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Degree	Signature	Class number	Class group structure	CM field

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Results (1-50 of 317423 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
5.3.4511.1	$ x^{5} - x^{3} - 2 x^{2} + 1 $	$5$	[3,1]	$-\,13\cdot 347$	$2$	$5.38089559333$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.628579167485$
5.3.4903.1	$ x^{5} - x^{4} - x^{3} + 2 x^{2} - x - 1 $	$5$	[3,1]	$-\,4903$	$1$	$5.47132330872$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.668925630977$
5.3.5519.1	$ x^{5} - x^{4} - x^{3} + 3 x^{2} - 1 $	$5$	[3,1]	$-\,5519$	$1$	$5.60237375466$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.732128382974$
5.3.5783.1	$ x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x - 1 $	$5$	[3,1]	$-\,5783$	$1$	$5.65497433803$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.757141624325$
5.3.7031.1	$ x^{5} - x^{3} - x^{2} - x + 1 $	$5$	[3,1]	$-\,79\cdot 89$	$2$	$5.88035329589$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.888380795899$
5.3.7367.1	$ x^{5} - 2 x^{4} + 3 x^{2} - 2 x - 1 $	$5$	[3,1]	$-\,53\cdot 139$	$2$	$5.93551127049$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.904106825927$
5.3.7463.1	$ x^{5} - 2 x^{4} + x^{3} - 2 x + 1 $	$5$	[3,1]	$-\,17\cdot 439$	$2$	$5.95090049275$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.926583855017$
5.3.8519.1	$ x^{5} - x^{4} - x^{2} - x + 1 $	$5$	[3,1]	$-\,7\cdot 1217$	$2$	$6.11051372122$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$0.999142814665$
5.3.8647.1	$ x^{5} - 3 x^{3} - 2 x^{2} + 2 x + 1 $	$5$	[3,1]	$-\,8647$	$1$	$6.12876673034$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.02787912946$
5.3.9439.1	$ x^{5} - x^{4} - x^{3} + x^{2} - 2 x + 1 $	$5$	[3,1]	$-\,9439$	$1$	$6.23713576052$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.21312946247$
5.3.9759.1	$ x^{5} - 2 x^{4} + x^{2} - 2 x - 1 $	$5$	[3,1]	$-\,3\cdot 3253$	$2$	$6.27886381559$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.24138586861$
5.3.10407.1	$ x^{5} - x^{4} - 3 x^{3} + 3 x - 1 $	$5$	[3,1]	$-\,3\cdot 3469$	$2$	$6.36011708725$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.29968455596$
5.3.11119.1	$ x^{5} - 2 x^{4} + x^{3} + x^{2} - 3 x + 1 $	$5$	[3,1]	$-\,11119$	$1$	$6.44485492951$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.19655267604$
5.3.11243.1	$ x^{5} - x^{4} - 2 x + 1 $	$5$	[3,1]	$-\,11243$	$1$	$6.45916594224$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.27597060679$
5.3.11551.1	$ x^{5} - x^{4} - 2 x^{3} + 3 x^{2} - x - 1 $	$5$	[3,1]	$-\,11551$	$1$	$6.49417394267$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.39602772946$
5.3.12447.1	$ x^{5} + x^{3} - x^{2} - 3 x - 1 $	$5$	[3,1]	$-\,3^{3}\cdot 461$	$2$	$6.59193532748$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.47353341675$
5.3.13219.1	$ x^{5} - 2 x^{2} - x + 1 $	$5$	[3,1]	$-\,13219$	$1$	$6.67174932739$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.4282230441$
5.3.13523.1	$ x^{5} - x^{4} - x^{3} - x^{2} - 3 x + 1 $	$5$	[3,1]	$-\,13523$	$1$	$6.7021571931$	not computed	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.94231467204$
5.3.13799.1	$ x^{5} - x^{4} - x^{3} + 2 x^{2} - 3 x + 1 $	$5$	[3,1]	$-\,13799$	$1$	$6.72929431099$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.4643954612$
5.3.13883.1	$ x^{5} - x^{4} - 2 x^{3} + x + 2 $	$5$	[3,1]	$-\,13883$	$1$	$6.73746721252$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.97769282832$
5.3.14103.1	$ x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1 $	$5$	[3,1]	$-\,3^{2}\cdot 1567$	$2$	$6.75868648308$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.60398325545$
5.3.14631.1	$ x^{5} - x^{4} - 3 x^{3} + 3 x^{2} - 1 $	$5$	[3,1]	$-\,3\cdot 4877$	$2$	$6.80855267956$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.65878969233$
5.3.14891.1	$ x^{5} - x^{4} - 3 x^{3} + 3 x^{2} + x - 2 $	$5$	[3,1]	$-\,14891$	$1$	$6.8325807449$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.0760375874$
5.3.14911.1	$ x^{5} - x^{4} - 2 x^{3} - x^{2} + 3 x + 1 $	$5$	[3,1]	$-\,13\cdot 31\cdot 37$	$3$	$6.83441511814$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.67981747987$
5.3.15536.1	$ x^{5} - 2 x^{4} + 2 $	$5$	[3,1]	$-\,2^{4}\cdot 971$	$2$	$6.89077139991$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.13808345853$
5.3.15919.1	$ x^{5} - 2 x^{3} - 3 x^{2} + 1 $	$5$	[3,1]	$-\,15919$	$1$	$6.92441608506$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.809226746$
5.3.16816.1	$ x^{5} - 2 x^{3} - 2 x^{2} - 4 x - 2 $	$5$	[3,1]	$-\,2^{4}\cdot 1051$	$2$	$7.0007495271$	not computed	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.2650046595$
5.3.17151.1	$ x^{5} - x^{3} - 2 x - 1 $	$5$	[3,1]	$-\,3\cdot 5717$	$2$	$7.02842296944$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.84474320275$
5.3.17348.1	$ x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x + 2 $	$5$	[3,1]	$-\,2^{2}\cdot 4337$	$2$	$7.04449528357$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.32166707121$
5.3.18063.1	$ x^{5} - x^{4} + x^{3} - 2 x^{2} - x + 1 $	$5$	[3,1]	$-\,3^{4}\cdot 223$	$2$	$7.10162893521$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.96979771022$
5.3.18463.1	$ x^{5} - x^{4} - 3 x^{3} + 4 x^{2} + x - 1 $	$5$	[3,1]	$-\,37\cdot 499$	$2$	$7.13280668679$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.93552863121$
5.3.18583.1	$ x^{5} - x^{4} - x^{3} - 2 x^{2} + x + 1 $	$5$	[3,1]	$-\,18583$	$1$	$7.14205458996$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.94636349026$
5.3.18839.1	$ x^{5} - x^{4} + 3 x^{2} - x - 1 $	$5$	[3,1]	$-\,18839$	$1$	$7.161624879$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.8261292549$
5.3.19015.1	$ x^{5} - 2 x^{3} - x^{2} - 2 x - 1 $	$5$	[3,1]	$-\,5\cdot 3803$	$2$	$7.17495639354$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.74644196144$
5.3.19951.1	$ x^{5} - 2 x^{4} + x^{3} - 3 x^{2} + 3 x + 1 $	$5$	[3,1]	$-\,71\cdot 281$	$2$	$7.24424173091$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.03268966315$
5.3.21191.1	$ x^{5} - x^{4} - x^{2} - 3 x - 1 $	$5$	[3,1]	$-\,21191$	$1$	$7.33213225923$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.93450979256$
5.3.21227.1	$ x^{5} - x^{4} - 4 x^{2} + 3 x + 2 $	$5$	[3,1]	$-\,21227$	$1$	$7.33462178381$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.67366796844$
5.3.22331.1	$ x^{5} - 2 x^{4} + 4 x^{2} - x - 1 $	$5$	[3,1]	$-\,137\cdot 163$	$2$	$7.40937600068$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.9891406347$
5.3.22424.1	$ x^{5} - 2 x^{3} - x^{2} - x + 1 $	$5$	[3,1]	$-\,2^{3}\cdot 2803$	$2$	$7.41553718415$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.76003508518$
5.3.22448.1	$ x^{5} - x^{4} - 2 x^{3} + 2 x^{2} - x - 1 $	$5$	[3,1]	$-\,2^{4}\cdot 23\cdot 61$	$3$	$7.41712384798$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.86477407146$
5.3.22583.1	$ x^{5} - x^{2} - 2 x + 1 $	$5$	[3,1]	$-\,11\cdot 2053$	$2$	$7.42602363112$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.93941948265$
5.3.22687.1	$ x^{5} - x^{4} + x^{3} - x^{2} - 2 x + 1 $	$5$	[3,1]	$-\,7^{2}\cdot 463$	$2$	$7.43285078176$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$1.95362445218$
5.3.22935.1	$ x^{5} + x^{3} - 2 x^{2} - 4 x + 1 $	$5$	[3,1]	$-\,3\cdot 5\cdot 11\cdot 139$	$4$	$7.44903043826$	not computed	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.31044863242$
5.3.23103.1	$ x^{5} - x^{4} + x^{2} - 3 x + 1 $	$5$	[3,1]	$-\,3^{2}\cdot 17\cdot 151$	$3$	$7.45991150572$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.33091635633$
5.3.23119.1	$ x^{5} - 3 x^{2} + 1 $	$5$	[3,1]	$-\,61\cdot 379$	$2$	$7.46094449307$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.27920752421$
5.3.23339.1	$ x^{5} - x^{4} + 2 x^{2} - 2 x - 1 $	$5$	[3,1]	$-\,23339$	$1$	$7.47509039368$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.08590583429$
5.3.23679.1	$ x^{5} - 2 x^{4} + x^{2} - 2 x + 3 $	$5$	[3,1]	$-\,3^{3}\cdot 877$	$2$	$7.49674384054$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.65227818165$
5.3.23831.1	$ x^{5} - 3 x^{3} - 2 x^{2} + 4 x - 1 $	$5$	[3,1]	$-\,23831$	$1$	$7.50634382705$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.12564475096$
5.3.23891.1	$ x^{5} - x^{4} - 3 x^{3} - x^{2} + 3 x + 2 $	$5$	[3,1]	$-\,7\cdot 3413$	$2$	$7.51011981412$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.89262586592$
5.3.24299.1	$ x^{5} - x^{4} - x^{3} + 3 x^{2} - x - 2 $	$5$	[3,1]	$-\,11\cdot 47^{2}$	$2$	$7.53559727162$	✓	$S_5$ (as 5T5)	trivial	$2$	$3$	$2.93068377955$

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