| 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 |
| 4.0.229.1 |
$x^{4} - x + 1$ |
$4$ |
[0,2] |
$229$ |
$1$ |
$3.89008302616$ |
$15.132745950421556$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$0.337377803572$ |
| 4.0.257.1 |
$x^{4} + x^{2} - x + 1$ |
$4$ |
[0,2] |
$257$ |
$1$ |
$4.00390054096$ |
$16.0312195418814$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$0.442137828732$ |
| 4.2.283.1 |
$x^{4} - x - 1$ |
$4$ |
[2,1] |
$-\,283$ |
$1$ |
$4.10153676581$ |
$16.822603841260722$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.37819933246$ |
| 4.2.331.1 |
$x^{4} - x^{3} + x^{2} + x - 1$ |
$4$ |
[2,1] |
$-\,331$ |
$1$ |
$4.26537283232$ |
$18.193405398660254$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.432203091185$ |
| 4.2.491.1 |
$x^{4} - x^{3} - x^{2} + 3 x - 1$ |
$4$ |
[2,1] |
$-\,491$ |
$1$ |
$4.70728369723$ |
$22.15851980616034$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.63355773488$ |
| 4.2.563.1 |
$x^{4} - x^{3} + x^{2} - x - 1$ |
$4$ |
[2,1] |
$-\,563$ |
$1$ |
$4.87110059796$ |
$23.727621035409346$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.704267195983$ |
| 4.0.592.1 |
$x^{4} + 2 x^{2} - 2 x + 1$ |
$4$ |
[0,2] |
$2^{4}\cdot 37$ |
$2$ |
$4.93265142912$ |
$13.655340178276088$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$0.917818607957$ |
| 4.2.643.1 |
$x^{4} - x^{3} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,643$ |
$1$ |
$5.03561760524$ |
$25.357444666211933$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.720184467868$ |
| 4.2.688.1 |
$x^{4} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 43$ |
$2$ |
$5.12149920406$ |
$14.720951755301632$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.998743211853$ |
| 4.0.697.1 |
$x^{4} - x^{3} + 2 x^{2} - x + 2$ |
$4$ |
[0,2] |
$17\cdot 41$ |
$2$ |
$5.13816675137$ |
$26.40075756488817$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.03324185123$ |
| 4.2.731.1 |
$x^{4} - x^{3} + 2 x^{2} - 1$ |
$4$ |
[2,1] |
$-\,17\cdot 43$ |
$2$ |
$5.19971265256$ |
$27.03701166919155$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.866830073687$ |
| 4.2.751.1 |
$x^{4} - 2 x^{3} + x^{2} - x - 1$ |
$4$ |
[2,1] |
$-\,751$ |
$1$ |
$5.23491921734$ |
$27.40437921208944$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.06794059626$ |
| 4.0.761.1 |
$x^{4} - x^{3} + x^{2} + 2 x + 1$ |
$4$ |
[0,2] |
$761$ |
$1$ |
$5.25225936605$ |
$27.586228448267445$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$0.990699508768$ |
| 4.0.788.1 |
$x^{4} - x^{3} + 2 x^{2} - 2 x + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 197$ |
$2$ |
$5.29823911269$ |
$22.280235493786417$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.39411358598$ |
| 4.2.848.1 |
$x^{4} - x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 53$ |
$2$ |
$5.39633575282$ |
$20.591260281974$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.992994938315$ |
| 4.0.892.1 |
$x^{4} - x^{3} - x^{2} + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 223$ |
$2$ |
$5.46501317895$ |
$29.866369046136157$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.29274426912$ |
| 4.2.976.1 |
$x^{4} - 2 x^{3} + 3 x^{2} - 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 61$ |
$2$ |
$5.58936478534$ |
$22.090722034374522$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$0.990699215006$ |
| 4.0.985.1 |
$x^{4} - x^{3} + 2 x^{2} - 3 x + 2$ |
$4$ |
[0,2] |
$5\cdot 197$ |
$2$ |
$5.6022057846$ |
$31.38470965295043$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.34361173004$ |
| 4.0.1016.1 |
$x^{4} - x^{3} + x^{2} - 2 x + 2$ |
$4$ |
[0,2] |
$2^{3}\cdot 127$ |
$2$ |
$5.64577318895$ |
$31.874754901018456$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.27428442991$ |
| 4.0.1076.1 |
$x^{4} - x^{3} + 3 x^{2} - 3 x + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 269$ |
$2$ |
$5.7273413495$ |
$26.035313035249676$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.77702641037$ |
| 4.2.1099.1 |
$x^{4} - x^{3} + x^{2} - 3 x + 1$ |
$4$ |
[2,1] |
$-\,7\cdot 157$ |
$2$ |
$5.75770517728$ |
$33.15116890850155$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.01244916602$ |
| 4.2.1107.1 |
$x^{4} - x^{3} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,3^{3}\cdot 41$ |
$2$ |
$5.76815477594$ |
$23.06924557594881$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.28804807411$ |
| 4.0.1129.1 |
$x^{4} - x^{3} - x + 2$ |
$4$ |
[0,2] |
$1129$ |
$1$ |
$5.79660204196$ |
$33.60059523282288$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.26901928105$ |
| 4.2.1192.1 |
$x^{4} - x^{3} + 2 x^{2} + x - 1$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 149$ |
$2$ |
$5.87582785684$ |
$34.52535300326414$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.5689723036$ |
| 4.0.1229.1 |
$x^{4} - x^{3} + 3 x^{2} - x + 3$ |
$4$ |
[0,2] |
$1229$ |
$1$ |
$5.92090333361$ |
$35.05709628591621$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.2420612621$ |
| 4.2.1255.1 |
$x^{4} - x^{2} - 3 x - 1$ |
$4$ |
[2,1] |
$-\,5\cdot 251$ |
$2$ |
$5.95197271229$ |
$35.4259791678367$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.58232994952$ |
| 4.0.1257.1 |
$x^{4} - x^{2} - x + 2$ |
$4$ |
[0,2] |
$3\cdot 419$ |
$2$ |
$5.95434260036$ |
$35.45419580247167$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.53881468575$ |
| 4.0.1264.1 |
$x^{4} + 3 x^{2} - 2 x + 1$ |
$4$ |
[0,2] |
$2^{4}\cdot 79$ |
$2$ |
$5.9626150026$ |
$25.13961017995307$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.15507261653$ |
| 4.2.1328.1 |
$x^{4} - 3 x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 83$ |
$2$ |
$6.03669895858$ |
$18.2208671582886$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.3668896797$ |
| 4.2.1371.1 |
$x^{4} + 2 x^{2} - x - 1$ |
$4$ |
[2,1] |
$-\,3\cdot 457$ |
$2$ |
$6.08498292217$ |
$37.027017163147235$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.34876542307$ |
| 4.0.1384.1 |
$x^{4} - x^{3} - x^{2} + 2 x + 2$ |
$4$ |
[0,2] |
$2^{3}\cdot 173$ |
$2$ |
$6.09935656242$ |
$37.20215047547655$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.81533171924$ |
| 4.0.1396.1 |
$x^{4} - x^{3} + x^{2} - x + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 349$ |
$2$ |
$6.11253493933$ |
$29.65509893469623$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$2.36819571191$ |
| 4.2.1399.1 |
$x^{4} - x^{3} + x - 2$ |
$4$ |
[2,1] |
$-\,1399$ |
$1$ |
$6.11581625121$ |
$37.403208418530085$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.70613352231$ |
| 4.2.1423.1 |
$x^{4} - x^{3} + x^{2} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,1423$ |
$1$ |
$6.14187855853$ |
$37.72267222772003$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.69769459199$ |
| 4.2.1424.1 |
$x^{4} + x^{2} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 89$ |
$2$ |
$6.14295731128$ |
$26.68332812825267$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.47325330706$ |
| 4.0.1436.1 |
$x^{4} - x^{3} + 3 x^{2} + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 359$ |
$2$ |
$6.15585823773$ |
$37.89459064299283$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.59591212771$ |
| 4.2.1456.1 |
$x^{4} - 2 x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 7\cdot 13$ |
$3$ |
$6.17718123878$ |
$21.415210999701447$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.76052319498$ |
| 4.2.1472.1 |
$x^{4} - 2 x^{3} + 2 x^{2} - 2$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 23$ |
$2$ |
$6.19408202936$ |
$13.564659966250536$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.95632588969$ |
| 4.0.1489.1 |
$x^{4} - x^{3} + 4 x^{2} - x + 2$ |
$4$ |
[0,2] |
$1489$ |
$1$ |
$6.21188882411$ |
$38.58756276314948$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.76588370435$ |
| 4.0.1492.1 |
$x^{4} - x^{3} + 2 x^{2} + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 373$ |
$2$ |
$6.21501535249$ |
$30.657806562465872$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$2.48028880687$ |
| 4.0.1509.1 |
$x^{4} - x^{3} + 2 x^{2} + 2 x + 1$ |
$4$ |
[0,2] |
$3\cdot 503$ |
$2$ |
$6.23264383702$ |
$38.84584919911006$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.15088729577$ |
| 4.0.1556.1 |
$x^{4} - x^{3} - x^{2} + x + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 389$ |
$2$ |
$6.28061826946$ |
$31.30844258052788$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$2.30874838432$ |
| 4.2.1588.1 |
$x^{4} - x^{3} - 3 x^{2} + 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 397$ |
$2$ |
$6.31266328029$ |
$39.84971769034255$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.93358038312$ |
| 4.0.1593.1 |
$x^{4} - 2 x^{3} + 3 x^{2} - x + 2$ |
$4$ |
[0,2] |
$3^{3}\cdot 59$ |
$2$ |
$6.31762645991$ |
$27.67371536012528$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$2.08381549833$ |
| 4.0.1616.1 |
$x^{4} - 2 x + 2$ |
$4$ |
[0,2] |
$2^{4}\cdot 101$ |
$2$ |
$6.34030775945$ |
$22.561207949875573$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.57794204827$ |
| 4.2.1732.1 |
$x^{4} - x^{3} + 3 x - 1$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 433$ |
$2$ |
$6.45114750206$ |
$41.617304093369626$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.05155660923$ |
| 4.0.1765.1 |
$x^{4} - x^{3} - x^{2} - x + 3$ |
$4$ |
[0,2] |
$5\cdot 353$ |
$2$ |
$6.48165897554$ |
$42.01190307520001$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$1.44579553159$ |
| 4.2.1791.1 |
$x^{4} - x^{3} - x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 199$ |
$2$ |
$6.50539836897$ |
$24.43358344574123$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.01913849925$ |
| 4.2.1823.1 |
$x^{4} - x^{3} + 3 x - 2$ |
$4$ |
[2,1] |
$-\,1823$ |
$1$ |
$6.53426385145$ |
$42.69660408041839$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.28192620748$ |
| 4.0.1825.1 |
$x^{4} + x^{2} - x + 2$ |
$4$ |
[0,2] |
$5^{2}\cdot 73$ |
$2$ |
$6.53605528791$ |
$24.982818506665623$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$1$ |
$2.1186594823$ |
