| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 10.0.209352647.1 |
$ x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 13 x^{6} - 12 x^{5} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,7^{2}\cdot 23\cdot 431^{2}$ |
$3$ |
$6.79341030426$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.568036883757$ |
| 10.0.212309359.1 |
$ x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 9 x^{6} - 10 x^{5} + 9 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,31\cdot 2617^{2}$ |
$2$ |
$6.80294428088$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.572857558707$ |
| 10.0.214816879.1 |
$ x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 9 x^{6} - 10 x^{5} + 10 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,17^{2}\cdot 79\cdot 97^{2}$ |
$3$ |
$6.81093664096$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.577674891408$ |
| 10.0.215067767.1 |
$ x^{10} - x^{9} - x^{8} + 2 x^{7} + x^{6} - 3 x^{5} + 3 x^{3} - x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,215067767$ |
$1$ |
$6.81173168317$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.5781462354099604$ |
| 10.0.216670707.1 |
$ x^{10} - 3 x^{9} + 5 x^{8} - 6 x^{7} + 6 x^{6} - 4 x^{5} + 2 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 11^{2}\cdot 7369$ |
$3$ |
$6.8167916456$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$1.74293786533$ |
| 10.0.220168975.1 |
$ x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{6} - x^{5} + 4 x^{4} - x^{3} - 3 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}$ |
$4$ |
$6.82771857501$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.586605631071$ |
| 10.0.220506347.1 |
$ x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 3 x^{6} - x^{4} + x^{3} - x + 1 $ |
$10$ |
[0,5] |
$-\,37\cdot 677\cdot 8803$ |
$3$ |
$6.82876408755$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.5880175904588231$ |
| 10.0.224198759.1 |
$ x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - 4 x^{5} + 3 x^{4} + x^{3} - 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,71\cdot 1777^{2}$ |
$2$ |
$6.84011369338$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.59340069383$ |
| 10.0.224415603.1 |
$ x^{10} + 2 x^{8} - 3 x^{7} + 3 x^{6} - 7 x^{5} + 8 x^{4} - 7 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 31^{4}$ |
$2$ |
$6.84077497824$ |
|
|
✓ |
$D_5\times C_5$ (as 10T6) |
trivial |
$6$ |
$4$ |
$1.78149530531$ |
| 10.0.226173952.1 |
$ x^{10} - x^{8} - 2 x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{2} + 1 $ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 220873$ |
$2$ |
$6.84611608122$ |
|
|
not computed |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$4$ |
$4$ |
$1.19443787527$ |
| 10.0.226876987.1 |
$ x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 2 x^{6} + x^{5} - x^{4} - 3 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,43\cdot 2297^{2}$ |
$2$ |
$6.8482411447$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.597809920275$ |
| 10.0.227991979.1 |
$ x^{10} - x^{9} - x^{8} + 3 x^{7} - x^{6} - 3 x^{5} + 3 x^{4} + x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,599\cdot 380621$ |
$2$ |
$6.85159930803$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.5998219105603662$ |
| 10.0.229203619.1 |
$ x^{10} - x^{9} + 2 x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,229203619$ |
$1$ |
$6.85523184156$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6020080437571057$ |
| 10.0.229345007.1 |
$ x^{10} - x^{9} + 6 x^{8} - 3 x^{7} + 11 x^{6} - 3 x^{5} + 11 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,47^{5}$ |
$1$ |
$6.8556546004$ |
|
✓ |
not computed |
$D_5$ (as 10T2) |
trivial |
$2$ |
$4$ |
$0.60186322759$ |
| 10.0.233043179.1 |
$ x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 5 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,97\cdot 463\cdot 5189$ |
$3$ |
$6.86662988937$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6084964369407401$ |
| 10.0.236184579.1 |
$ x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 7 x^{6} - 6 x^{5} + 4 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 37\cdot 109\cdot 241$ |
$4$ |
$6.87583036876$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$1.84211740914$ |
| 10.0.236438047.1 |
$ x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 3 x^{6} + x^{5} + x^{4} - x + 1 $ |
$10$ |
[0,5] |
$-\,236438047$ |
$1$ |
$6.87656791137$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.614960446273$ |
| 10.0.240232739.1 |
$ x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{6} + 4 x^{5} - 4 x^{4} + x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,467\cdot 514417$ |
$2$ |
$6.88752549237$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.622824662223$ |
| 10.0.243226747.1 |
$ x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + 2 x^{6} - x^{5} + x^{4} - 2 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,243226747$ |
$1$ |
$6.89606161454$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6261475736016512$ |
| 10.0.243415027.1 |
$ x^{10} - x^{7} + x^{6} + 2 x^{5} - x^{3} - 2 x^{2} + 1 $ |
$10$ |
[0,5] |
$-\,17\cdot 14318531$ |
$2$ |
$6.89659524764$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6267229276822098$ |
| 10.0.244175707.1 |
$ x^{10} - x^{9} + x^{7} - x^{6} - x^{4} + x^{3} + x^{2} - x + 1 $ |
$10$ |
[0,5] |
$-\,19^{2}\cdot 676387$ |
$2$ |
$6.89874743162$ |
|
|
not computed |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6277987643994235$ |
| 10.0.246071287.1 |
$ x^{10} - 3 x^{9} + 7 x^{8} - 12 x^{7} + 15 x^{6} - 15 x^{5} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,7^{5}\cdot 11^{4}$ |
$2$ |
$6.90408443551$ |
|
|
✓ |
$D_5\times C_5$ (as 10T6) |
trivial |
$2$ |
$4$ |
$0.634803768223$ |
| 10.0.246944619.1 |
$ x^{10} - x^{9} + x^{6} - x^{5} - x^{4} + 3 x^{3} - x^{2} - x + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 73\cdot 13921$ |
$3$ |
$6.90653086059$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$1.90076515959$ |
| 10.0.250679267.1 |
$ x^{10} - x^{9} - 2 x^{8} + x^{7} + 3 x^{6} - 2 x^{4} - 2 x^{3} + 2 x + 1 $ |
$10$ |
[0,5] |
$-\,250679267$ |
$1$ |
$6.91690548889$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6409749870444131$ |
| 10.0.252486127.1 |
$ x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 4 x^{5} + 5 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,787\cdot 320821$ |
$2$ |
$6.92187499705$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.642537334981687$ |
| 10.0.254121139.1 |
$ x^{10} - 2 x^{8} - x^{7} + 2 x^{6} + 3 x^{5} - 3 x^{3} - x^{2} + x + 1 $ |
$10$ |
[0,5] |
$-\,149\cdot 991\cdot 1721$ |
$3$ |
$6.92634435313$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6480210196495108$ |
| 10.0.260270739.1 |
$ x^{10} - x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 2 x^{4} - 4 x^{3} + x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 163\cdot 6571$ |
$3$ |
$6.9429259695$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$1.96704129047$ |
| 10.0.262091507.1 |
$ x^{10} - x^{9} - 2 x^{6} + 3 x^{5} + 3 x^{4} - 4 x^{3} - 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,83\cdot 1777^{2}$ |
$2$ |
$6.94776778804$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.656821013577$ |
| 10.0.262477979.1 |
$ x^{10} - x^{9} + x^{8} - 2 x^{6} + x^{5} - x^{4} + x^{2} + 1 $ |
$10$ |
[0,5] |
$-\,251\cdot 1045729$ |
$2$ |
$6.94879160514$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6577090020502393$ |
| 10.0.262864627.1 |
$ x^{10} - 2 x^{8} - x^{7} + x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,353\cdot 744659$ |
$2$ |
$6.94981453173$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6619032898743505$ |
| 10.0.262909719.1 |
$ x^{10} - x^{8} - x^{7} - 2 x^{6} + 4 x^{4} + x^{3} - 2 x^{2} + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 73\cdot 14821$ |
$3$ |
$6.94993374018$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$1.97569183141$ |
| 10.0.263786699.1 |
$ x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,11\cdot 59^{2}\cdot 83^{2}$ |
$3$ |
$6.95224853606$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.663236848943$ |
| 10.0.268043264.1 |
$ x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 6 x^{5} + 7 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 261761$ |
$2$ |
$6.96338631704$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$4$ |
$4$ |
$1.33676061738$ |
| 10.0.274127275.1 |
$ x^{10} - x^{9} + x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,5^{2}\cdot 59\cdot 185849$ |
$3$ |
$6.9790325665$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6754062116693342$ |
| 10.0.274550779.1 |
$ x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + 3 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,19\cdot 14450041$ |
$2$ |
$6.98011002054$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6811521995711005$ |
| 10.0.277010267.1 |
$ x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,107\cdot 1609^{2}$ |
$2$ |
$6.98633789626$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.679993136866$ |
| 10.0.278005859.1 |
$ x^{10} - x^{9} - x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,278005859$ |
$1$ |
$6.98884477745$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6840713547835329$ |
| 10.0.278645219.1 |
$ x^{10} + 3 x^{8} - x^{7} + 4 x^{6} - x^{5} + 4 x^{4} + 2 x^{2} + 1 $ |
$10$ |
[0,5] |
$-\,317\cdot 879007$ |
$2$ |
$6.99045041632$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6850935429811508$ |
| 10.0.281268947.1 |
$ x^{10} + 3 x^{8} - x^{7} + 4 x^{6} - x^{5} + 4 x^{4} - x^{3} + 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,281268947$ |
$1$ |
$6.99700491098$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6911023529825022$ |
| 10.0.282748447.1 |
$ x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 5 x^{5} + x^{4} + 4 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,282748447$ |
$1$ |
$7.00067671564$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.689666096131428$ |
| 10.0.283885691.1 |
$ x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,8941\cdot 31751$ |
$2$ |
$7.00348737806$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6905689191175234$ |
| 10.0.284152779.1 |
$ x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 3 x^{5} - 2 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 1169353$ |
$2$ |
$7.00414600793$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$6$ |
$4$ |
$2.07998415618$ |
| 10.0.285267739.1 |
$ x^{10} - x^{9} + x^{8} - x^{7} - x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,285267739$ |
$1$ |
$7.00688945735$ |
|
|
not computed |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.6944480441748214$ |
| 10.0.288806267.1 |
$ x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{5} + x^{3} - x + 1 $ |
$10$ |
[0,5] |
$-\,1321\cdot 218627$ |
$2$ |
$7.01553283007$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7003014151706757$ |
| 10.0.290432899.1 |
$ x^{10} - 3 x^{8} - x^{7} + 4 x^{6} + 3 x^{5} - 2 x^{4} - 4 x^{3} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,89\cdot 3263291$ |
$2$ |
$7.01947418146$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7058632532986308$ |
| 10.0.290491759.1 |
$ x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,290491759$ |
$1$ |
$7.01961642725$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7034426859963029$ |
| 10.0.290954507.1 |
$ x^{10} - x^{9} + 2 x^{8} + 2 x^{7} - x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 107$ |
$3$ |
$7.02073383839$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.702250275284$ |
| 10.0.291458939.1 |
$ x^{10} - x^{9} + 2 x^{8} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 2 x^{2} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,197\cdot 1479487$ |
$2$ |
$7.02195008451$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7047631819012555$ |
| 10.0.292693979.1 |
$ x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,127\cdot 239\cdot 9643$ |
$3$ |
$7.02491993562$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7063782727510773$ |
| 10.0.293025059.1 |
$ x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 5 x^{6} - 6 x^{5} + 8 x^{4} + \cdots + 1 $ |
$10$ |
[0,5] |
$-\,293025059$ |
$1$ |
$7.02571415335$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$0.7066552938338644$ |
