278$ |
$40335.637070503304$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$12$ |
$28726471148.4$ |
| 15.15.664...064.1 |
$x^{15} - 5 x^{14} - 97 x^{13} + 473 x^{12} + 2481 x^{11} - 13381 x^{10} - 15393 x^{9} + 124473 x^{8} - 25813 x^{7} - 367383 x^{6} + 182005 x^{5} + 402515 x^{4} - 197917 x^{3} - 110047 x^{2} + 54733 x - 3877$ |
$15$ |
[15,0] |
$2^{12}\cdot 7^{10}\cdot 13^{4}\cdot 83^{2}\cdot 293^{2}\cdot 18439^{2}$ |
$6$ |
$179.817516029$ |
$790236.1655745264$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$14$ |
$2157836539700$ |
| 15.7.622...529.1 |
$x^{15} - 148 x^{13} - 2 x^{12} + 9164 x^{11} + 196 x^{10} - 303942 x^{9} - 7001 x^{8} + 5695781 x^{7} + 103900 x^{6} - 57180412 x^{5} - 407256 x^{4} + 240215638 x^{3} - 2362248 x^{2} - 5490 x + 27$ |
$15$ |
[7,4] |
$7^{10}\cdot 3848209^{2}\cdot 3858721^{2}$ |
$3$ |
$208.749589734$ |
$14100993.36106469$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$10$ |
$1308217127750$ |
| 15.15.103...169.1 |
$x^{15} - 164 x^{13} - 14 x^{12} + 10901 x^{11} + 1470 x^{10} - 375360 x^{9} - 54292 x^{8} + 7059483 x^{7} + 798140 x^{6} - 68843164 x^{5} - 2899414 x^{4} + 272554703 x^{3} - 17470362 x^{2} + 322560 x - 1512$ |
$15$ |
[15,0] |
$7^{12}\cdot 83^{2}\cdot 349^{2}\cdot 94524289^{2}$ |
$4$ |
$215.975600653$ |
$8374749.701373385$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$14$ |
$11611996840600$ |
