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 |
15.1.403...192.1 |
$x^{15} - 2 x^{14} - 22 x^{13} + 68 x^{12} + 413 x^{11} - 450 x^{10} - 652 x^{9} - 4616 x^{8} + 132244 x^{7} - 235016 x^{6} + 907904 x^{5} - 1886720 x^{4} + 3758400 x^{3} - 5200000 x^{2} + 6720000 x - 3200000$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 11^{12}\cdot 19^{10}$ |
$3$ |
$127.955377577833$ |
$137.13917807673286$ |
|
|
|
$D_{15}$ (as 15T2) |
$[15]$ |
$2$ |
$7$ |
$103999637383.03754$ |
15.15.464...121.2 |
$x^{15} - x^{14} - 200 x^{13} - 235 x^{12} + 14183 x^{11} + 39397 x^{10} - 404770 x^{9} - 1625940 x^{8} + 4071591 x^{7} + 23923079 x^{6} - 3550930 x^{5} - 131623425 x^{4} - 118897750 x^{3} + 169055000 x^{2} + 288950000 x + 110453125$ |
$15$ |
[15,0] |
$19^{10}\cdot 31^{14}$ |
$2$ |
$175.565824969$ |
$175.5658249685855$ |
|
✓ |
|
$C_{15}$ (as 15T1) |
$[3]$ |
$2$ |
$14$ |
$4307906685437.854$ |
18.6.542...456.1 |
$x^{18} - 342 x^{16} - 36 x^{15} + 48735 x^{14} + 10260 x^{13} - 3707052 x^{12} - 1169640 x^{11} + 159067791 x^{10} + 67033368 x^{9} - 3672377190 x^{8} - 1962305028 x^{7} + 36541480257 x^{6} + 25207730388 x^{5} - 20070476568 x^{4} - 138100642416 x^{3} - 388291940784 x^{2} + 4030534525824 x + 2619356183744$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{24}\cdot 19^{10}\cdot 103^{6}$ |
$4$ |
$208.236126851$ |
|
|
|
|
$C_3\wr A_5$ (as 18T722) |
trivial |
$2$ |
$11$ |
$116981440829000$ |
30.0.667...871.2 |
$x^{30} - x^{29} + x^{28} - 435 x^{27} + 435 x^{26} - 435 x^{25} + 71828 x^{24} - 73254 x^{23} + 73254 x^{22} - 5793808 x^{21} + 6053340 x^{20} + 14165418 x^{19} + 224311506 x^{18} - 239334416 x^{17} - 2796258713 x^{16} - 4288134645 x^{15} + 4572312203 x^{14} + 136203241821 x^{13} + 113469981164 x^{12} - 74180478523 x^{11} - 2235550162996 x^{10} - 2568144065606 x^{9} + 8584872397430 x^{8} + 7838656364939 x^{7} + 22733400061847 x^{6} - 97839113997555 x^{5} + 78561638673700 x^{4} - 205965358815375 x^{3} + 563597213463125 x^{2} - 552854548037500 x + 184810498046875$ |
$30$ |
[0,15] |
$-\,19^{20}\cdot 31^{29}$ |
$2$ |
$196.857532883$ |
$196.85753288303582$ |
✓ |
✓ |
|
$C_{30}$ (as 30T1) |
not computed |
$2$ |
$14$ |
|