| 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 |
| 10.2.1229312000000.1 |
$x^{10} - 2 x^{5} - 7$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$16.1795415671$ |
$44.85913848622377$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$221.023142466$ |
| 10.0.2626093750000.1 |
$x^{10} - x^{5} + 2$ |
$10$ |
[0,5] |
$-\,2^{4}\cdot 5^{10}\cdot 7^{5}$ |
$3$ |
$17.4554489244$ |
$33.35078970092884$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$358.43996516$ |
| 10.2.3137425850000.1 |
$x^{10} - 2 x^{9} + 5 x^{8} + x^{7} - 8 x^{6} + 33 x^{5} - 40 x^{4} + 47 x^{3} - 29 x^{2} + 9 x - 1$ |
$10$ |
[2,4] |
$2^{4}\cdot 5^{5}\cdot 13^{7}$ |
$3$ |
$17.7687692302$ |
$26.65425283047811$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$345.754087382$ |
| 10.2.3317760000000.1 |
$x^{10} - 2 x^{9} + 7 x^{8} - 6 x^{6} + 16 x^{5} + 18 x^{4} + x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{4}\cdot 5^{7}$ |
$3$ |
$17.8683518913$ |
$30.052561791840834$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$316.983661586$ |
| 10.0.4000000000000.1 |
$x^{10} - 8 x^{5} + 20$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{12}$ |
$2$ |
$18.2056420303$ |
$60.87423301804088$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$798.275763248$ |
| 10.2.5120000000000.1 |
$x^{10} - 4 x^{5} + 2$ |
$10$ |
[2,4] |
$2^{19}\cdot 5^{10}$ |
$2$ |
$18.6606598307$ |
$27.020295676770523$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$463.484759448$ |
| 10.2.5120000000000.2 |
$x^{10} - 4 x^{5} - 4$ |
$10$ |
[2,4] |
$2^{19}\cdot 5^{10}$ |
$2$ |
$18.6606598307$ |
$27.020295676770523$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$460.148189147$ |
| 10.0.5697685546875.1 |
$x^{10} - 5 x^{5} + 7$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 5^{10}\cdot 7^{4}$ |
$3$ |
$18.8612229067$ |
$52.29432532936716$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$6$ |
$4$ |
$966.014131559$ |
| 10.0.6250000000000.3 |
$x^{10} - 4 x^{5} + 5$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 5^{14}$ |
$2$ |
$19.0365393872$ |
$52.47338784029768$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$845.582607098$ |
| 10.2.8493465600000.2 |
$x^{10} - 8 x^{8} + 19 x^{6} - 4 x^{5} - 32 x^{4} - 4 x^{3} + 21 x^{2} + 4 x - 6$ |
$10$ |
[2,4] |
$2^{25}\cdot 3^{4}\cdot 5^{5}$ |
$3$ |
$19.6294663617$ |
$36.22550880125431$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$661.800404962$ |
| 10.0.12960000000000.3 |
$x^{10} - 4 x^{9} - x^{8} + 36 x^{7} - 76 x^{6} + 4 x^{5} + 252 x^{4} - 512 x^{3} + 527 x^{2} - 332 x + 109$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$20.4767251108$ |
$55.38678134438504$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$1644.89465662$ |
| 10.0.15366400000000.1 |
$x^{10} - 2 x^{9} + x^{8} - 8 x^{7} + 44 x^{6} - 98 x^{5} + 118 x^{4} - 84 x^{3} + 77 x^{2} - 16 x + 1$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{8}\cdot 7^{4}$ |
$3$ |
$20.8284625336$ |
$44.4433225403395$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$1597.7483886$ |
| 10.0.25920000000000.2 |
$x^{10} - 2 x^{5} + 3$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$21.9464105734$ |
$49.314553191475$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$1005.43390155$ |
| 10.0.26214400000000.3 |
$x^{10} - 4 x^{9} + 13 x^{8} - 16 x^{7} + 2 x^{6} + 40 x^{5} - 58 x^{4} - 24 x^{3} + 118 x^{2} - 96 x + 26$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 5^{8}$ |
$2$ |
$21.9712108661$ |
$64.8262638677105$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$3285.52322575$ |
| 10.2.38880000000000.2 |
$x^{10} - 10 x^{5} - 2$ |
$10$ |
[2,4] |
$2^{14}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$22.8545474245$ |
$33.092968553609026$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$1946.20076541$ |
| 10.2.38880000000000.3 |
$x^{10} - 2 x^{5} - 2$ |
$10$ |
[2,4] |
$2^{14}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$22.8545474245$ |
$33.092968553609026$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$1272.297362$ |
| 10.0.39319091796875.3 |
$x^{10} - 3 x^{5} + 5$ |
$10$ |
[0,5] |
$-\,5^{12}\cdot 11^{5}$ |
$2$ |
$22.88022799595464$ |
$76.50465323972388$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$1476.0029860207223$ |
| 10.0.42017500000000.2 |
$x^{10} - 2 x^{5} + 8$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 5^{10}\cdot 7^{5}$ |
$3$ |
$23.0326029419$ |
$33.35078970092884$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$2023.00449362$ |
| 10.2.49766400000000.1 |
$x^{10} - 4 x^{5} - 2$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{5}\cdot 5^{8}$ |
$3$ |
$23.4257563872$ |
$41.1465213085208$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$2597.0635105$ |
| 10.2.49766400000000.2 |
$x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} - 13 x^{6} + 26 x^{5} - 9 x^{4} + 4 x^{3} + x^{2} - 6 x + 3$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{5}\cdot 5^{8}$ |
$3$ |
$23.4257563872$ |
$44.09974961415671$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$3007.20122744$ |
| 10.2.50198813600000.2 |
$x^{10} - x^{9} - 4 x^{8} - 2 x^{7} + 21 x^{6} + 3 x^{5} - 44 x^{4} + 4 x^{3} + 36 x^{2} - 10$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{5}\cdot 13^{7}$ |
$3$ |
$23.4460315639$ |
$26.65425283047811$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$1520.82585843$ |
| 10.0.65610000000000.1 |
$x^{10} - 4 x^{9} + 17 x^{8} - 16 x^{7} + 48 x^{6} + 32 x^{5} + 78 x^{4} + 56 x^{3} + 37 x^{2} + 14 x + 2$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$24.0822468528$ |
$58.36204567714984$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$3300.66400903$ |
| 10.2.77760000000000.4 |
$x^{10} + 10 x^{8} + 35 x^{6} - 10 x^{5} + 50 x^{4} - 50 x^{3} + 25 x^{2} - 50 x + 19$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$24.4948974278$ |
$59.36208242021212$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$3386.18599518$ |
| 10.0.100000000000000.3 |
$x^{10} - 6 x^{5} + 10$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{14}$ |
$2$ |
$25.1188643151$ |
$69.23905036032698$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$3286.75748645$ |
| 10.0.100000000000000.7 |
$x^{10} - 12 x^{5} + 40$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{14}$ |
$2$ |
$25.1188643151$ |
$69.23905036032698$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$3181.64612642$ |
| 10.0.100000000000000.8 |
$x^{10} - 16 x^{5} + 80$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{14}$ |
$2$ |
$25.1188643151$ |
$69.23905036032698$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$3452.56686242$ |
| 10.0.118652343750000.1 |
$x^{10} - x^{5} + 4$ |
$10$ |
[0,5] |
$-\,2^{4}\cdot 3^{5}\cdot 5^{15}$ |
$3$ |
$25.5521608181$ |
$41.562889344091865$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$4$ |
$1804.64761862$ |
| 10.2.129600000000000.2 |
$x^{10} - 26 x^{5} - 81$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{4}\cdot 5^{11}$ |
$3$ |
$25.7786695923$ |
$43.356828069359494$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$2354.74011406$ |
| 10.2.196830000000000.4 |
$x^{10} - 6 x^{5} - 3$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{9}\cdot 5^{10}$ |
$3$ |
$26.8787537952$ |
$38.91994610896826$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$3183.78101653$ |
| 10.2.196830000000000.7 |
$x^{10} - 12 x^{5} + 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{9}\cdot 5^{10}$ |
$3$ |
$26.8787537952$ |
$38.91994610896826$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$4551.99225427$ |
| 10.2.200000000000000.1 |
$x^{10} - 10 x^{8} + 35 x^{6} - 6 x^{5} - 50 x^{4} + 30 x^{3} + 25 x^{2} - 30 x - 41$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{14}$ |
$2$ |
$26.921732182$ |
$44.338776096061444$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$3168.78653493$ |
| 10.2.200000000000000.5 |
$x^{10} + 10 x^{8} + 35 x^{6} - 18 x^{5} + 50 x^{4} - 90 x^{3} + 25 x^{2} - 90 x + 31$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{14}$ |
$2$ |
$26.921732182$ |
$44.338776096061444$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$3153.77901251$ |
| 10.2.204800000000000.10 |
$x^{10} - 5 x^{8} + 10 x^{6} - 32 x^{5} + 30 x^{4} + 20 x^{2} - 80 x + 76$ |
$10$ |
[2,4] |
$2^{22}\cdot 5^{11}$ |
$2$ |
$26.9856569535$ |
$42.82013114405259$ |
|
|
|
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$2284.9030591$ |
| 10.2.204800000000000.11 |
$x^{10} + 5 x^{8} - 20 x^{7} - 5 x^{6} - 108 x^{5} + 5 x^{4} - 180 x^{3} + 155 x^{2} - 80 x + 271$ |
$10$ |
[2,4] |
$2^{22}\cdot 5^{11}$ |
$2$ |
$26.9856569535$ |
$42.82013114405259$ |
|
|
|
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$2545.03282151$ |
| 10.2.221852656250000.1 |
$x^{10} - 5 x^{5} + 2$ |
$10$ |
[2,4] |
$2^{4}\cdot 5^{10}\cdot 17^{5}$ |
$3$ |
$27.2023524498$ |
$51.973451949027215$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$5220.84151455$ |
| 10.2.251942400000000.1 |
$x^{10} - 18 x^{5} + 27$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{9}\cdot 5^{8}$ |
$3$ |
$27.5505406738$ |
$48.3915605608158$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$6350.88631492$ |
| 10.2.268738560000000.15 |
$x^{10} - 4 x^{9} + 12 x^{8} - 12 x^{7} + 12 x^{5} - 78 x^{4} + 84 x^{3} + 66 x^{2} - 100 x + 10$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{8}\cdot 5^{7}$ |
$3$ |
$27.7289227957$ |
$30.052561791840834$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$3487.09018118$ |
| 10.2.290072656250000.1 |
$x^{10} - 37 x^{5} - 64$ |
$10$ |
[2,4] |
$2^{4}\cdot 5^{11}\cdot 13^{5}$ |
$3$ |
$27.9415619121$ |
$39.95868408682308$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$4012.5771005$ |
| 10.2.327680000000000.1 |
$x^{10} - 10 x^{8} + 35 x^{6} - 4 x^{5} - 50 x^{4} + 20 x^{3} + 25 x^{2} - 20 x - 28$ |
$10$ |
[2,4] |
$2^{25}\cdot 5^{10}$ |
$2$ |
$28.2842712475$ |
$48.7041079571417$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$4688.57830172$ |
| 10.2.327680000000000.2 |
$x^{10} + 10 x^{8} + 35 x^{6} - 4 x^{5} + 50 x^{4} - 20 x^{3} + 25 x^{2} - 20 x - 4$ |
$10$ |
[2,4] |
$2^{25}\cdot 5^{10}$ |
$2$ |
$28.2842712475$ |
$48.7041079571417$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$4199.41202639$ |
| 10.0.379687500000000.1 |
$x^{10} - 20 x^{8} + 140 x^{6} - 10 x^{5} - 400 x^{4} + 100 x^{3} + 400 x^{2} - 200 x + 52$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{14}$ |
$3$ |
$28.7040137869$ |
$47.27410672366759$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$6$ |
$4$ |
$7311.10948819$ |
| 10.0.379687500000000.4 |
$x^{10} - 20 x^{8} + 140 x^{6} - 20 x^{5} - 400 x^{4} + 200 x^{3} + 400 x^{2} - 400 x + 112$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{14}$ |
$3$ |
$28.7040137869$ |
$47.27410672366759$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$6$ |
$4$ |
$7786.79299083$ |
| 10.0.384160000000000.2 |
$x^{10} - 10 x^{8} + 50 x^{6} - 6 x^{5} - 100 x^{4} - 20 x^{3} + 100 x^{2} + 100 x + 34$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{10}\cdot 7^{4}$ |
$3$ |
$28.7376475603$ |
$44.4433225403395$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$4$ |
$4$ |
$6880.27102658$ |
| 10.2.413515226250000.1 |
$x^{10} - 2 x^{9} - 45 x^{6} - 12 x^{5} + 69 x^{4} - 120 x^{2} + 10 x - 5$ |
$10$ |
[2,4] |
$2^{4}\cdot 3^{9}\cdot 5^{7}\cdot 7^{5}$ |
$4$ |
$28.9500388289$ |
$41.400887305536884$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$[2]$ |
$2$ |
$5$ |
$8566.28937855$ |
| 10.0.414720000000000.2 |
$x^{10} - 4 x^{5} + 6$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$65.07094305238193$ |
|
|
✓ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$6373.95677269$ |
| 10.0.414720000000000.4 |
$x^{10} - 4 x^{5} + 12$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$65.07094305238193$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$3610.14664543$ |
| 10.0.414720000000000.7 |
$x^{10} - 8 x^{5} + 18$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$57.209677623540124$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$6083.54672061$ |
| 10.0.414720000000000.8 |
$x^{10} - 8 x^{5} + 48$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$65.07094305238193$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$4$ |
$4157.65595695$ |
| 10.2.414720000000000.3 |
$x^{10} + 10 x^{8} + 35 x^{6} - 12 x^{5} + 50 x^{4} - 60 x^{3} + 25 x^{2} - 60 x + 4$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$50.159560671712846$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$6494.59921782$ |
| 10.2.414720000000000.5 |
$x^{10} - 10 x^{8} + 35 x^{6} - 4 x^{5} - 50 x^{4} + 20 x^{3} + 25 x^{2} - 20 x - 14$ |
$10$ |
[2,4] |
$2^{19}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$28.9584623647$ |
$50.159560671712846$ |
|
|
? |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
trivial |
$2$ |
$5$ |
$6845.2120417$ |
