| 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 |
| 10.2.10859007357952.1 |
$x^{10} - 4 x^{9} + 2 x^{8} + 10 x^{7} + 19 x^{6} - 32 x^{5} - 37 x^{4} - 22 x^{3} + 28 x^{2} + 16 x + 3$ |
$10$ |
[2,4] |
$2^{10}\cdot 13^{9}$ |
$2$ |
$20.1177317396$ |
$35.84572283738149$ |
|
|
|
$S_5\times C_2$ (as 10T22) |
trivial |
$2$ |
$5$ |
$875.494052893$ |
| 10.0.173744117727232.1 |
$x^{10} + 52 x^{4} + 208$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 13^{9}$ |
$2$ |
$26.5455061772$ |
$49.25036163819202$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$6537.47155015$ |
| 10.2.173744117727232.1 |
$x^{10} - 2 x^{9} + 7 x^{8} - 2 x^{7} + 2 x^{6} + 12 x^{5} - 2 x^{4} - 2 x^{3} - 7 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$2^{14}\cdot 13^{9}$ |
$2$ |
$26.5455061772$ |
$49.25036163819202$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$2893.36038246$ |
| 10.0.694976470908928.1 |
$x^{10} - 2 x^{9} + 7 x^{8} - 2 x^{7} + 2 x^{6} - 14 x^{5} + 76 x^{4} - 262 x^{3} + 409 x^{2} - 392 x + 233$ |
$10$ |
[0,5] |
$-\,2^{16}\cdot 13^{9}$ |
$2$ |
$30.4927792783$ |
$45.16278075151432$ |
|
|
? |
$S_5\times C_2$ (as 10T22) |
$[2]$ |
$2$ |
$4$ |
$5695.26758414$ |
| 10.0.11119623534542848.1 |
$x^{10} + 13 x^{8} + 52 x^{6} + 78 x^{4} + 39 x^{2} + 13$ |
$10$ |
[0,5] |
$-\,2^{20}\cdot 13^{9}$ |
$2$ |
$40.2354634792$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$13469.6623084$ |
| 10.0.11119623534542848.2 |
$x^{10} + 39 x^{6} + 130 x^{4} - 364 x^{2} + 468$ |
$10$ |
[0,5] |
$-\,2^{20}\cdot 13^{9}$ |
$2$ |
$40.2354634792$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$21272.7921606$ |
| 10.2.11119623534542848.1 |
$x^{10} - 13 x^{8} + 52 x^{6} - 78 x^{4} + 39 x^{2} - 13$ |
$10$ |
[2,4] |
$2^{20}\cdot 13^{9}$ |
$2$ |
$40.2354634792$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$37773.8784424$ |
| 10.2.11119623534542848.2 |
$x^{10} + 39 x^{6} - 130 x^{4} - 364 x^{2} - 468$ |
$10$ |
[2,4] |
$2^{20}\cdot 13^{9}$ |
$2$ |
$40.2354634792$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$32760.5669342$ |
| 10.2.42417997492000000.1 |
$x^{10} - 832$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{6}\cdot 13^{9}$ |
$3$ |
$45.9997017892$ |
$58.559925677795036$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$46399.87788012415$ |
| 10.0.44478494138171392.1 |
$x^{10} + 26 x^{6} + 78 x^{4} + 104 x^{2} + 52$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$89.03058187004619$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$51319.7587518$ |
| 10.0.44478494138171392.2 |
$x^{10} - 26 x^{6} + 416 x^{2} + 832$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2, 2]$ |
$2$ |
$4$ |
$14302.6460684$ |
| 10.0.44478494138171392.3 |
$x^{10} + 26 x^{8} + 260 x^{6} + 1144 x^{4} + 2080 x^{2} + 832$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$101.38701477938378$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$31877.6457532$ |
| 10.0.44478494138171392.4 |
$x^{10} + 52 x^{6} - 78 x^{4} + 572 x^{2} + 4212$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$101.38701477938378$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$67602.9883033$ |
| 10.10.44478494138171392.1 |
$x^{10} - 2 x^{9} - 32 x^{8} + 24 x^{7} + 288 x^{6} - 40 x^{5} - 912 x^{4} - 184 x^{3} + 799 x^{2} + 258 x - 92$ |
$10$ |
[10,0] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$67.66771401142387$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$9$ |
$324741.838244$ |
| 10.2.44478494138171392.1 |
$x^{10} - 5 x^{9} + 21 x^{8} - 54 x^{7} + 109 x^{6} - 159 x^{5} + 63 x^{4} + 86 x^{3} - 73 x^{2} + 11 x - 9$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$67.66771401142387$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$53875.7611688$ |
| 10.6.44478494138171392.1 |
$x^{10} - 3 x^{9} - 7 x^{8} + 16 x^{7} + 2 x^{6} + 18 x^{5} + 2 x^{4} + 16 x^{3} - 7 x^{2} - 3 x + 1$ |
$10$ |
[6,2] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$67.66771401142387$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$7$ |
$149708.542246$ |
| 10.2.44478494138171392.2 |
$x^{10} + 26 x^{6} - 78 x^{4} + 104 x^{2} - 52$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$89.03058187004619$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$42984.5118421$ |
| 10.2.44478494138171392.3 |
$x^{10} - 26 x^{6} + 416 x^{2} - 832$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$85.25597728125919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$115255.336177$ |
| 10.2.44478494138171392.4 |
$x^{10} - 26 x^{8} + 260 x^{6} - 1144 x^{4} + 2080 x^{2} - 832$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$98.50072327638404$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$80654.5198332$ |
| 10.2.44478494138171392.5 |
$x^{10} + 52 x^{6} + 78 x^{4} + 572 x^{2} - 4212$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{9}$ |
$2$ |
$46.2184107111$ |
$98.50072327638404$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$31302.6560809$ |
| 10.2.103559564189453125.1 |
$x^{10} - 13$ |
$10$ |
[2,4] |
$5^{10}\cdot 13^{9}$ |
$2$ |
$50.294329349$ |
$64.0272017890382$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[4]$ |
$2$ |
$5$ |
$21665.751690171244$ |
| 10.6.498898015566732613.1 |
$x^{10} - 4 x^{9} + 2 x^{8} - 81 x^{7} - 7 x^{6} - 175 x^{5} + 1263 x^{4} - 490 x^{3} - 1792 x^{2} + 1680 x - 400$ |
$10$ |
[6,2] |
$13^{9}\cdot 19^{6}$ |
$2$ |
$58.8574141257$ |
$91.54069761661445$ |
|
|
? |
$S_5\times C_2$ (as 10T22) |
trivial |
$2$ |
$7$ |
$394857.269809$ |
| 10.0.711655906210742272.1 |
$x^{10} - 2 x^{9} - 6 x^{8} + 24 x^{7} + 132 x^{6} - 560 x^{5} + 1428 x^{4} - 1536 x^{3} + 1865 x^{2} - 210 x + 38$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 13^{9}$ |
$2$ |
$60.9855585566$ |
$80.4709269583546$ |
✓ |
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2, 10]$ |
$2$ |
$4$ |
$13616.2502779$ |
| 10.4.711655906210742272.1 |
$x^{10} + 13 x^{8} - 312 x^{4} - 208 x^{2} + 1872$ |
$10$ |
[4,3] |
$-\,2^{26}\cdot 13^{9}$ |
$2$ |
$60.9855585566$ |
$80.4709269583546$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$6$ |
$851777.667481$ |
| 10.0.711655906210742272.2 |
$x^{10} - 26 x^{6} + 260 x^{4} + 1729 x^{2} + 468$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 13^{9}$ |
$2$ |
$60.9855585566$ |
$80.4709269583546$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$99055.9781045$ |
| 10.6.711655906210742272.1 |
$x^{10} - 13 x^{8} - 52 x^{6} + 780 x^{4} + 52 x^{2} - 1300$ |
$10$ |
[6,2] |
$2^{26}\cdot 13^{9}$ |
$2$ |
$60.9855585566$ |
$104.3578810790265$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$7$ |
$527955.067064$ |
| 10.2.711655906210742272.1 |
$x^{10} + 39 x^{8} + 494 x^{6} + 2210 x^{4} + 3029 x^{2} - 637$ |
$10$ |
[2,4] |
$2^{26}\cdot 13^{9}$ |
$2$ |
$60.9855585566$ |
$104.3578810790265$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$5$ |
$142723.911276$ |
| 10.0.806934703161302768.1 |
$x^{10} - x^{9} + 5 x^{8} + 3 x^{7} + 5 x^{6} + 28 x^{5} + 15 x^{4} + 27 x^{3} + 135 x^{2} - 81 x + 243$ |
$10$ |
[0,5] |
$-\,2^{4}\cdot 13^{9}\cdot 163^{2}\cdot 179$ |
$4$ |
$61.7566656039$ |
$3436.36534351439$ |
✓ |
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2, 8]$ |
$2$ |
$4$ |
$5863.27829979$ |
| 10.2.108...125.1 |
$x^{10} - 85293$ |
$10$ |
[2,4] |
$3^{8}\cdot 5^{6}\cdot 13^{9}$ |
$3$ |
$63.6250334184$ |
$80.99785614491518$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$269072.7566702542$ |
| 10.0.271...000.1 |
$x^{10} + 832$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{6}\cdot 13^{9}$ |
$3$ |
$69.7225100564$ |
$88.76024948345159$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$179316.05163615893$ |
| 10.8.284...088.1 |
$x^{10} - 39 x^{8} + 494 x^{6} - 2210 x^{4} + 3029 x^{2} + 637$ |
$10$ |
[8,1] |
$-\,2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$104.3578810790265$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$8$ |
$867553.906862$ |
| 10.4.284...088.1 |
$x^{10} + 13 x^{8} - 52 x^{6} - 780 x^{4} + 52 x^{2} + 1300$ |
$10$ |
[4,3] |
$-\,2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$104.3578810790265$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$6$ |
$501237.883118$ |
| 10.6.284...088.1 |
$x^{10} - 130 x^{6} + 780 x^{4} - 1183 x^{2} - 468$ |
$10$ |
[6,2] |
$2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$7$ |
$766836.072013$ |
| 10.2.284...088.1 |
$x^{10} - 338 x^{6} - 2964 x^{4} - 5967 x^{2} - 52$ |
$10$ |
[2,4] |
$2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$5$ |
$134370.596215$ |
| 10.6.284...088.2 |
$x^{10} - 2 x^{9} - 32 x^{8} + 128 x^{7} + 314 x^{6} - 2068 x^{5} - 1172 x^{4} + 11776 x^{3} + 1215 x^{2} - 21998 x + 6356$ |
$10$ |
[6,2] |
$2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$7$ |
$1241489.14224$ |
| 10.2.284...088.2 |
$x^{10} + 234 x^{6} - 156 x^{4} + 273 x^{2} - 52$ |
$10$ |
[2,4] |
$2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$5$ |
$592799.089111$ |
| 10.2.284...088.3 |
$x^{10} + 39 x^{8} + 494 x^{6} + 1794 x^{4} - 4979 x^{2} - 26325$ |
$10$ |
[2,4] |
$2^{28}\cdot 13^{9}$ |
$2$ |
$70.0540107926$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$5$ |
$170186.00881$ |
| 10.6.838...125.1 |
$x^{10} - 520 x^{6} - 780 x^{5} + 4550 x^{4} + 7995 x^{3} - 5655 x^{2} - 10725 x - 3263$ |
$10$ |
[6,2] |
$3^{4}\cdot 5^{10}\cdot 13^{9}$ |
$3$ |
$78.0490323932$ |
$262.37568549441204$ |
|
|
? |
$(A_5^2 : C_2):C_2$ (as 10T41) |
trivial |
$2$ |
$7$ |
$2149261.4164$ |
| 10.0.103...000.1 |
$x^{10} + 202176$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{6}\cdot 13^{9}$ |
$4$ |
$79.6738206318$ |
$101.42876656139832$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[4]$ |
$2$ |
$4$ |
$481267.96320692974$ |
| 10.0.113...352.1 |
$x^{10} + 234 x^{6} + 156 x^{4} + 273 x^{2} + 52$ |
$10$ |
[0,5] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$4$ |
$606722.370349$ |
| 10.8.113...352.1 |
$x^{10} - 338 x^{6} + 2964 x^{4} - 5967 x^{2} + 52$ |
$10$ |
[8,1] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$8$ |
$6096807.28302$ |
| 10.4.113...352.1 |
$x^{10} - 130 x^{6} + 52 x^{4} + 3263 x^{2} + 52$ |
$10$ |
[4,3] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$6$ |
$467445.131876$ |
| 10.0.113...352.2 |
$x^{10} + 39 x^{8} + 390 x^{6} + 1274 x^{4} + 923 x^{2} + 117$ |
$10$ |
[0,5] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
✓ |
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 42]$ |
$2$ |
$4$ |
$13616.2502779$ |
| 10.8.113...352.2 |
$x^{10} - 13 x^{8} + 52 x^{6} - 52 x^{4} - 52 x^{2} + 52$ |
$10$ |
[8,1] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$8$ |
$3281061.84262$ |
| 10.4.113...352.2 |
$x^{10} - 130 x^{6} - 780 x^{4} - 1183 x^{2} + 468$ |
$10$ |
[4,3] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$6$ |
$1805833.19683$ |
| 10.8.113...352.3 |
$x^{10} - 13 x^{8} - 208 x^{6} + 3952 x^{4} - 15808 x^{2} + 832$ |
$10$ |
[8,1] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$8$ |
$2895059.329$ |
| 10.4.113...352.3 |
$x^{10} + 39 x^{8} + 338 x^{6} - 338 x^{4} - 2197 x^{2} + 2197$ |
$10$ |
[4,3] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$6$ |
$921395.884486$ |
| 10.0.113...352.3 |
$x^{10} - 13 x^{8} + 52 x^{6} + 156 x^{4} + 364 x^{2} + 468$ |
$10$ |
[0,5] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$4$ |
$240275.360345$ |
| 10.8.113...352.4 |
$x^{10} - 364 x^{6} + 1456 x^{4} - 1924 x^{2} + 832$ |
$10$ |
[8,1] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$195.58416308264313$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$8$ |
$1962910.18888$ |
| 10.4.113...352.4 |
$x^{10} - 2 x^{9} - 6 x^{8} - 80 x^{7} - 258 x^{6} + 324 x^{5} + 2104 x^{4} + 2208 x^{3} - 7001 x^{2} - 10974 x + 2378$ |
$10$ |
[4,3] |
$-\,2^{30}\cdot 13^{9}$ |
$2$ |
$80.4709269584$ |
$141.32723931785225$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$6$ |
$512322.075567$ |
