| 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 |
| 13.13.491...641.1 |
$x^{13} - x^{12} - 24 x^{11} + 19 x^{10} + 190 x^{9} - 116 x^{8} - 601 x^{7} + 246 x^{6} + 738 x^{5} - 215 x^{4} - 291 x^{3} + 68 x^{2} + 10 x - 1$ |
$13$ |
[13,0] |
$53^{12}$ |
$1$ |
$39.0516388455$ |
$39.05163884547241$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$1314145.36669$ |
| 13.13.590...441.1 |
$x^{13} - x^{12} - 36 x^{11} + 77 x^{10} + 365 x^{9} - 1193 x^{8} - 617 x^{7} + 5541 x^{6} - 4414 x^{5} - 4575 x^{4} + 6321 x^{3} + 411 x^{2} - 2196 x + 293$ |
$13$ |
[13,0] |
$79^{12}$ |
$1$ |
$56.4489381067$ |
$56.44893810672074$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$14045368.3938$ |
| 13.13.255...961.1 |
$x^{13} - x^{12} - 60 x^{11} + 27 x^{10} + 1199 x^{9} - 33 x^{8} - 9610 x^{7} - 3352 x^{6} + 33548 x^{5} + 20328 x^{4} - 47723 x^{3} - 34869 x^{2} + 21271 x + 15667$ |
$13$ |
[13,0] |
$131^{12}$ |
$1$ |
$90.0335289186$ |
$90.03352891861981$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$292369424.433$ |
| 13.13.224...601.1 |
$x^{13} - x^{12} - 72 x^{11} + 129 x^{10} + 1672 x^{9} - 3386 x^{8} - 16810 x^{7} + 32367 x^{6} + 81708 x^{5} - 121902 x^{4} - 196272 x^{3} + 127412 x^{2} + 217458 x + 61399$ |
$13$ |
[13,0] |
$157^{12}$ |
$1$ |
$106.410453613$ |
$106.41045361273743$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$1334709178.87$ |
| 13.13.542...361.1 |
$x^{13} - 78 x^{11} - 65 x^{10} + 2080 x^{9} + 2457 x^{8} - 24128 x^{7} - 27027 x^{6} + 137683 x^{5} + 110214 x^{4} - 376064 x^{3} - 128206 x^{2} + 363883 x - 12167$ |
$13$ |
[13,0] |
$13^{24}$ |
$1$ |
$113.896611641$ |
$113.89661164093096$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$2733056590.62$ |
| 13.13.884...681.1 |
$x^{13} - x^{12} - 144 x^{11} + 161 x^{10} + 6530 x^{9} - 9620 x^{8} - 109398 x^{7} + 196143 x^{6} + 512628 x^{5} - 917970 x^{4} - 650724 x^{3} + 1134730 x^{2} + 253950 x - 409375$ |
$13$ |
[13,0] |
$313^{12}$ |
$1$ |
$201.17749146$ |
$201.177491460457$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$927977436616.0109$ |
| 13.13.571...001.1 |
$x^{13} - x^{12} - 204 x^{11} - 181 x^{10} + 10752 x^{9} + 9116 x^{8} - 208418 x^{7} - 161679 x^{6} + 1686466 x^{5} + 1207646 x^{4} - 4904338 x^{3} - 3051848 x^{2} + 896956 x + 144209$ |
$13$ |
[13,0] |
$443^{12}$ |
$1$ |
$277.226159648$ |
$277.22615964805635$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$983737918371.0616$ |
| 13.13.399...641.1 |
$x^{13} - x^{12} - 240 x^{11} - 293 x^{10} + 19153 x^{9} + 45777 x^{8} - 616830 x^{7} - 1795569 x^{6} + 7791196 x^{5} + 23224049 x^{4} - 29107980 x^{3} - 68466088 x^{2} + 31673025 x + 4516075$ |
$13$ |
[13,0] |
$521^{12}$ |
$1$ |
$321.995799388$ |
$321.99579938787$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$15429359577074.87$ |
| 13.13.717...241.1 |
$x^{13} - x^{12} - 252 x^{11} + 1123 x^{10} + 15626 x^{9} - 107844 x^{8} - 204415 x^{7} + 3094114 x^{6} - 4853400 x^{5} - 22393129 x^{4} + 91453411 x^{3} - 116380476 x^{2} + 47088126 x - 1165671$ |
$13$ |
[13,0] |
$547^{12}$ |
$1$ |
$336.800646612$ |
$336.80064661199583$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$468882596177901.8$ |
| 13.13.213...801.1 |
$x^{13} - x^{12} - 276 x^{11} + 1967 x^{10} + 8169 x^{9} - 109375 x^{8} + 114077 x^{7} + 1684091 x^{6} - 4924742 x^{5} - 5465967 x^{4} + 34969245 x^{3} - 20502539 x^{2} - 55304818 x + 57031547$ |
$13$ |
[13,0] |
$599^{12}$ |
$1$ |
$366.250819642$ |
$366.25081964246385$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$1689788670896.741$ |
| 13.13.926...521.1 |
$x^{13} - x^{12} - 312 x^{11} + 765 x^{10} + 31073 x^{9} - 114643 x^{8} - 1071164 x^{7} + 4472586 x^{6} + 13888428 x^{5} - 61633266 x^{4} - 43862553 x^{3} + 238916059 x^{2} - 140970591 x - 1052321$ |
$13$ |
[13,0] |
$677^{12}$ |
$1$ |
$410.063466568$ |
$410.06346656832307$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$3454123871256.3633$ |
| 13.13.161...281.1 |
$x^{13} - x^{12} - 396 x^{11} + 1235 x^{10} + 45719 x^{9} - 158783 x^{8} - 2232951 x^{7} + 7665285 x^{6} + 47857178 x^{5} - 162308625 x^{4} - 381260855 x^{3} + 1359880245 x^{2} + 391778734 x - 2211739517$ |
$13$ |
[13,0] |
$859^{12}$ |
$1$ |
$510.859391801$ |
$510.85939180125763$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$107792443172161.95$ |
| 13.13.326...521.1 |
$x^{13} - x^{12} - 420 x^{11} + 4253 x^{10} + 2721 x^{9} - 193733 x^{8} + 735262 x^{7} + 31458 x^{6} - 3569396 x^{5} + 1482536 x^{4} + 4833237 x^{3} + 1733969 x^{2} - 40719 x - 57869$ |
$13$ |
[13,0] |
$911^{12}$ |
$1$ |
$539.340604042$ |
$539.3406040422938$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$345319680754792.2$ |
| 13.13.458...681.1 |
$x^{13} - x^{12} - 432 x^{11} + 1203 x^{10} + 46006 x^{9} - 37046 x^{8} - 2039413 x^{7} - 3276218 x^{6} + 27799988 x^{5} + 87214801 x^{4} - 38878963 x^{3} - 420910202 x^{2} - 520002704 x - 190078187$ |
$13$ |
[13,0] |
$937^{12}$ |
$1$ |
$553.533918196$ |
$553.5339181962555$ |
|
✓ |
|
$C_{13}$ (as 13T1) |
trivial |
$2$ |
$12$ |
$169264238822310.44$ |
