| 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 |
| 10.2.817298432.1 |
$x^{10} + x^{8} - 2 x^{7} + x^{4} + 2 x^{3} - x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 798143$ |
$2$ |
$7.78463163117$ |
$3422.0470085736833$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.66778396748$ |
| 10.2.964631552.1 |
$x^{10} - 2 x^{9} + x^{8} + 4 x^{7} - 7 x^{6} + 2 x^{5} + 5 x^{4} - 6 x^{3} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 61\cdot 15443$ |
$3$ |
$7.91473076926$ |
$3717.7173637419914$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.8507144334675927$ |
| 10.2.1054194688.1 |
$x^{10} - x^{8} + x^{6} - 2 x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1029487$ |
$2$ |
$7.98531554693$ |
$3886.4765357359815$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.9748032437163785$ |
| 10.0.1069597696.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 1044529$ |
$2$ |
$7.99690700837$ |
$3914.766539643522$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$2.014994650294586$ |
| 10.2.1205582848.1 |
$x^{10} + x^{8} - 2 x^{7} - 4 x^{6} + x^{4} + 2 x^{3} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 433\cdot 2719$ |
$3$ |
$8.09318943758$ |
$4156.178281400404$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$2.1493708643137945$ |
| 10.2.1473993728.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 3 x^{6} + 2 x^{5} - 2 x^{4} - 2 x^{3} - 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1439447$ |
$2$ |
$8.25751865602$ |
$4595.613071578301$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$2.4990075970568686$ |
| 10.2.1659075584.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 2 x^{5} - 5 x^{4} + 6 x^{3} - 3 x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 97\cdot 16703$ |
$3$ |
$8.35577269495$ |
$4875.607363623645$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$2.633083710367652$ |
| 10.2.2132098048.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 3 x^{6} - 2 x^{5} - x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 2082127$ |
$2$ |
$8.56802484679$ |
$5527.124210604444$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.147139546410656$ |
| 10.2.2208676864.1 |
$x^{10} - 2 x^{6} - 2 x^{5} + x^{4} + 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1297\cdot 1663$ |
$3$ |
$8.59831236101$ |
$5625.507774887711$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.2685583613878677$ |
| 10.0.2296054784.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 3 x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 937\cdot 2393$ |
$3$ |
$8.63173750158$ |
$5735.704403595827$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$3.1569848420896713$ |
| 10.2.2359204864.1 |
$x^{10} - 2 x^{9} + 4 x^{7} - 3 x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 101\cdot 22811$ |
$3$ |
$8.65518919249$ |
$5814.046029654347$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.323609392878388$ |
| 10.2.2368093184.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 2 x^{3} - 5 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 107\cdot 21613$ |
$3$ |
$8.65844452555$ |
$5824.987961915435$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.4182119441280725$ |
| 10.0.2479178752.1 |
$x^{10} - 2 x^{9} + 2 x^{7} + x^{6} - 2 x^{5} - 2 x^{4} + 4 x^{3} - 2 x + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2421073$ |
$2$ |
$8.69822793594$ |
$5960.045274853087$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$2.7067592531405533$ |
| 10.2.2578807808.1 |
$x^{10} - 2 x^{9} + 4 x^{7} - 5 x^{6} + 4 x^{4} - 4 x^{3} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 2518367$ |
$2$ |
$8.73256642154$ |
$6078.621845482041$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.4013120429741486$ |
| 10.0.2621719552.1 |
$x^{10} - 2 x^{9} + 2 x^{7} - 3 x^{6} + 2 x^{5} + 2 x^{4} - 2 x + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2560273$ |
$2$ |
$8.74698986452$ |
$6128.987769878812$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$2.620458102564021$ |
| 10.2.2686499840.1 |
$x^{10} - 2 x^{9} + 3 x^{6} - 3 x^{4} - 2 x^{3} + x^{2} + 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 5\cdot 524707$ |
$3$ |
$8.76836625273$ |
$6204.246548923042$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.7582377322404477$ |
| 10.2.2770902016.1 |
$x^{10} - x^{8} - 4 x^{7} + 2 x^{5} + 5 x^{4} - x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 31\cdot 41\cdot 2129$ |
$4$ |
$8.79553207823$ |
$6300.952745413752$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$4.405427883393783$ |
| 10.0.2784461824.3 |
$x^{10} - 3 x^{8} + 5 x^{6} - 3 x^{4} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 17^{2}\cdot 97^{2}$ |
$3$ |
$8.79982684928$ |
$155.54496030380426$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$2.56948274463$ |
| 10.0.2784461824.4 |
$x^{10} + 2 x^{8} + x^{6} + x^{4} + 3 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 17^{2}\cdot 97^{2}$ |
$3$ |
$8.79982684928$ |
$155.54496030380426$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$2.91684796275$ |
| 10.0.2792932352.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 7 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 7\cdot 31\cdot 12569$ |
$4$ |
$8.80250016073$ |
$6325.951335546709$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$2.9078799769647667$ |
| 10.0.2803778560.1 |
$x^{10} - 4 x^{9} + 9 x^{8} - 12 x^{7} + 11 x^{6} - 6 x^{5} + 4 x^{3} - 3 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 5\cdot 11\cdot 49783$ |
$4$ |
$8.80591260684$ |
$6338.222685336574$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$3.0082758937132694$ |
| 10.2.2871786496.1 |
$x^{10} - 2 x^{9} + 2 x^{8} + 2 x^{7} - 3 x^{6} + 2 x^{4} - 4 x^{2} + 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 89\cdot 31511$ |
$3$ |
$8.82704244487$ |
$6414.631502535551$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$4.5128034925790255$ |
| 10.2.2913688576.1 |
$x^{10} - 2 x^{9} + x^{8} + 2 x^{6} - 2 x^{5} - 3 x^{4} + 10 x^{3} - 9 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 23\cdot 193\cdot 641$ |
$4$ |
$8.83983814184$ |
$6461.259799798214$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.6636642772173023$ |
| 10.2.2958089216.1 |
$x^{10} - 2 x^{9} + 5 x^{6} - 8 x^{5} + 5 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 17\cdot 251\cdot 677$ |
$4$ |
$8.85321735746$ |
$6510.304057838015$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$3.815820617627826$ |
| 10.0.2993112064.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 7 x^{6} - 6 x^{5} + 8 x^{4} - 4 x^{3} + 4 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2922961$ |
$2$ |
$8.86364385793$ |
$6548.730631356973$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$4$ |
$4.531034085151527$ |
| 10.0.3233514496.3 |
$x^{10} - 2 x^{6} - x^{4} + 2 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 1777^{2}$ |
$2$ |
$8.93238597983$ |
$161.46906501368989$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$3.35313007593$ |
| 10.2.3570351104.1 |
$x^{10} - x^{8} - 2 x^{7} - 3 x^{6} + 2 x^{5} + 6 x^{4} + 2 x^{3} - x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 19\cdot 183509$ |
$3$ |
$9.02134086458$ |
$7152.388584884884$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$4.336028233823944$ |
| 10.2.3920428032.1 |
$x^{10} - 2 x^{9} + 2 x^{8} + 2 x^{7} - x^{6} + 3 x^{4} - 3 x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 3\cdot 61\cdot 20921$ |
$4$ |
$9.10611956939$ |
$7494.840263096144$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$5.485206914530048$ |
| 10.4.4278387712.1 |
$x^{10} + 2 x^{8} - 3 x^{6} - 4 x^{5} - 3 x^{4} + 3 x^{2} + 4 x + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 4178113$ |
$2$ |
$9.18603326599$ |
$7829.530268378556$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.909096319482492$ |
| 10.0.4996793344.1 |
$x^{10} - x^{8} + x^{6} + x^{4} - 2 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 47^{4}$ |
$2$ |
$9.32973135944$ |
$26.259989346721234$ |
|
|
✓ |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
trivial |
$2$ |
$4$ |
$3.40459819781$ |
| 10.4.5240996864.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{6} + 4 x^{5} - 5 x^{4} + 2 x^{3} - 2 x^{2} + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 43\cdot 119027$ |
$3$ |
$9.37435487205$ |
$8665.678813131688$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$6.786950124400048$ |
| 10.0.5402838016.2 |
$x^{10} + x^{8} + x^{6} + x^{4} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2297^{2}$ |
$2$ |
$9.4029081689$ |
$183.58031647172328$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$4.70705900665$ |
| 10.4.5497725952.1 |
$x^{10} - 4 x^{9} + 6 x^{8} - 4 x^{7} - 3 x^{6} + 10 x^{5} - 5 x^{4} - 2 x^{3} - x^{2} + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 659\cdot 8147$ |
$3$ |
$9.41929305038$ |
$8875.384609989489$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$6.888473502806637$ |
| 10.4.5862433792.1 |
$x^{10} - 5 x^{8} + 8 x^{6} - 2 x^{5} - 5 x^{4} + 6 x^{3} + 3 x^{2} - 4 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 61\cdot 127\cdot 739$ |
$4$ |
$9.47998816376$ |
$9165.045255517438$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$7.228913520877232$ |
| 10.4.6450439168.1 |
$x^{10} + 2 x^{8} - 3 x^{6} - 2 x^{5} - 5 x^{4} - 2 x^{3} - x^{2} + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 277\cdot 22741$ |
$3$ |
$9.57103552892$ |
$9613.6936819812$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$7.693396194522481$ |
| 10.4.6709363712.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 2 x^{3} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 6552113$ |
$2$ |
$9.60877742322$ |
$9804.745065555871$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$7.787797480160848$ |
| 10.0.7013057536.2 |
$x^{10} - 2 x^{8} + 3 x^{6} - 2 x^{4} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2617^{2}$ |
$2$ |
$9.65140944407$ |
$195.9509971831376$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$4.06386377514$ |
| 10.0.7013057536.4 |
$x^{10} + x^{8} - x^{6} - 2 x^{4} + x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 2617^{2}$ |
$2$ |
$9.65140944407$ |
$195.9509971831376$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$4.85514211532$ |
| 10.4.7357563904.1 |
$x^{10} + x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + x^{4} + 2 x^{3} - 5 x^{2} + 4 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 7185121$ |
$2$ |
$9.69780404105$ |
$10267.451491321332$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$8.239607418380537$ |
| 10.0.9320743936.4 |
$x^{10} + 5 x^{8} + 10 x^{6} + 9 x^{4} + 3 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 7^{2}\cdot 431^{2}$ |
$3$ |
$9.92990417929$ |
$210.39396182774803$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$6.13869575268$ |
| 10.4.9446523904.1 |
$x^{10} - 3 x^{8} - 2 x^{7} + 6 x^{5} + 7 x^{4} - 6 x^{3} - 5 x^{2} + 2 x + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 643\cdot 14347$ |
$3$ |
$9.94322353105$ |
$11634.069455561847$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$9.604138646551347$ |
| 10.0.9770927104.1 |
$x^{10} - x^{8} + x^{6} + 2 x^{4} - 3 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3089^{2}$ |
$2$ |
$9.97685309187$ |
$212.8896611659375$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$4.95638871543$ |
| 10.0.9770927104.3 |
$x^{10} - x^{6} + 2 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3089^{2}$ |
$2$ |
$9.97685309187$ |
$212.8896611659375$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$9.48218376352$ |
| 10.4.10151576576.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 2 x^{7} + 7 x^{6} - 9 x^{4} - 2 x^{3} + 3 x^{2} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 19\cdot 313\cdot 1667$ |
$4$ |
$10.0150552498$ |
$12060.418709754282$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$9.981277687157105$ |
| 10.4.10328179712.1 |
$x^{10} - 2 x^{9} - x^{8} + 6 x^{7} - 3 x^{6} - 2 x^{5} + 2 x^{3} + x^{2} - 2 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 29^{2}\cdot 67\cdot 179$ |
$4$ |
$10.0323431523$ |
$3959.5108013641834$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$10.897549164179722$ |
| 10.0.10703143936.2 |
$x^{10} + x^{4} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 53^{2}\cdot 61^{2}$ |
$3$ |
$10.0681838316$ |
$217.79528265527523$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$9.88513472077$ |
| 10.0.10703143936.4 |
$x^{10} + 3 x^{6} - 5 x^{4} + 3 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 53^{2}\cdot 61^{2}$ |
$3$ |
$10.0681838316$ |
$217.79528265527523$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$9.82939779065$ |
| 10.4.10791289856.1 |
$x^{10} - x^{8} - 4 x^{7} - 3 x^{6} + 5 x^{4} + 8 x^{3} + 6 x^{2} + 4 x + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 19\cdot 373\cdot 1487$ |
$4$ |
$10.0764449317$ |
$12434.61425652297$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$10.175443862916179$ |
| 10.4.10861659136.1 |
$x^{10} - 2 x^{9} - x^{8} + 2 x^{7} + 3 x^{6} - 4 x^{5} - x^{4} + 6 x^{3} - 6 x^{2} + 4 x - 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 857\cdot 12377$ |
$3$ |
$10.0829965119$ |
$12475.091021475902$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$10.521328564302069$ |
| 10.4.11130545152.1 |
$x^{10} + 2 x^{8} - 2 x^{7} - 2 x^{6} - 2 x^{5} - 3 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$10$ |
[4,3] |
$-\,2^{10}\cdot 1019\cdot 10667$ |
$3$ |
$10.1076837117$ |
$12628.560702986004$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$10.65655163432146$ |
