| 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 |
| 5.5.14641.1 |
$ x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$11^{4}$ |
$1$ |
$6.80948312752$ |
|
✓ |
✓ |
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1.63569412559$ |
| 5.5.24217.1 |
$ x^{5} - 5 x^{3} - x^{2} + 3 x + 1 $ |
$5$ |
[5,0] |
$61\cdot 397$ |
$2$ |
$7.53050443021$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$2.39942113132$ |
| 5.5.36497.1 |
$ x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} + x - 1 $ |
$5$ |
[5,0] |
$36497$ |
$1$ |
$8.17431620701$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$3.55065765574$ |
| 5.5.38569.1 |
$ x^{5} - 5 x^{3} + 4 x - 1 $ |
$5$ |
[5,0] |
$38569$ |
$1$ |
$8.26509168848$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$3.15543791633$ |
| 5.5.65657.1 |
$ x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 $ |
$5$ |
[5,0] |
$65657$ |
$1$ |
$9.19297770826$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$5.50318166396$ |
| 5.5.70601.1 |
$ x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$17\cdot 4153$ |
$2$ |
$9.327433695$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$4.61496156169$ |
| 5.5.81509.1 |
$ x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2 $ |
$5$ |
[5,0] |
$81509$ |
$1$ |
$9.59933422509$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$7.63162348973$ |
| 5.5.81589.1 |
$ x^{5} - 6 x^{3} + 8 x - 1 $ |
$5$ |
[5,0] |
$83\cdot 983$ |
$2$ |
$9.60121780954$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$7.60787640263$ |
| 5.5.89417.1 |
$ x^{5} - 6 x^{3} - x^{2} + 8 x + 3 $ |
$5$ |
[5,0] |
$89417$ |
$1$ |
$9.77876521496$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$6.74148650938$ |
| 5.5.101833.1 |
$ x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 2 x - 1 $ |
$5$ |
[5,0] |
$101833$ |
$1$ |
$10.0363941276$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$6.32919746615$ |
| 5.5.106069.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 3 x - 4 $ |
$5$ |
[5,0] |
$73\cdot 1453$ |
$2$ |
$10.1185363196$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.17408549814$ |
| 5.5.117688.1 |
$ x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 1 $ |
$5$ |
[5,0] |
$2^{3}\cdot 47\cdot 313$ |
$3$ |
$10.3310969354$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.71347669051$ |
| 5.5.122821.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 4 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$263\cdot 467$ |
$2$ |
$10.4196834623$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$7.04707403444$ |
| 5.5.124817.1 |
$ x^{5} - 7 x^{3} - 6 x^{2} + 2 x + 1 $ |
$5$ |
[5,0] |
$7\cdot 11\cdot 1621$ |
$3$ |
$10.4533320988$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$7.92197613589$ |
| 5.5.126032.1 |
$ x^{5} - 6 x^{3} + 6 x - 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 7877$ |
$2$ |
$10.4736043891$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$12.0598883245$ |
| 5.5.135076.1 |
$ x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 2 $ |
$5$ |
[5,0] |
$2^{2}\cdot 33769$ |
$2$ |
$10.6197828931$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.6288832988$ |
| 5.5.138136.1 |
$ x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2 $ |
$5$ |
[5,0] |
$2^{3}\cdot 31\cdot 557$ |
$3$ |
$10.6674686497$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.0050313668$ |
| 5.5.138917.1 |
$ x^{5} - 6 x^{3} - 2 x^{2} + 3 x + 1 $ |
$5$ |
[5,0] |
$138917$ |
$1$ |
$10.6795039123$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.4150840208$ |
| 5.5.144209.1 |
$ x^{5} - 6 x^{3} - x^{2} + 6 x - 1 $ |
$5$ |
[5,0] |
$13\cdot 11093$ |
$2$ |
$10.759658142$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$8.38185695843$ |
| 5.5.147109.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 2 $ |
$5$ |
[5,0] |
$157\cdot 937$ |
$2$ |
$10.8025888908$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.6668990641$ |
| 5.5.149169.1 |
$ x^{5} - 6 x^{3} - 3 x^{2} + 4 x + 1 $ |
$5$ |
[5,0] |
$3\cdot 19\cdot 2617$ |
$3$ |
$10.8326750486$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$8.79855118605$ |
| 5.5.153424.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 8 x^{2} - 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 43\cdot 223$ |
$3$ |
$10.8937815003$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.5954695752$ |
| 5.5.157457.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 4 x - 1 $ |
$5$ |
[5,0] |
$157457$ |
$1$ |
$10.9504607918$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.8429578526$ |
| 5.5.160801.1 |
$ x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$401^{2}$ |
$1$ |
$10.9965828103$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$4$ |
$9.17494614126$ |
| 5.5.161121.1 |
$ x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 5 x + 1 $ |
$5$ |
[5,0] |
$3\cdot 43\cdot 1249$ |
$3$ |
$11.0009560526$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.2054995686$ |
| 5.5.170701.1 |
$ x^{5} - x^{4} - 6 x^{3} + 4 x + 1 $ |
$5$ |
[5,0] |
$170701$ |
$1$ |
$11.1287711835$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$8.997051159$ |
| 5.5.173513.1 |
$ x^{5} - 2 x^{4} - 5 x^{3} + 3 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$167\cdot 1039$ |
$2$ |
$11.1651973477$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$7.25222447496$ |
| 5.5.176281.1 |
$ x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 4 x - 1 $ |
$5$ |
[5,0] |
$7\cdot 25183$ |
$2$ |
$11.2005951843$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.26719739114$ |
| 5.5.176684.1 |
$ x^{5} - 6 x^{3} - x^{2} + 5 x - 1 $ |
$5$ |
[5,0] |
$2^{2}\cdot 44171$ |
$2$ |
$11.2057116947$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$12.6809122173$ |
| 5.5.179024.1 |
$ x^{5} - 8 x^{3} + 6 x - 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 67\cdot 167$ |
$3$ |
$11.2352373438$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$15.1926139168$ |
| 5.5.180769.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} - 1 $ |
$5$ |
[5,0] |
$41\cdot 4409$ |
$2$ |
$11.2570550811$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$9.64320519613$ |
| 5.5.181057.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 2 x - 3 $ |
$5$ |
[5,0] |
$331\cdot 547$ |
$2$ |
$11.2606397308$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$11.9801284306$ |
| 5.5.186037.1 |
$ x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 5 x - 2 $ |
$5$ |
[5,0] |
$186037$ |
$1$ |
$11.3219143597$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$12.8893052818$ |
| 5.5.195829.1 |
$ x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 7 x + 1 $ |
$5$ |
[5,0] |
$113\cdot 1733$ |
$2$ |
$11.4386665825$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$12.9763440515$ |
| 5.5.202817.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 2 x - 1 $ |
$5$ |
[5,0] |
$202817$ |
$1$ |
$11.5191615986$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$10.5466728882$ |
| 5.5.205225.1 |
$ x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 7 x - 3 $ |
$5$ |
[5,0] |
$5^{2}\cdot 8209$ |
$2$ |
$11.5463854905$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$13.7910879608$ |
| 5.5.207184.1 |
$ x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x - 1 $ |
$5$ |
[5,0] |
$2^{4}\cdot 23\cdot 563$ |
$3$ |
$11.568345285$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$13.8472207557$ |
| 5.5.210557.1 |
$ x^{5} - x^{4} - 6 x^{3} + 4 x^{2} + 8 x - 1 $ |
$5$ |
[5,0] |
$210557$ |
$1$ |
$11.6057693921$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$10.7293738318$ |
| 5.5.216637.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + x - 2 $ |
$5$ |
[5,0] |
$23\cdot 9419$ |
$2$ |
$11.6720335329$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$14.9557752479$ |
| 5.5.218524.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 1 $ |
$5$ |
[5,0] |
$2^{2}\cdot 54631$ |
$2$ |
$11.6922967258$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$14.6003975231$ |
| 5.5.220036.1 |
$ x^{5} - 2 x^{4} - 5 x^{3} + 11 x^{2} - 2 x - 1 $ |
$5$ |
[5,0] |
$2^{2}\cdot 55009$ |
$2$ |
$11.7084322771$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$16.188166415$ |
| 5.5.220669.1 |
$ x^{5} - 7 x^{3} - 2 x^{2} + 11 x + 5 $ |
$5$ |
[5,0] |
$149\cdot 1481$ |
$2$ |
$11.7151611068$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$16.1498365364$ |
| 5.5.223824.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 3\cdot 4663$ |
$3$ |
$11.7484704958$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$17.8718319712$ |
| 5.5.223952.1 |
$ x^{5} - 6 x^{3} - 2 x^{2} + 6 x + 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 13997$ |
$2$ |
$11.7498139266$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$15.4493023517$ |
| 5.5.224773.1 |
$ x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x + 2 $ |
$5$ |
[5,0] |
$53\cdot 4241$ |
$2$ |
$11.7584162009$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$15.2067902478$ |
| 5.5.230224.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 3 x - 2 $ |
$5$ |
[5,0] |
$2^{4}\cdot 14389$ |
$2$ |
$11.814901874$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$22.6110814528$ |
| 5.5.233489.1 |
$ x^{5} - x^{4} - 6 x^{3} + x^{2} + 5 x - 1 $ |
$5$ |
[5,0] |
$233489$ |
$1$ |
$11.8482247846$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$8.87058361542$ |
| 5.5.236549.1 |
$ x^{5} - x^{4} - 6 x^{3} + 7 x^{2} + 2 x - 1 $ |
$5$ |
[5,0] |
$236549$ |
$1$ |
$11.8791187361$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$14.655875922$ |
| 5.5.240133.1 |
$ x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 1 $ |
$5$ |
[5,0] |
$439\cdot 547$ |
$2$ |
$11.9148991107$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$15.8564126109$ |
| 5.5.240881.1 |
$ x^{5} - 2 x^{4} - 5 x^{3} + 9 x^{2} + 5 x - 7 $ |
$5$ |
[5,0] |
$240881$ |
$1$ |
$11.9223127196$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$4$ |
$10.6079997587$ |
