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Results (1-50 of 1678348 matches)

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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
4.0.117.1	x^4 - x^3 - x^2 + x + 1	$4$	[0,2]	$3^{2}\cdot 13$	$2$	$3.28886816799$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$0.543535072498$
4.0.125.1	x^4 - x^3 + x^2 - x + 1	$4$	[0,2]	$5^{3}$	$1$	$3.34370152488$	✓	✓	✓	$C_4$ (as 4T1)	trivial	$10$	$1$	$0.962423650119$
4.0.144.1	x^4 - x^2 + 1	$4$	[0,2]	$2^{4}\cdot 3^{2}$	$2$	$3.46410161514$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$12$	$1$	$1.31695789692$
4.0.189.1	x^4 - x^3 + 2x + 1	$4$	[0,2]	$3^{3}\cdot 7$	$2$	$3.70779275107$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$0.862554627662$
4.0.225.1	x^4 - x^3 + 2x^2 + x + 1	$4$	[0,2]	$3^{2}\cdot 5^{2}$	$2$	$3.87298334621$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$0.962423650119$
4.0.229.1	x^4 - x + 1	$4$	[0,2]	$229$	$1$	$3.89008302616$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$0.337377803572$
4.0.256.1	x^4 + 1	$4$	[0,2]	$2^{8}$	$1$	$4.0$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$8$	$1$	$1.76274717404$
4.0.257.1	x^4 + x^2 - x + 1	$4$	[0,2]	$257$	$1$	$4.00390054096$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$0.442137828732$
4.0.272.1	x^4 + x^2 - 2x + 1	$4$	[0,2]	$2^{4}\cdot 17$	$2$	$4.06108636974$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$0.732857675974$
4.0.320.1	x^4 - 2x^3 + 2	$4$	[0,2]	$2^{6}\cdot 5$	$2$	$4.22948505376$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.06127506191$
4.0.333.1	x^4 - x^3 - 2x^2 + 3	$4$	[0,2]	$3^{2}\cdot 37$	$2$	$4.27180144563$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.46078161311$
4.0.392.1	x^4 - x^3 + x + 1	$4$	[0,2]	$2^{3}\cdot 7^{2}$	$2$	$4.44960558625$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.632974319201$
4.0.400.1	x^4 + 3x^2 + 1	$4$	[0,2]	$2^{4}\cdot 5^{2}$	$2$	$4.472135955$	✓	✓	✓	$C_2^2$ (as 4T2)	trivial	$4$	$1$	$0.962423650119$
4.0.432.1	x^4 - 3x^2 + 3	$4$	[0,2]	$2^{4}\cdot 3^{3}$	$2$	$4.55901411391$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.66288589106$
4.0.441.1	x^4 - x^3 - x^2 - 2x + 4	$4$	[0,2]	$3^{2}\cdot 7^{2}$	$2$	$4.58257569496$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$1.56679923697$
4.0.512.1	x^4 - 2x^2 + 2	$4$	[0,2]	$2^{9}$	$1$	$4.75682846001$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.52857091948$
4.0.513.1	x^4 - x^3 - 3x^2 + 2x + 4	$4$	[0,2]	$3^{3}\cdot 19$	$2$	$4.75914943092$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$1.96497837511$
4.0.549.1	x^4 - 2x^3 - 2x^2 + 3x + 3	$4$	[0,2]	$3^{2}\cdot 61$	$2$	$4.84053189512$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.11437619251$
4.0.576.1	x^4 - 2x^2 + 4	$4$	[0,2]	$2^{6}\cdot 3^{2}$	$2$	$4.89897948557$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$2.29243166956$
4.0.576.2	x^4 + 2x^2 + 4	$4$	[0,2]	$2^{6}\cdot 3^{2}$	$2$	$4.89897948557$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$1.76274717404$
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	$2$	$1$	$0.917818607957$
4.0.605.1	x^4 - x^3 + x^2 + x + 1	$4$	[0,2]	$5\cdot 11^{2}$	$2$	$4.95951083803$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.767197218251$
4.0.656.1	x^4 - 2x^3 - x^2 + 2x + 2	$4$	[0,2]	$2^{4}\cdot 41$	$2$	$5.06087906887$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$2.42610665212$
4.0.657.1	x^4 - x^3 + 5x^2 - 2x + 4	$4$	[0,2]	$3^{2}\cdot 73$	$2$	$5.06280665599$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.0335456547$
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	$2$	$1$	$1.03324185123$
4.0.761.1	x^4 - x^3 + x^2 + 2x + 1	$4$	[0,2]	$761$	$1$	$5.25225936605$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$0.990699508768$
4.0.784.1	x^4 - 3x^2 + 4	$4$	[0,2]	$2^{4}\cdot 7^{2}$	$2$	$5.29150262213$	✓	✓		$C_2^2$ (as 4T2)	trivial	$4$	$1$	$2.76865938331$
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	$2$	$1$	$1.39411358598$
4.0.832.1	x^4 - 2x^3 - 2x + 5	$4$	[0,2]	$2^{6}\cdot 13$	$2$	$5.37069922857$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$2.13862208632$
4.0.837.1	x^4 - x^3 - 3x^2 - x + 7	$4$	[0,2]	$3^{3}\cdot 31$	$2$	$5.37875006697$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.41883810412$
4.0.873.1	x^4 - x^3 - 4x^2 + x + 7	$4$	[0,2]	$3^{2}\cdot 97$	$2$	$5.43567598422$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.42800256046$
4.0.892.1	x^4 - x^3 - x^2 + 2	$4$	[0,2]	$2^{2}\cdot 223$	$2$	$5.46501317895$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$1.29274426912$
4.0.981.1	x^4 - x^3 - 4x^2 + 4x + 7	$4$	[0,2]	$3^{2}\cdot 109$	$2$	$5.59650958426$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.15221875719$
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	$2$	$1$	$1.34361173004$
4.0.1008.1	x^4 - 5x^2 + 7	$4$	[0,2]	$2^{4}\cdot 3^{2}\cdot 7$	$3$	$5.63462649452$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$3.39588318368$
4.0.1008.2	x^4 + 5x^2 + 7	$4$	[0,2]	$2^{4}\cdot 3^{2}\cdot 7$	$3$	$5.63462649452$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.41611328691$
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	$2$	$1$	$1.27428442991$
4.0.1025.1	x^4 - x^3 + 3x^2 - 2x + 4	$4$	[0,2]	$5^{2}\cdot 41$	$2$	$5.65823481195$	✓			$D_{4}$ (as 4T3)	trivial	$2$	$1$	$0.962423650119$
4.0.1040.1	x^4 - 3x^2 - 2x + 5	$4$	[0,2]	$2^{4}\cdot 5\cdot 13$	$3$	$5.67882302887$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.8522660627$
4.0.1040.2	x^4 + x^2 - 4x + 4	$4$	[0,2]	$2^{4}\cdot 5\cdot 13$	$3$	$5.67882302887$			✓	$D_{4}$ (as 4T3)	trivial	$4$	$1$	$3.46864904298$
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	$2$	$1$	$1.77702641037$
4.0.1088.1	x^4 - 2x^3 + x^2 - 2x + 3	$4$	[0,2]	$2^{6}\cdot 17$	$2$	$5.74324342205$			✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$1.17996602392$
4.0.1088.2	x^4 - 2x^3 + 5x^2 - 4x + 2	$4$	[0,2]	$2^{6}\cdot 17$	$2$	$5.74324342205$	✓		✓	$D_{4}$ (as 4T3)	trivial	$2$	$1$	$1.76274717404$
4.0.1089.1	x^4 - x^3 - 2x^2 - 3x + 9	$4$	[0,2]	$3^{2}\cdot 11^{2}$	$2$	$5.74456264654$	✓	✓		$C_2^2$ (as 4T2)	trivial	$6$	$1$	$3.82816847133$
4.0.1129.1	x^4 - x^3 - x + 2	$4$	[0,2]	$1129$	$1$	$5.79660204196$			✓	$S_4$ (as 4T5)	trivial	$2$	$1$	$1.26901928105$
4.0.1161.1	x^4 - x^3 + 6x^2 - x + 7	$4$	[0,2]	$3^{3}\cdot 43$	$2$	$5.83724678892$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$3.48142350173$
4.0.1168.1	x^4 - x^2 - 4x + 5	$4$	[0,2]	$2^{4}\cdot 73$	$2$	$5.84602557138$				$D_{4}$ (as 4T3)	trivial	$4$	$1$	$1.8902413596$
4.0.1197.1	x^4 - 2x^3 - 4x^2 + 5x + 7	$4$	[0,2]	$3^{2}\cdot 7\cdot 19$	$3$	$5.8819799204$			✓	$D_{4}$ (as 4T3)	trivial	$6$	$1$	$2.3192389338$
4.0.1197.2	x^4 - x^3 - 5x^2 + 3x + 9	$4$	[0,2]	$3^{2}\cdot 7\cdot 19$	$3$	$5.8819799204$				$D_{4}$ (as 4T3)	trivial	$6$	$1$	$3.57713438377$
4.0.1225.1	x^4 - x^3 + 5x^2 + 2x + 4	$4$	[0,2]	$5^{2}\cdot 7^{2}$	$2$	$5.9160797831$	✓	✓		$C_2^2$ (as 4T2)	trivial	$2$	$1$	$0.962423650119$

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