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 |
13.5.28261626739249.1 |
$x^{13} - 3 x^{12} + 3 x^{11} + 3 x^{10} - 13 x^{9} + 14 x^{8} + 2 x^{7} - 20 x^{6} + 18 x^{5} + x^{4} - 11 x^{3} + 6 x^{2} + x - 1$ |
$13$ |
[5,4] |
$2161\cdot 13078031809$ |
$2$ |
$10.8319706242$ |
$5316166.545477013$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$33.0726626498$ |
13.5.28318356165577.1 |
$x^{13} - 3 x^{11} - 4 x^{10} + 2 x^{9} + 9 x^{8} + 6 x^{7} - 4 x^{6} - 10 x^{5} - 3 x^{4} + 4 x^{3} + 4 x^{2} - 1$ |
$13$ |
[5,4] |
$1721\cdot 16454593937$ |
$2$ |
$10.8336416122$ |
$5321499.428316891$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$33.1184429974$ |
13.5.132939170094109.1 |
$x^{13} - x^{12} - x^{11} - 3 x^{10} + x^{9} + 5 x^{8} + 5 x^{7} + 3 x^{6} - 7 x^{5} - 7 x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1$ |
$13$ |
[5,4] |
$132939170094109$ |
$1$ |
$12.2021074028$ |
$11529924.982154436$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$84.1149437602$ |
13.5.197683647463424.1 |
$x^{13} - 2 x^{12} + x^{11} - 3 x^{10} - 5 x^{9} + 7 x^{8} + 2 x^{7} + 6 x^{6} + 4 x^{5} - 6 x^{4} - 8 x^{3} + 6 x - 2$ |
$13$ |
[5,4] |
$2^{14}\cdot 12065652311$ |
$2$ |
$12.5802727589$ |
$549595.2837715879$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$173.327894786$ |
13.5.1204994394291500.1 |
$x^{13} - 3 x^{12} + 2 x^{10} + 6 x^{9} - 9 x^{7} - 3 x^{6} + x^{5} + 4 x^{4} - 8 x^{3} - 3 x^{2} + 3 x + 1$ |
$13$ |
[5,4] |
$2^{2}\cdot 5^{3}\cdot 83\cdot 11171\cdot 2599231$ |
$5$ |
$14.4569197834$ |
$10381617.17294946$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$546.676164956$ |
13.5.5020153876560896.1 |
$x^{13} - 4 x^{12} + 13 x^{10} + 6 x^{9} - 39 x^{8} - 16 x^{7} + 54 x^{6} + 45 x^{5} - 47 x^{4} - 48 x^{3} + 9 x^{2} + 24 x + 4$ |
$13$ |
[5,4] |
$2^{10}\cdot 83\cdot 173\cdot 341423081$ |
$4$ |
$16.1342010261$ |
$8856630.528664047$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$8$ |
$1981.72650066$ |
13.5.5749519947196921.1 |
$x^{13} - 2 x^{12} - 3 x^{11} + 7 x^{10} + 5 x^{9} - 16 x^{8} - 6 x^{7} + 18 x^{6} + 2 x^{5} - 16 x^{4} - 4 x^{3} + 7 x^{2} + x - 1$ |
$13$ |
[5,4] |
$7^{4}\cdot 241^{2}\cdot 6421^{2}$ |
$3$ |
$16.3034438732$ |
$27143.05132536518$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$8$ |
$838.358604129$ |
13.5.274918279650903001.1 |
$x^{13} - 3 x^{11} - 2 x^{10} + 2 x^{9} + 4 x^{8} - 2 x^{7} - 3 x^{6} - x^{5} + 3 x^{4} - 4 x^{2} + 1$ |
$13$ |
[5,4] |
$47^{2}\cdot 89^{2}\cdot 163^{2}\cdot 769^{2}$ |
$4$ |
$21.9521570645$ |
$101667.42283652654$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$8$ |
$12272.0363797$ |
13.5.842...704.1 |
$x^{13} - x^{12} - 3 x^{11} - 7 x^{10} + 37 x^{9} - 9 x^{8} - 168 x^{7} + 24 x^{6} + 396 x^{5} + 20 x^{4} - 128 x^{3} + 192 x^{2} - 176 x - 16$ |
$13$ |
[5,4] |
$2^{28}\cdot 3^{22}$ |
$2$ |
$28.563292541$ |
$90.51754317479573$ |
|
|
|
$\PSL(3,3)$ (as 13T7) |
trivial |
$2$ |
$8$ |
$185892.213477$ |
13.5.842...704.2 |
$x^{13} - 2 x^{12} - 8 x^{10} + 55 x^{9} - 90 x^{8} - 108 x^{7} + 684 x^{6} - 1341 x^{5} + 1526 x^{4} - 1090 x^{3} + 468 x^{2} - 100 x + 8$ |
$13$ |
[5,4] |
$2^{28}\cdot 3^{22}$ |
$2$ |
$28.563292541$ |
$90.51754317479573$ |
|
|
|
$\PSL(3,3)$ (as 13T7) |
trivial |
$2$ |
$8$ |
$185892.213477$ |