| 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 |
| 15.1.481...000.1 |
$x^{15} + 155 x^{13} - 3120 x^{12} - 43740 x^{11} - 4322064 x^{10} + 29553325 x^{9} + 336699800 x^{8} + 5895045565 x^{7} - 7268082900 x^{6} + 689232153107 x^{5} - 7105193819530 x^{4} - 16823896467110 x^{3} + 241484266064340 x^{2} - 2845372937103000 x + 25424027623886288$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 5^{18}\cdot 11^{12}\cdot 61^{8}$ |
$4$ |
$1110.44245927$ |
$4229.059693568257$ |
|
|
|
$C_5^2:D_{15}$ (as 15T31) |
$[5, 5]$ |
$2$ |
$7$ |
$17603642299200000$ |
| 15.1.481...000.2 |
$x^{15} - 5 x^{14} - 615 x^{13} - 1345 x^{12} + 178955 x^{11} + 1097623 x^{10} - 49110085 x^{9} + 112654015 x^{8} + 11648990810 x^{7} - 91266360040 x^{6} - 1546253890847 x^{5} + 9883081080065 x^{4} + 92007754171735 x^{3} - 302495276454075 x^{2} - 908213995898190 x + 8093159542525366$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 5^{18}\cdot 11^{12}\cdot 61^{8}$ |
$4$ |
$1110.44245927$ |
$4229.059693568257$ |
|
|
|
$C_5^2:D_{15}$ (as 15T31) |
$[5, 5]$ |
$2$ |
$7$ |
$21001356499000000$ |
| 15.1.481...000.3 |
$x^{15} - 5 x^{14} - 615 x^{13} + 9875 x^{12} + 126595 x^{11} - 1569657 x^{10} - 2348425 x^{9} + 412242755 x^{8} + 732981090 x^{7} - 22446808360 x^{6} + 76738261693 x^{5} + 1900405609625 x^{4} - 1387206519825 x^{3} - 38238130553415 x^{2} + 13759052300650 x + 602197229407786$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 5^{18}\cdot 11^{12}\cdot 61^{8}$ |
$4$ |
$1110.442459269198$ |
$4229.059693568257$ |
|
|
|
$C_5^2:D_{15}$ (as 15T31) |
$[5, 5]$ |
$2$ |
$7$ |
$14040275790386718$ |
| 15.1.481...000.4 |
$x^{15} - 5 x^{14} - 615 x^{13} + 9875 x^{12} + 126595 x^{11} - 1569657 x^{10} - 2348425 x^{9} + 412242755 x^{8} + 732981090 x^{7} - 22446808360 x^{6} + 76738261693 x^{5} + 1900405609625 x^{4} - 1387206519825 x^{3} - 38238130553415 x^{2} + 13759052300650 x + 602197229407786$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 5^{18}\cdot 11^{12}\cdot 61^{8}$ |
$4$ |
$1110.442459269198$ |
$4229.059693568257$ |
|
|
|
$C_5^2:D_{15}$ (as 15T31) |
$[5, 5]$ |
$2$ |
$7$ |
$14040275790386718$ |
| 15.15.142...192.1 |
$x^{15} - 7 x^{14} - 61709 x^{13} - 2007357 x^{12} + 1231831520 x^{11} + 93277045460 x^{10} - 6650961625168 x^{9} - 987072530657200 x^{8} - 28319323358595040 x^{7} + 860907007423227232 x^{6} + 60370334006953788288 x^{5} + 755175919354707053120 x^{4} - 12434446258906106164736 x^{3} - 331068493589414852154368 x^{2} - 1831737201071142890547968 x - 2179454923921583313202432$ |
$15$ |
[15,0] |
$2^{10}\cdot 37^{7}\cdot 109964946338501^{4}$ |
$3$ |
$47516.9554237$ |
$1651166767440.7258$ |
|
|
|
$C_5^2:D_{15}$ (as 15T31) |
not computed |
$2$ |
$14$ |
|
