| 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 |
| 5.1.2209.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + 1$ |
$5$ |
[1,2] |
$47^{2}$ |
$1$ |
$4.66486567972$ |
$6.855654600401044$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$0.346947612066$ |
| 5.1.6241.1 |
$x^{5} - x^{4} + x^{3} - 2 x^{2} + 3 x - 1$ |
$5$ |
[1,2] |
$79^{2}$ |
$1$ |
$5.74183669575$ |
$8.888194417315589$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$0.803647538428$ |
| 5.1.10609.1 |
$x^{5} - 2 x^{4} + 3 x^{3} - 3 x^{2} + x + 1$ |
$5$ |
[1,2] |
$103^{2}$ |
$1$ |
$6.38461758703$ |
$10.14889156509222$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$1.17533265698$ |
| 5.1.14161.1 |
$x^{5} - x^{4} - x^{2} + 3 x - 1$ |
$5$ |
[1,2] |
$7^{2}\cdot 17^{2}$ |
$2$ |
$6.76423651557$ |
$10.908712114635714$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$1.11888701515$ |
| 5.1.16129.1 |
$x^{5} - x^{4} - 2 x^{3} + x^{2} + 3 x - 1$ |
$5$ |
[1,2] |
$127^{2}$ |
$1$ |
$6.94258951984$ |
$11.269427669584644$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$1.56204861479$ |
| 5.1.17161.1 |
$x^{5} - x^{4} + 2 x^{3} - x^{2} + x + 2$ |
$5$ |
[1,2] |
$131^{2}$ |
$1$ |
$7.02924237174$ |
$11.445523142259598$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$2.28609483361$ |
| 5.1.20449.1 |
$x^{5} - x^{4} - x^{3} + 3 x - 1$ |
$5$ |
[1,2] |
$11^{2}\cdot 13^{2}$ |
$2$ |
$7.28005088662$ |
$11.958260743101398$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$1.36161206374$ |
| 5.1.25281.1 |
$x^{5} + x^{3} - 3 x^{2} + x - 3$ |
$5$ |
[1,2] |
$3^{2}\cdot 53^{2}$ |
$2$ |
$7.5955434025$ |
$12.609520212918492$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$2.754377469$ |
| 5.1.32041.1 |
$x^{5} - x^{4} + 3 x^{2} - x + 2$ |
$5$ |
[1,2] |
$179^{2}$ |
$1$ |
$7.96418266547$ |
$13.379088160259652$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$3.52163918236$ |
| 5.1.51529.1 |
$x^{5} - x^{3} - 2 x^{2} + 3 x + 4$ |
$5$ |
[1,2] |
$227^{2}$ |
$1$ |
$8.75810893805$ |
$15.066519173319364$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$4.90397090943$ |
| 5.1.57121.1 |
$x^{5} - 2 x^{4} + 4 x^{3} - 5 x^{2} + 2 x + 1$ |
$5$ |
[1,2] |
$239^{2}$ |
$1$ |
$8.94044550549$ |
$15.459624833740307$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$1.96209656107$ |
| 5.1.87616.1 |
$x^{5} - x^{4} + 3 x^{3} - 3 x^{2} + 2 x + 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 37^{2}$ |
$2$ |
$9.73905199423$ |
$17.204650534085253$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$12.7934094137$ |
| 5.1.91809.1 |
$x^{5} + 3 x^{3} - x^{2} + 3 x + 3$ |
$5$ |
[1,2] |
$3^{2}\cdot 101^{2}$ |
$2$ |
$9.83053268291$ |
$17.406895185529212$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$6.76331519205$ |
| 5.1.101761.1 |
$x^{5} - x^{4} - x^{3} - 3 x^{2} + 6 x + 1$ |
$5$ |
[1,2] |
$11^{2}\cdot 29^{2}$ |
$2$ |
$10.0349744997$ |
$17.86057109949175$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$4.34034396658$ |
| 5.1.118336.1 |
$x^{5} - x^{4} - x^{3} + 5 x^{2} - 2 x + 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 43^{2}$ |
$2$ |
$10.3424487385$ |
$18.547236990991408$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$15.6281189632$ |
| 5.1.120409.1 |
$x^{5} - x^{4} + 4 x^{3} - x^{2} + 5 x - 4$ |
$5$ |
[1,2] |
$347^{2}$ |
$1$ |
$10.3784330937$ |
$18.627936010197157$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$8.46225218598$ |
| 5.1.140625.1 |
$x^{5} - 5 x^{2} - 3$ |
$5$ |
[1,2] |
$3^{2}\cdot 5^{6}$ |
$2$ |
$10.7056368417$ |
$14.035297835467638$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$8.89638200899$ |
| 5.5.160801.1 |
$x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 3 x - 1$ |
$5$ |
[5,0] |
$401^{2}$ |
$1$ |
$10.9965828103$ |
$20.024984394500787$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$4$ |
$9.17494614126$ |
| 5.1.172225.1 |
$x^{5} - x^{4} - 9 x^{2} + 13 x - 1$ |
$5$ |
[1,2] |
$5^{2}\cdot 83^{2}$ |
$2$ |
$11.14857189$ |
$20.37154878746336$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$7.77157519443$ |
| 5.1.192721.1 |
$x^{5} - 3 x^{3} - 4 x^{2} + 8 x + 1$ |
$5$ |
[1,2] |
$439^{2}$ |
$1$ |
$11.4021252701$ |
$20.952326839756964$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$5.64645281548$ |
| 5.1.196249.1 |
$x^{5} - x^{4} - x^{3} + 5 x^{2} + 3 x - 5$ |
$5$ |
[1,2] |
$443^{2}$ |
$1$ |
$11.443568945$ |
$21.047565179849187$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$11.4144843712$ |
| 5.1.207025.1 |
$x^{5} - 2 x^{4} + 3 x^{3} - 9 x^{2} + 5 x - 5$ |
$5$ |
[1,2] |
$5^{2}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$11.5665691519$ |
$21.330729007701542$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$7.41824886206$ |
| 5.1.229441.1 |
$x^{5} - 2 x^{4} + 5 x^{3} - 7 x^{2} + 3 x + 1$ |
$5$ |
[1,2] |
$479^{2}$ |
$1$ |
$11.8068543384$ |
$21.88606862823929$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$2.67330189793$ |
| 5.1.238144.1 |
$x^{5} - 2 x^{4} + 3 x^{3} + 10 x + 8$ |
$5$ |
[1,2] |
$2^{6}\cdot 61^{2}$ |
$2$ |
$11.8950953815$ |
$22.090722034374522$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$25.0432874437$ |
| 5.1.250000.1 |
$x^{5} - 5 x^{3} + 10 x - 4$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{6}$ |
$2$ |
$12.0112443398$ |
$16.206565966927624$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$25.8196052017$ |
| 5.1.273529.1 |
$x^{5} - x^{4} + 3 x^{3} + 5 x^{2} - x + 3$ |
$5$ |
[1,2] |
$523^{2}$ |
$1$ |
$12.2292739989$ |
$22.869193252058544$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$17.6474472599$ |
| 5.1.326041.1 |
$x^{5} - x^{4} - 2 x^{3} + 7 x^{2} - 3 x + 2$ |
$5$ |
[1,2] |
$571^{2}$ |
$1$ |
$12.6664362976$ |
$23.895606290697042$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$18.7596092027$ |
| 5.1.358801.1 |
$x^{5} - x^{4} + 3 x^{3} - 9 x^{2} + 6 x - 5$ |
$5$ |
[1,2] |
$599^{2}$ |
$1$ |
$12.9113224957$ |
$24.474476501040833$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$10.4183175513$ |
| 5.1.373321.1 |
$x^{5} + 3 x^{3} - 6 x^{2} - x - 4$ |
$5$ |
[1,2] |
$13^{2}\cdot 47^{2}$ |
$2$ |
$13.014170258$ |
$24.71841418861655$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$14.5313182575$ |
| 5.1.378225.1 |
$x^{5} - x^{4} + 7 x^{3} + 2 x^{2} - 5 x + 5$ |
$5$ |
[1,2] |
$3^{2}\cdot 5^{2}\cdot 41^{2}$ |
$3$ |
$13.0481832187$ |
$24.79919353527449$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$18.0319026306$ |
| 5.1.383161.1 |
$x^{5} - x^{4} + 4 x^{3} - 5 x^{2} + 3 x + 2$ |
$5$ |
[1,2] |
$619^{2}$ |
$1$ |
$13.0820637034$ |
$24.879710609249457$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$20.2706474615$ |
| 5.1.403225.1 |
$x^{5} - x^{4} + 3 x^{3} - 7 x^{2} - x - 5$ |
$5$ |
[1,2] |
$5^{2}\cdot 127^{2}$ |
$2$ |
$13.2162878843$ |
$25.199206336708304$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$20.1229192311$ |
| 5.1.440896.1 |
$x^{5} - x^{4} - 4 x^{2} - x - 27$ |
$5$ |
[1,2] |
$2^{6}\cdot 83^{2}$ |
$2$ |
$13.454489737$ |
$25.768197453450252$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$43.583375851$ |
| 5.1.450241.1 |
$x^{5} - x^{4} + 2 x^{3} + 7 x^{2} - 9 x + 7$ |
$5$ |
[1,2] |
$11^{2}\cdot 61^{2}$ |
$2$ |
$13.5110471036$ |
$25.903667693977237$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$9.09134512444$ |
| 5.1.466489.1 |
$x^{5} - 2 x^{4} + 5 x^{3} + 6 x^{2} - 7 x + 2$ |
$5$ |
[1,2] |
$683^{2}$ |
$1$ |
$13.6071847519$ |
$26.13426869074396$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$19.0486448954$ |
| 5.1.477481.1 |
$x^{5} - 2 x^{4} + 3 x^{3} - 8 x^{2} - x - 6$ |
$5$ |
[1,2] |
$691^{2}$ |
$1$ |
$13.6707146695$ |
$26.28687885618983$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$23.1045477195$ |
| 5.1.488601.1 |
$x^{5} - 2 x^{4} - x^{3} + 8 x^{2} + 3 x - 6$ |
$5$ |
[1,2] |
$3^{2}\cdot 233^{2}$ |
$2$ |
$13.7338047959$ |
$26.43860813280457$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$34.5455225942$ |
| 5.1.524176.1 |
$x^{5} - 2 x^{4} + 3 x^{3} + 6 x^{2} - 10 x + 8$ |
$5$ |
[1,2] |
$2^{4}\cdot 181^{2}$ |
$2$ |
$13.928213859$ |
$26.90724809414742$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$48.5683321005$ |
| 5.1.546121.1 |
$x^{5} - 4 x^{3} - x^{2} + 10 x - 4$ |
$5$ |
[1,2] |
$739^{2}$ |
$1$ |
$14.0429314337$ |
$27.184554438136374$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$25.6203376862$ |
| 5.1.564001.1 |
$x^{5} - x^{3} - 7 x^{2} - x - 3$ |
$5$ |
[1,2] |
$751^{2}$ |
$1$ |
$14.1337034497$ |
$27.40437921208944$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$10.4884541124$ |
| 5.1.602176.1 |
$x^{5} - x^{4} + 7 x^{3} + 5 x^{2} + 8 x - 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 97^{2}$ |
$2$ |
$14.3200550826$ |
$27.85677655436824$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$39.6198768537$ |
| 5.1.606841.1 |
$x^{5} - 2 x^{4} - 3 x^{3} + 15 x - 4$ |
$5$ |
[1,2] |
$19^{2}\cdot 41^{2}$ |
$2$ |
$14.3421738675$ |
$27.910571473905726$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$18.7410452728$ |
| 5.1.619369.1 |
$x^{5} + 2 x^{3} - 7 x^{2} + 10 x - 4$ |
$5$ |
[1,2] |
$787^{2}$ |
$1$ |
$14.4009085648$ |
$28.053520278211074$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$29.1312463645$ |
| 5.1.620944.1 |
$x^{5} - 2 x^{3} - 2 x^{2} - 3 x - 10$ |
$5$ |
[1,2] |
$2^{4}\cdot 197^{2}$ |
$2$ |
$14.408225171$ |
$28.071337695236398$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$45.6368471784$ |
| 5.1.644809.1 |
$x^{5} - x^{4} + 2 x^{3} - 19 x^{2} + 33 x - 20$ |
$5$ |
[1,2] |
$11^{2}\cdot 73^{2}$ |
$2$ |
$14.517312251$ |
$28.337254630609507$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$21.7322140023$ |
| 5.1.664225.1 |
$x^{5} - 2 x^{4} + 5 x^{3} - 12 x^{2} + 8 x - 7$ |
$5$ |
[1,2] |
$5^{2}\cdot 163^{2}$ |
$2$ |
$14.6037047321$ |
$28.548204847240395$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$15.4480842501$ |
| 5.5.667489.1 |
$x^{5} - x^{4} - 6 x^{3} + 5 x^{2} + 3 x - 1$ |
$5$ |
[5,0] |
$19^{2}\cdot 43^{2}$ |
$2$ |
$14.6180291174$ |
$28.583211855912904$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$4$ |
$16.8508075263$ |
| 5.1.678976.2 |
$x^{5} + x^{3} - 6 x^{2} + 10 x - 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 103^{2}$ |
$2$ |
$14.667999439$ |
$28.705400188814647$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$45.1185006705$ |
| 5.1.698896.1 |
$x^{5} - x^{4} - 3 x^{3} + 9 x^{2} - 4 x + 2$ |
$5$ |
[1,2] |
$2^{4}\cdot 11^{2}\cdot 19^{2}$ |
$3$ |
$14.7530736663$ |
$28.91366458960192$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$43.2624522198$ |
| 5.1.717409.1 |
$x^{5} - 2 x^{4} + 6 x^{3} - 9 x^{2} + 4 x + 1$ |
$5$ |
[1,2] |
$7^{2}\cdot 11^{4}$ |
$2$ |
$14.8304170508$ |
$18.016198912314337$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
$[5]$ |
$2$ |
$2$ |
$3.31809382251$ |
