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 |
15.1.154669958288795403.1 |
$x^{15} - x^{12} + 2 x^{9} - 3 x^{6} + 3 x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$255.941349852$ |
15.1.154669958288795403.2 |
$x^{15} - 2 x^{12} + 2 x^{9} - x^{6} + 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$288.777984962$ |
15.1.154669958288795403.3 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
15.1.154669958288795403.4 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
15.1.154669958288795403.5 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
15.1.154669958288795403.6 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
15.3.726...941.1 |
$x^{15} + 3 x^{13} - 5 x^{12} + 9 x^{11} - 15 x^{10} - 20 x^{9} + 45 x^{8} - 165 x^{7} + 216 x^{6} - 351 x^{5} + 336 x^{4} - 242 x^{3} + 81 x^{2} - 15 x + 1$ |
$15$ |
[3,6] |
$3^{15}\cdot 47^{7}$ |
$2$ |
$18.0897926306$ |
$35.143128879205776$ |
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$8$ |
$2590.79097197$ |
15.3.726...941.2 |
$x^{15} + 6 x^{13} - 4 x^{12} + 9 x^{11} + 3 x^{10} - 18 x^{9} + 45 x^{8} - 126 x^{7} + 216 x^{6} - 324 x^{5} + 243 x^{4} - 205 x^{3} + 90 x^{2} - 30 x + 11$ |
$15$ |
[3,6] |
$3^{15}\cdot 47^{7}$ |
$2$ |
$18.0897926306$ |
$35.143128879205776$ |
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$8$ |
$2652.22907153$ |
15.5.662...523.1 |
$x^{15} - 2 x^{12} - 6 x^{9} + 15 x^{6} - 8 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{13}\cdot 401^{6}$ |
$2$ |
$28.4946178223$ |
|
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$9$ |
$276624.713435$ |
15.5.596...707.1 |
$x^{15} - 20 x^{9} - 27 x^{6} - 10 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 401^{6}$ |
$2$ |
$32.9897484308$ |
|
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$9$ |
$568023.433984$ |
15.5.596...707.2 |
$x^{15} - 4 x^{12} + x^{9} + 7 x^{6} - 3 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 401^{6}$ |
$2$ |
$32.98974843077385$ |
$92.09596346702632$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$9$ |
$570718.1182507712$ |
15.5.596...707.3 |
$x^{15} - 4 x^{12} + x^{9} + 7 x^{6} - 3 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 401^{6}$ |
$2$ |
$32.98974843077385$ |
$92.09596346702632$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$9$ |
$570718.1182507712$ |
15.15.691...125.1 |
$x^{15} - x^{14} - 4452 x^{13} - 50296 x^{12} + 5784843 x^{11} + 91964349 x^{10} - 3060924423 x^{9} - 54750997444 x^{8} + 781942057449 x^{7} + 14664282257229 x^{6} - 102907697118067 x^{5} - 1901998615798914 x^{4} + 6977459265924253 x^{3} + 113854569421380357 x^{2} - 202156325407652112 x - 2402311520555338669$ |
$15$ |
[15,0] |
$3^{12}\cdot 5^{5}\cdot 79^{4}\cdot 401^{7}\cdot 50329^{4}$ |
$5$ |
$3884.54196168$ |
$7923243.703822074$ |
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
$[3]$ |
$2$ |
$14$ |
$5820768023810000000000$ |