Number field search results

Results (1-50 of 797781 matches)

 

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