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Results (1-50 of 3170756 matches)

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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
4.0.117.1	$x^{4} - x^{3} - x^{2} + x + 1$	$4$	[0,2]	$3^{2}\cdot 13$	$2$	$3.28886816799$	$6.244997998398398$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$0.543535072498$
4.0.125.1	$x^{4} - x^{3} + x^{2} - x + 1$	$4$	[0,2]	$5^{3}$	$1$	$3.34370152488$	$3.34370152488211$	✓	✓	✓	$C_4$ (as 4T1)	trivial	$10$	$1$	$0.962423650119$
4.0.144.1	$x^{4} - x^{2} + 1$	$4$	[0,2]	$2^{4}\cdot 3^{2}$	$2$	$3.46410161514$	$3.4641016151377544$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$12$	$1$	$1.31695789692$
4.0.189.1	$x^{4} - x^{3} + 2 x + 1$	$4$	[0,2]	$3^{3}\cdot 7$	$2$	$3.70779275107$	$6.03100878451909$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$0.862554627662$
4.0.225.1	$x^{4} - x^{3} + 2 x^{2} + x + 1$	$4$	[0,2]	$3^{2}\cdot 5^{2}$	$2$	$3.87298334621$	$3.872983346207417$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$0.962423650119$
4.0.229.1	$x^{4} - x + 1$	$4$	[0,2]	$229$	$1$	$3.89008302616$	$15.132745950421556$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$0.337377803572$
4.0.256.1	$x^{4} + 1$	$4$	[0,2]	$2^{8}$	$1$	$4.0$	$4.0$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$8$	$1$	$1.76274717404$
4.0.257.1	$x^{4} + x^{2} - x + 1$	$4$	[0,2]	$257$	$1$	$4.00390054096$	$16.0312195418814$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$0.442137828732$
4.0.272.1	$x^{4} + x^{2} - 2 x + 1$	$4$	[0,2]	$2^{4}\cdot 17$	$2$	$4.06108636974$	$8.246211251235321$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$0.732857675974$
4.2.275.1	$x^{4} - x^{3} + 2 x - 1$	$4$	[2,1]	$-\,5^{2}\cdot 11$	$2$	$4.07223819929$	$7.416198487095663$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.369184373575$
4.2.283.1	$x^{4} - x - 1$	$4$	[2,1]	$-\,283$	$1$	$4.10153676581$	$16.822603841260722$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$0.37819933246$
4.0.320.1	$x^{4} - 2 x^{3} + 2$	$4$	[0,2]	$2^{6}\cdot 5$	$2$	$4.22948505376$	$6.324555320336759$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.06127506191$
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	$2$	$2$	$0.432203091185$
4.0.333.1	$x^{4} - x^{3} - 2 x^{2} + 3$	$4$	[0,2]	$3^{2}\cdot 37$	$2$	$4.27180144563$	$10.535653752852738$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.46078161311$
4.0.392.1	$x^{4} - x^{3} + x + 1$	$4$	[0,2]	$2^{3}\cdot 7^{2}$	$2$	$4.44960558625$	$7.483314773547883$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.632974319201$
4.2.400.1	$x^{4} - x^{2} - 1$	$4$	[2,1]	$-\,2^{4}\cdot 5^{2}$	$2$	$4.472135955$	$6.324555320336759$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.51069810943$
4.0.400.1	$x^{4} + 3 x^{2} + 1$	$4$	[0,2]	$2^{4}\cdot 5^{2}$	$2$	$4.472135955$	$4.47213595499958$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$4$	$1$	$0.962423650119$
4.0.432.1	$x^{4} - 3 x^{2} + 3$	$4$	[0,2]	$2^{4}\cdot 3^{3}$	$2$	$4.55901411391$	$6.4474195909412515$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.66288589106$
4.0.441.1	$x^{4} - x^{3} - x^{2} - 2 x + 4$	$4$	[0,2]	$3^{2}\cdot 7^{2}$	$2$	$4.58257569496$	$4.58257569495584$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$1.56679923697$
4.2.448.1	$x^{4} - 2 x^{3} + x^{2} - 2 x + 1$	$4$	[2,1]	$-\,2^{6}\cdot 7$	$2$	$4.60065326758$	$7.483314773547883$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.557886846205$
4.2.475.1	$x^{4} - 2 x^{3} + 2 x^{2} - x - 1$	$4$	[2,1]	$-\,5^{2}\cdot 19$	$2$	$4.66845742379$	$9.746794344808963$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.57693147741$
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	$2$	$2$	$0.63355773488$
4.2.507.1	$x^{4} - x^{3} - x^{2} - x + 1$	$4$	[2,1]	$-\,3\cdot 13^{2}$	$2$	$4.74517233601$	$6.244997998398398$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.649395711926$
4.0.512.1	$x^{4} - 2 x^{2} + 2$	$4$	[0,2]	$2^{9}$	$1$	$4.75682846001$	$6.727171322029716$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.52857091948$
4.0.513.1	$x^{4} - x^{3} - 3 x^{2} + 2 x + 4$	$4$	[0,2]	$3^{3}\cdot 19$	$2$	$4.75914943092$	$9.93614090235369$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.96497837511$
4.0.549.1	$x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 3$	$4$	[0,2]	$3^{2}\cdot 61$	$2$	$4.84053189512$	$13.527749258468683$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.11437619251$
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	$2$	$2$	$0.704267195983$
4.0.576.1	$x^{4} - 2 x^{2} + 4$	$4$	[0,2]	$2^{6}\cdot 3^{2}$	$2$	$4.89897948557$	$4.898979485566356$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$2.29243166956$
4.0.576.2	$x^{4} + 2 x^{2} + 4$	$4$	[0,2]	$2^{6}\cdot 3^{2}$	$2$	$4.89897948557$	$4.898979485566356$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$1.76274717404$
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	$2$	$1$	$0.917818607957$
4.0.605.1	$x^{4} - x^{3} + x^{2} + x + 1$	$4$	[0,2]	$5\cdot 11^{2}$	$2$	$4.95951083803$	$7.416198487095663$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.767197218251$
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	$2$	$2$	$0.720184467868$
4.0.656.1	$x^{4} - 2 x^{3} - x^{2} + 2 x + 2$	$4$	[0,2]	$2^{4}\cdot 41$	$2$	$5.06087906887$	$12.806248474865697$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$2.42610665212$
4.0.657.1	$x^{4} - x^{3} + 5 x^{2} - 2 x + 4$	$4$	[0,2]	$3^{2}\cdot 73$	$2$	$5.06280665599$	$14.798648586948742$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.0335456547$
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	$2$	$1$	$1.03324185123$
4.4.725.1	$x^{4} - x^{3} - 3 x^{2} + x + 1$	$4$	[4,0]	$5^{2}\cdot 29$	$2$	$5.18900992827$	$12.041594578792296$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$0.825068847935$
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	$2$	$1$	$0.990699508768$
4.2.775.1	$x^{4} - x^{3} - 3 x - 1$	$4$	[2,1]	$-\,5^{2}\cdot 31$	$2$	$5.27625073458$	$12.449899597988733$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$0.867905309463$
4.0.784.1	$x^{4} - 3 x^{2} + 4$	$4$	[0,2]	$2^{4}\cdot 7^{2}$	$2$	$5.29150262213$	$5.291502622129181$	✓	✓		$C_2^2$ (as 4T2)	trivial	$4$	$1$	$2.76865938331$
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	$2$	$1$	$1.39411358598$
4.0.832.1	$x^{4} - 2 x^{3} - 2 x + 5$	$4$	[0,2]	$2^{6}\cdot 13$	$2$	$5.37069922857$	$10.198039027185569$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$2.13862208632$
4.0.837.1	$x^{4} - x^{3} - 3 x^{2} - x + 7$	$4$	[0,2]	$3^{3}\cdot 31$	$2$	$5.37875006697$	$12.691758156532355$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.41883810412$
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	$2$	$2$	$0.992994938315$
4.0.873.1	$x^{4} - x^{3} - 4 x^{2} + x + 7$	$4$	[0,2]	$3^{2}\cdot 97$	$2$	$5.43567598422$	$17.05872210923198$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.42800256046$
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	$2$	$2$	$0.990699215006$
4.0.981.1	$x^{4} - x^{3} - 4 x^{2} + 4 x + 7$	$4$	[0,2]	$3^{2}\cdot 109$	$2$	$5.59650958426$	$18.083141320025124$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.15221875719$

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