| 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 |
| 10.2.37968750000000000.17 |
$x^{10} + 10 x^{8} - 50 x^{7} + 5 x^{6} - 460 x^{5} + 450 x^{4} - 1300 x^{3} + 2065 x^{2} - 4950 x + 4398$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{5}\cdot 5^{16}$ |
$3$ |
$45.4927960472$ |
$76.14002785301618$ |
|
|
|
$D_5^2$ (as 10T9) |
trivial |
$2$ |
$5$ |
$124538.478587$ |
| 10.2.80000000000000000.10 |
$x^{10} - 20 x^{8} + 110 x^{6} - 224 x^{5} + 650 x^{4} + 1200 x^{3} + 1005 x^{2} + 560 x - 98$ |
$10$ |
[2,4] |
$2^{19}\cdot 5^{16}$ |
$2$ |
$49.0127418939$ |
$87.91893115408898$ |
|
|
|
$D_5^2$ (as 10T9) |
trivial |
$2$ |
$5$ |
$217914.981688$ |
| 10.6.388...000.9 |
$x^{10} - 40 x^{8} - 40 x^{7} + 440 x^{6} + 1264 x^{5} - 1000 x^{4} - 7920 x^{3} - 4680 x^{2} + 5440 x - 1664$ |
$10$ |
[6,2] |
$2^{20}\cdot 3^{5}\cdot 5^{16}$ |
$3$ |
$90.9855920944$ |
$181.0925257186244$ |
|
|
? |
$A_5 \wr C_2$ (as 10T40) |
$[3]$ |
$2$ |
$7$ |
$3949039.55312$ |
| 10.2.196...000.77 |
$x^{10} - 30 x^{8} - 100 x^{7} - 690 x^{6} - 3168 x^{5} + 4600 x^{4} + 20400 x^{3} - 25920 x^{2} - 46080 x + 279648$ |
$10$ |
[2,4] |
$2^{16}\cdot 3^{9}\cdot 5^{16}$ |
$3$ |
$107.006246214$ |
$355.5457809039788$ |
|
|
? |
$(A_5^2 : C_2):C_2$ (as 10T41) |
$[2]$ |
$2$ |
$5$ |
$2853215.12468$ |
| 10.4.131...000.24 |
$x^{10} - 80 x^{8} - 80 x^{7} + 2420 x^{6} + 4816 x^{5} - 31200 x^{4} - 97440 x^{3} + 102210 x^{2} + 660560 x + 652064$ |
$10$ |
[4,3] |
$-\,2^{33}\cdot 5^{16}$ |
$2$ |
$129.3454013154715$ |
$427.37299590924493$ |
|
|
? |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$2$ |
$6$ |
$24581480.895741507$ |
| 10.2.398...000.110 |
$x^{10} - 50 x^{8} - 100 x^{7} + 250 x^{6} + 4700 x^{5} + 19375 x^{4} - 122500 x^{3} + 248125 x^{2} - 712500 x + 480625$ |
$10$ |
[2,4] |
$2^{14}\cdot 3^{13}\cdot 5^{16}$ |
$3$ |
$144.561162507$ |
$950.265841342682$ |
|
|
? |
$(A_5^2 : C_2):C_2$ (as 10T41) |
trivial |
$2$ |
$5$ |
$36595186.2326$ |
| 10.0.794...875.8 |
$x^{10} + 110 x^{8} - 825 x^{7} + 5280 x^{6} - 84260 x^{5} + 296450 x^{4} - 3000800 x^{3} + 18227440 x^{2} - 37758050 x + 396143473$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 5^{16}\cdot 11^{8}$ |
$3$ |
$154.891213554$ |
$259.2371174970958$ |
|
|
? |
$D_5\times C_5$ (as 10T6) |
$[5]$ |
$6$ |
$4$ |
$6510785.96422$ |
| 10.4.188...000.12 |
$x^{10} - 200 x^{7} + 1200 x^{5} - 1250 x^{4} + 15000 x^{2} - 45000$ |
$10$ |
[4,3] |
$-\,2^{21}\cdot 3^{10}\cdot 5^{16}$ |
$3$ |
$168.902567962$ |
$1173.9863021963665$ |
|
|
? |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$2$ |
$6$ |
$87854721.2326$ |
| 10.0.895...000.1 |
$x^{10} + 20 x^{8} + 210 x^{6} - 408 x^{5} + 1100 x^{4} + 1200 x^{3} + 1030 x^{2} - 480 x + 48$ |
$10$ |
[0,5] |
$-\,2^{28}\cdot 3^{7}\cdot 5^{16}$ |
$3$ |
$197.342612424$ |
$1219.2726587564941$ |
|
|
|
$S_5^2 \wr C_2$ (as 10T43) |
$[5]$ |
$2$ |
$4$ |
$79830167.8085$ |
| 15.5.982108001708984375.1 |
$x^{15} - 4 x^{13} - 11 x^{12} + 9 x^{11} + 30 x^{10} + 5 x^{9} + 7 x^{8} - 32 x^{7} - 7 x^{6} - 78 x^{5} - 120 x^{4} + 36 x^{3} + 154 x^{2} + 134 x + 43$ |
$15$ |
[5,5] |
$-\,5^{16}\cdot 23^{5}$ |
$2$ |
$15.8298676303$ |
$105.41109538118516$ |
|
|
? |
$C_5\wr S_3$ (as 15T32) |
trivial |
$2$ |
$9$ |
$1326.38565727$ |
