| 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 |
| 5.1.35152.1 |
$x^{5} - x^{4} + 2 x^{3} - 4 x^{2} + x - 1$ |
$5$ |
[1,2] |
$2^{4}\cdot 13^{3}$ |
$2$ |
$8.1131593856$ |
$11.920144243683046$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$3.16212424374$ |
| 5.1.44217.1 |
$x^{5} - x^{4} + x^{2} + 3 x + 1$ |
$5$ |
[1,2] |
$3^{2}\cdot 17^{3}$ |
$2$ |
$8.49410948845$ |
$14.500978825806921$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$2.81444638921$ |
| 5.1.50000.1 |
$x^{5} - 2$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{5}$ |
$2$ |
$8.70550563296$ |
$11.08254495193135$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$4.83493544802$ |
| 5.1.78125.1 |
$x^{5} + 5 x^{3} + 5 x - 1$ |
$5$ |
[1,2] |
$5^{7}$ |
$1$ |
$9.51826969358$ |
$12.117234333213267$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$6.32782810091$ |
| 5.1.162000.1 |
$x^{5} - x^{4} + 4 x^{3} + 4 x^{2} - x + 13$ |
$5$ |
[1,2] |
$2^{4}\cdot 3^{4}\cdot 5^{3}$ |
$3$ |
$11.0129331475$ |
$14.020015815993006$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$10.6812030681$ |
| 5.1.165888.1 |
$x^{5} - 2 x^{4} - 2 x^{3} + 8 x^{2} - x - 10$ |
$5$ |
[1,2] |
$2^{11}\cdot 3^{4}$ |
$2$ |
$11.0652949378$ |
$16.20054003982431$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$15.5971072693$ |
| 5.1.171125.1 |
$x^{5} - x^{4} - 2 x^{3} + x^{2} + 2 x - 3$ |
$5$ |
[1,2] |
$5^{3}\cdot 37^{2}$ |
$2$ |
$11.1342941949$ |
$20.33894234805392$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$11.0635533322$ |
| 5.1.200000.1 |
$x^{5} + 5 x^{3} + 5 x - 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{5}$ |
$2$ |
$11.48698355$ |
$18.00364738986388$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$12.9332824614$ |
| 5.1.247808.1 |
$x^{5} + 2 x^{3} - 4 x^{2} - x - 4$ |
$5$ |
[1,2] |
$2^{11}\cdot 11^{2}$ |
$2$ |
$11.9901071588$ |
$22.311503175611666$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$19.8796965515$ |
| 5.1.253125.1 |
$x^{5} - 3$ |
$5$ |
[1,2] |
$3^{4}\cdot 5^{5}$ |
$2$ |
$12.0411234264$ |
$15.328953569291674$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$12.249655921$ |
| 5.1.256000.1 |
$x^{5} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 9 x - 14$ |
$5$ |
[1,2] |
$2^{11}\cdot 5^{3}$ |
$2$ |
$12.0683526731$ |
$22.493653007613965$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$18.1966893824$ |
| 5.1.300125.1 |
$x^{5} - 7$ |
$5$ |
[1,2] |
$5^{3}\cdot 7^{4}$ |
$2$ |
$12.4583473323$ |
$15.860100510897633$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$15.3460441472$ |
| 5.1.338000.1 |
$x^{5} - x^{4} - 2 x^{3} + 6 x^{2} - 3 x - 13$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{3}\cdot 13^{2}$ |
$3$ |
$12.7580218044$ |
$20.99051895628543$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$16.5858365851$ |
| 5.1.346112.1 |
$x^{5} - 2 x^{4} - 2 x^{3} - x - 2$ |
$5$ |
[1,2] |
$2^{11}\cdot 13^{2}$ |
$2$ |
$12.8186807453$ |
$24.255161140409015$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$25.3523677638$ |
| 5.1.351125.1 |
$x^{5} - x^{4} - x^{3} + 9 x^{2} - 11 x + 8$ |
$5$ |
[1,2] |
$5^{3}\cdot 53^{2}$ |
$2$ |
$12.8555999847$ |
$24.342514538096598$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$16.6244641445$ |
| 5.1.390224.1 |
$x^{5} - 2 x^{4} - 2 x^{3} + 4 x^{2} + 2 x + 2$ |
$5$ |
[1,2] |
$2^{4}\cdot 29^{3}$ |
$2$ |
$13.1299416258$ |
$21.758176478524742$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$14.553248086$ |
| 5.1.392000.1 |
$x^{5} - 2 x^{4} + 4 x^{3} - 8 x^{2} + 11 x - 10$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{3}\cdot 7^{2}$ |
$3$ |
$13.1418714098$ |
$25.021971019484877$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$20.8258433809$ |
| 5.1.450000.1 |
$x^{5} - 5 x^{3} + 5 x - 4$ |
$5$ |
[1,2] |
$2^{4}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$13.5096003852$ |
$22.049874807078353$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$20.7933540907$ |
| 5.1.460800.1 |
$x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - 5 x - 3$ |
$5$ |
[1,2] |
$2^{11}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$13.5738327611$ |
$26.054222497305222$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$29.3409154854$ |
| 5.1.528125.1 |
$x^{5} + 5 x^{3} + 5 x - 3$ |
$5$ |
[1,2] |
$5^{5}\cdot 13^{2}$ |
$2$ |
$13.9491371794$ |
$22.950237339189933$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$18.7054338228$ |
| 5.1.578000.2 |
$x^{5} - x^{4} - 4 x^{3} + 4 x^{2} + 11 x - 15$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{3}\cdot 17^{2}$ |
$3$ |
$14.2031792378$ |
$24.00357675738704$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$22.5023612543$ |
| 5.1.595125.1 |
$x^{5} - 2 x^{4} + 3 x^{3} + 8 x^{2} + 3 x + 2$ |
$5$ |
[1,2] |
$3^{2}\cdot 5^{3}\cdot 23^{2}$ |
$3$ |
$14.2863616199$ |
$27.77487087706129$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$23.2745956147$ |
| 5.1.614125.1 |
$x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - 3 x + 4$ |
$5$ |
[1,2] |
$5^{3}\cdot 17^{3}$ |
$2$ |
$14.3764399758$ |
$27.99395075493803$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$15.7679275437$ |
| 5.1.648000.1 |
$x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - x - 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{4}\cdot 5^{3}$ |
$3$ |
$14.531652409$ |
$22.775582886985283$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$28.5504650503$ |
| 5.1.666125.1 |
$x^{5} - 2 x^{4} - 3 x^{3} + 8 x^{2} + 7 x - 16$ |
$5$ |
[1,2] |
$5^{3}\cdot 73^{2}$ |
$2$ |
$14.6120498999$ |
$28.56859835181669$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$24.7688005156$ |
| 5.1.739328.1 |
$x^{5} - x^{4} + 6 x^{3} - 6 x^{2} + 11 x - 3$ |
$5$ |
[1,2] |
$2^{11}\cdot 19^{2}$ |
$2$ |
$14.9199521684$ |
$29.323059968612448$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$39.1907308152$ |
| 5.1.810448.1 |
$x^{5} - 2 x^{4} + 8 x^{3} - 12 x^{2} - 4$ |
$5$ |
[1,2] |
$2^{4}\cdot 37^{3}$ |
$2$ |
$15.1965509669$ |
$26.12012732284832$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$24.1748851923$ |
| 5.1.878800.1 |
$x^{5} - 2 x^{4} + 2 x^{3} + 8 x^{2} - 20 x + 18$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{2}\cdot 13^{3}$ |
$3$ |
$15.4446478198$ |
$26.65425283047811$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$27.7727692166$ |
| 5.1.882000.1 |
$x^{5} - 2 x^{4} + 2 x^{3} + 8 x^{2} - 8 x + 4$ |
$5$ |
[1,2] |
$2^{4}\cdot 3^{2}\cdot 5^{3}\cdot 7^{2}$ |
$4$ |
$15.4558792818$ |
$26.67848399443575$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$29.5839110818$ |
| 5.1.903125.1 |
$x^{5} + 5 x^{3} + 5 x - 8$ |
$5$ |
[1,2] |
$5^{5}\cdot 17^{2}$ |
$2$ |
$15.529217508$ |
$26.244600465513358$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$25.1074416608$ |
| 5.1.990125.1 |
$x^{5} - 2 x^{4} + 7 x^{3} - 12 x^{2} + 7 x - 6$ |
$5$ |
[1,2] |
$5^{3}\cdot 89^{2}$ |
$2$ |
$15.8175059049$ |
$31.544417096966722$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$28.9767614911$ |
| 5.1.1030301.1 |
$x^{5} - 2 x^{4} + 7 x^{3} - 4 x^{2} + 11 x + 6$ |
$5$ |
[1,2] |
$101^{3}$ |
$1$ |
$15.9438362112$ |
$31.859652191026974$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$24.7444548043$ |
| 5.1.1058000.1 |
$x^{5} + 5 x^{3} - 10 x^{2} + 5 x - 4$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{3}\cdot 23^{2}$ |
$3$ |
$16.0286569292$ |
$32.07165835515686$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$36.873415354$ |
| 5.1.1083392.1 |
$x^{5} - x^{4} + 4 x^{3} - 4 x^{2} + 12 x + 4$ |
$5$ |
[1,2] |
$2^{11}\cdot 23^{2}$ |
$2$ |
$16.1048663423$ |
$32.262380288915416$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$45.7612176941$ |
| 5.1.1266325.1 |
$x^{5} - 2 x^{4} - 3 x^{3} + 18 x^{2} - 25 x + 13$ |
$5$ |
[1,2] |
$5^{2}\cdot 37^{3}$ |
$2$ |
$16.615332482$ |
$33.54565647151909$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$21.8107354459$ |
| 5.1.1352000.1 |
$x^{5} - x^{4} + x^{3} + 9 x^{2} - 9 x + 5$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{3}\cdot 13^{2}$ |
$3$ |
$16.8343106967$ |
$34.09919864600766$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$42.0043120597$ |
| 5.1.1378125.1 |
$x^{5} - 5 x^{3} + 5 x - 5$ |
$5$ |
[1,2] |
$3^{2}\cdot 5^{5}\cdot 7^{2}$ |
$3$ |
$16.8988722262$ |
$29.169242589818822$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$32.8940191447$ |
| 5.1.1485125.1 |
$x^{5} - 2 x^{4} + 8 x^{3} - 7 x^{2} + 13 x + 2$ |
$5$ |
[1,2] |
$5^{3}\cdot 109^{2}$ |
$2$ |
$17.1534942695$ |
$34.90926879408082$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$37.6249865962$ |
| 5.1.1682000.2 |
$x^{5} - x^{4} - 2 x^{3} - 4 x^{2} + 7 x - 3$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{3}\cdot 29^{2}$ |
$3$ |
$17.5859242563$ |
$31.350935080608856$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$40.1385031151$ |
| 5.1.1711125.1 |
$x^{5} - x^{4} + 4 x^{3} + 4 x^{2} - x - 2$ |
$5$ |
[1,2] |
$3^{4}\cdot 5^{3}\cdot 13^{2}$ |
$3$ |
$17.646409261$ |
$29.033285393546965$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$40.8159344408$ |
| 5.1.1800000.1 |
$x^{5} - 5 x^{3} + 5 x - 10$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{2}\cdot 5^{5}$ |
$3$ |
$17.8260245797$ |
$31.18323200079904$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$47.3405983139$ |
| 5.1.1830125.1 |
$x^{5} - 2 x^{4} + 6 x^{3} + 2 x^{2} + 4 x + 1$ |
$5$ |
[1,2] |
$5^{3}\cdot 11^{4}$ |
$2$ |
$17.8852967681$ |
$22.76887911715532$ |
|
|
✓ |
$F_5$ (as 5T3) |
$[5]$ |
$2$ |
$2$ |
$8.55270873142$ |
| 5.1.1922000.1 |
$x^{5} - 2 x^{4} + 4 x^{3} - 8 x^{2} - 4 x - 40$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{3}\cdot 31^{2}$ |
$3$ |
$18.0613694643$ |
$37.23388438035803$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$50.2916514728$ |
| 5.1.1953125.1 |
$x^{5} - 5$ |
$5$ |
[1,2] |
$5^{9}$ |
$1$ |
$18.1194915919$ |
$23.067020864764707$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$36.8883690747$ |
| 5.1.1975509.1 |
$x^{5} - x^{4} - 5 x^{3} + 19 x^{2} - 7 x + 1$ |
$5$ |
[1,2] |
$3^{4}\cdot 29^{3}$ |
$2$ |
$18.1608345757$ |
$30.095080005394955$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$34.7346263252$ |
| 5.1.2080125.1 |
$x^{5} - x^{4} - 5 x^{2} - 5$ |
$5$ |
[1,2] |
$3^{2}\cdot 5^{3}\cdot 43^{2}$ |
$3$ |
$18.3492317879$ |
$37.97714899103623$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$48.2492878811$ |
| 5.1.2178000.1 |
$x^{5} + 10 x^{3} + 20 x - 2$ |
$5$ |
[1,2] |
$2^{4}\cdot 3^{2}\cdot 5^{3}\cdot 11^{2}$ |
$4$ |
$18.5187460028$ |
$33.44324956582635$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$52.9817667017$ |
| 5.1.2230272.1 |
$x^{5} - 2 x^{4} + 6 x^{3} - 16 x^{2} + 9 x - 22$ |
$5$ |
[1,2] |
$2^{11}\cdot 3^{2}\cdot 11^{2}$ |
$3$ |
$18.6067947252$ |
$38.644657093393754$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$76.3064921276$ |
| 5.5.2382032.1 |
$x^{5} - 9 x^{3} - 4 x^{2} + 17 x + 12$ |
$5$ |
[5,0] |
$2^{4}\cdot 53^{3}$ |
$2$ |
$18.8533929035$ |
$39.28591727995504$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
$2$ |
$4$ |
$88.1862063965$ |
| 5.1.2382032.2 |
$x^{5} - x^{4} + 2 x^{3} - 14 x^{2} + 5 x - 17$ |
$5$ |
[1,2] |
$2^{4}\cdot 53^{3}$ |
$2$ |
$18.8533929035$ |
$34.2003774176698$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
$2$ |
$2$ |
$38.6962102279$ |
