| 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 |
| 15.3.872411699045053489.1 |
$x^{15} - x^{14} - 10 x^{12} + 17 x^{11} - 6 x^{10} - 17 x^{9} + 35 x^{8} - 10 x^{7} - 19 x^{6} + 23 x^{5} - 16 x^{4} - 5 x^{3} + 10 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$7^{8}\cdot 73^{6}$ |
$2$ |
$15.7053673385$ |
$31.265121691698095$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$8$ |
$1080.93773334$ |
| 15.3.872411699045053489.2 |
$x^{15} - 4 x^{14} + 10 x^{13} - 12 x^{12} + 5 x^{11} + 9 x^{10} - 5 x^{9} - 17 x^{8} + 21 x^{7} + 4 x^{6} - 27 x^{5} + 17 x^{4} - 10 x^{3} + 7 x^{2} - x + 1$ |
$15$ |
[3,6] |
$7^{8}\cdot 73^{6}$ |
$2$ |
$15.7053673385$ |
$31.265121691698095$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$8$ |
$1080.93773334$ |
| 15.3.669...664.1 |
$x^{15} - 7 x^{14} + 6 x^{13} + 40 x^{12} - 102 x^{11} + 12 x^{10} - 120 x^{9} - 56 x^{8} + 863 x^{7} - 1541 x^{6} - 780 x^{5} - 4768 x^{4} - 2933 x^{3} - 1795 x^{2} - 316 x - 20$ |
$15$ |
[3,6] |
$2^{18}\cdot 7^{10}\cdot 67^{6}$ |
$3$ |
$45.19231711829813$ |
$84.7190521533498$ |
|
|
|
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$2$ |
$8$ |
$14068105.95552779$ |
| 15.3.117...169.1 |
$x^{15} - 30 x^{13} - 21 x^{12} + 369 x^{11} + 420 x^{10} - 2808 x^{9} - 1755 x^{8} + 14124 x^{7} - 44 x^{6} - 56097 x^{5} + 28083 x^{4} + 129444 x^{3} - 80937 x^{2} - 185679 x + 169809$ |
$15$ |
[3,6] |
$3^{24}\cdot 23^{10}$ |
$2$ |
$46.90428984384278$ |
$53.64476966753421$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$8$ |
$5865297.502273302$ |
| 15.3.117...169.2 |
$x^{15} - 30 x^{13} - 12 x^{12} + 369 x^{11} + 171 x^{10} - 2769 x^{9} - 234 x^{8} + 16218 x^{7} + 2328 x^{6} - 58374 x^{5} - 50094 x^{4} + 18009 x^{3} + 57132 x^{2} - 42849 x + 4761$ |
$15$ |
[3,6] |
$3^{24}\cdot 23^{10}$ |
$2$ |
$46.90428984384278$ |
$53.64476966753421$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
$[2, 2]$ |
$2$ |
$8$ |
$1466324.3755683254$ |
| 15.15.108...009.1 |
$x^{15} - 72 x^{13} - 104 x^{12} + 1827 x^{11} + 5091 x^{10} - 15385 x^{9} - 74160 x^{8} - 28503 x^{7} + 259443 x^{6} + 396594 x^{5} - 64647 x^{4} - 586080 x^{3} - 509652 x^{2} - 173151 x - 20691$ |
$15$ |
[15,0] |
$3^{24}\cdot 11^{10}\cdot 23^{6}$ |
$3$ |
$100.541863879$ |
$167.24042866948324$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$14$ |
$43649743656.5$ |
| 15.15.108...009.2 |
$x^{15} - 72 x^{13} - 13 x^{12} + 1827 x^{11} + 525 x^{10} - 19165 x^{9} - 6696 x^{8} + 74394 x^{7} + 32521 x^{6} - 112068 x^{5} - 53361 x^{4} + 60236 x^{3} + 22869 x^{2} - 9438 x - 121$ |
$15$ |
[15,0] |
$3^{24}\cdot 11^{10}\cdot 23^{6}$ |
$3$ |
$100.541863879$ |
$167.24042866948324$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$14$ |
$43649743656.5$ |
| 15.15.840...081.1 |
$x^{15} - 2 x^{14} - 92 x^{13} + 200 x^{12} + 3160 x^{11} - 7448 x^{10} - 49570 x^{9} + 125874 x^{8} + 341063 x^{7} - 935891 x^{6} - 757822 x^{5} + 2472302 x^{4} - 235746 x^{3} - 928580 x^{2} + 204505 x + 18913$ |
$15$ |
[15,0] |
$7^{10}\cdot 19^{6}\cdot 293^{6}$ |
$3$ |
$115.25165800997272$ |
$273.0293304050999$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$2$ |
$14$ |
$24260952073.0449$ |
| 15.15.840...081.2 |
$x^{15} - 2 x^{14} - 92 x^{13} + 277 x^{12} + 2782 x^{11} - 10934 x^{10} - 30166 x^{9} + 166397 x^{8} + 33938 x^{7} - 937228 x^{6} + 863826 x^{5} + 1159088 x^{4} - 1812853 x^{3} + 393041 x^{2} + 171535 x - 4187$ |
$15$ |
[15,0] |
$7^{10}\cdot 19^{6}\cdot 293^{6}$ |
$3$ |
$115.25165800997272$ |
$273.0293304050999$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$2$ |
$14$ |
$24260952073.0449$ |
| 15.15.931...424.1 |
$x^{15} - 7 x^{14} - 173 x^{13} + 1761 x^{12} + 4856 x^{11} - 114315 x^{10} + 327406 x^{9} + 1509135 x^{8} - 12222628 x^{7} + 32857530 x^{6} - 40218201 x^{5} + 15523653 x^{4} + 10460292 x^{3} - 10183180 x^{2} + 1842432 x + 169439$ |
$15$ |
[15,0] |
$2^{10}\cdot 7^{8}\cdot 331^{10}$ |
$3$ |
$214.43266724124695$ |
$277.9525650999282$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$2$ |
$14$ |
$2162852821862.0637$ |
| 15.15.125...824.1 |
$x^{15} - 246 x^{13} - 276 x^{12} + 23881 x^{11} + 49971 x^{10} - 1139708 x^{9} - 3309546 x^{8} + 27214087 x^{7} + 98599630 x^{6} - 292575499 x^{5} - 1334323716 x^{4} + 798522313 x^{3} + 6808612687 x^{2} + 4097115989 x - 2301371389$ |
$15$ |
[15,0] |
$2^{10}\cdot 7^{8}\cdot 11^{10}\cdot 31^{10}$ |
$4$ |
$218.73009308538917$ |
$283.52298751771315$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
$[3]$ |
$2$ |
$14$ |
$1789533950300.736$ |
