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 |
15.1.100...407.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 8 x^{12} + 4 x^{11} - 19 x^{10} + 3 x^{9} + 33 x^{8} - 23 x^{7} - 47 x^{6} + 39 x^{5} + 43 x^{4} - 13 x^{3} - 23 x^{2} - 8 x - 1$ |
$15$ |
[1,7] |
$-\,3^{6}\cdot 11^{8}\cdot 23^{5}$ |
$3$ |
$15.8550352766$ |
$56.56381504121475$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$7$ |
$824.556928356$ |
15.5.245...375.1 |
$x^{15} - 15 x^{13} - 20 x^{12} + 70 x^{11} + 199 x^{10} + 50 x^{9} - 440 x^{8} - 740 x^{7} - 400 x^{6} + 200 x^{5} + 425 x^{4} + 275 x^{3} + 90 x^{2} + 15 x + 1$ |
$15$ |
[5,5] |
$-\,5^{18}\cdot 23^{5}$ |
$2$ |
$19.6188381268$ |
$50.27593132583481$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$9$ |
$9764.00443856$ |
15.3.657...329.1 |
$x^{15} - x^{14} - 4 x^{13} + 11 x^{12} + 7 x^{11} - 61 x^{10} - 20 x^{9} + 174 x^{8} + 70 x^{7} - 242 x^{6} - 84 x^{5} + 175 x^{4} + 14 x^{3} - 83 x^{2} + x + 9$ |
$15$ |
[3,6] |
$3^{7}\cdot 11^{8}\cdot 107^{5}$ |
$3$ |
$28.4791666441$ |
$122.00191969369786$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$8$ |
$276860.988076$ |
15.1.129...375.1 |
$x^{15} - 5 x^{12} + 15 x^{11} + 10 x^{10} - 100 x^{9} + 75 x^{8} - 240 x^{7} + 820 x^{6} - 1430 x^{5} + 2425 x^{4} - 3250 x^{3} + 2740 x^{2} - 1705 x + 1003$ |
$15$ |
[1,7] |
$-\,5^{18}\cdot 23^{7}$ |
$2$ |
$29.8014225521$ |
$50.27593132583481$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$7$ |
$129581.415621$ |
15.5.778...223.1 |
$x^{15} - 4 x^{14} - 12 x^{13} + 63 x^{12} + 75 x^{11} - 365 x^{10} - 859 x^{9} - 1340 x^{8} - 2526 x^{7} + 965 x^{6} - 1651 x^{5} + 7887 x^{4} + 935 x^{3} + 418 x^{2} - 2167 x - 671$ |
$15$ |
[5,5] |
$-\,3^{6}\cdot 11^{12}\cdot 23^{7}$ |
$3$ |
$45.6494595421$ |
$56.56381504121475$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$[5]$ |
$2$ |
$9$ |
$1212792.08283$ |
15.3.122...129.1 |
$x^{15} + 29 x^{13} - 15 x^{12} + 365 x^{11} + 708 x^{10} + 1338 x^{9} + 15525 x^{8} - 1890 x^{7} + 53930 x^{6} - 173362 x^{5} + 36562 x^{4} - 32759 x^{3} - 167023 x^{2} + 651327 x - 295769$ |
$15$ |
[3,6] |
$3^{5}\cdot 11^{12}\cdot 107^{7}$ |
$3$ |
$86.9361351667$ |
$122.00191969369786$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$[5]$ |
$2$ |
$8$ |
$66275507.7691$ |
15.15.736...000.1 |
$x^{15} - 2 x^{14} - 138 x^{13} + 459 x^{12} + 6294 x^{11} - 29158 x^{10} - 90469 x^{9} + 640304 x^{8} - 282922 x^{7} - 3320427 x^{6} + 5075634 x^{5} + 1483772 x^{4} - 5986612 x^{3} + 1193096 x^{2} + 1830056 x - 504860$ |
$15$ |
[15,0] |
$2^{10}\cdot 5^{14}\cdot 19^{8}\cdot 37^{5}$ |
$4$ |
$114.233766454$ |
$824.9951818970933$ |
|
|
|
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$14$ |
$276528967045$ |
15.15.820...000.1 |
$x^{15} - 855 x^{13} - 2470 x^{12} + 273125 x^{11} + 1334484 x^{10} - 41415725 x^{9} - 270977430 x^{8} + 3053529330 x^{7} + 26183048420 x^{6} - 86339970012 x^{5} - 1200406622100 x^{4} - 952711121780 x^{3} + 19747269239240 x^{2} + 70001430753280 x + 71323937370032$ |
$15$ |
[15,0] |
$2^{10}\cdot 5^{18}\cdot 19^{12}\cdot 37^{7}$ |
$4$ |
$622.70309025$ |
$824.9951818970933$ |
|
|
|
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$14$ |
$607452564706000000$ |