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Results (1-50 of 743786 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
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	$2$	$3$	$0.825068847935$
4.4.1125.1	$x^{4} - x^{3} - 4 x^{2} + 4 x + 1$	$4$	[4,0]	$3^{2}\cdot 5^{3}$	$2$	$5.79146092644$	$5.791460926441346$	✓	✓	$C_4$ (as 4T1)	trivial	$2$	$3$	$1.16545519432$
4.4.1600.1	$x^{4} - 6 x^{2} + 4$	$4$	[4,0]	$2^{6}\cdot 5^{2}$	$2$	$6.32455532034$	$6.324555320336759$	✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$1.54250590983$
4.4.1957.1	$x^{4} - 4 x^{2} - x + 1$	$4$	[4,0]	$19\cdot 103$	$2$	$6.65116476425$	$44.23799272118933$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$1.91836302339$
4.4.2000.1	$x^{4} - 5 x^{2} + 5$	$4$	[4,0]	$2^{4}\cdot 5^{3}$	$2$	$6.68740304976$	$6.68740304976422$	✓	✓	$C_4$ (as 4T1)	trivial	$2$	$3$	$1.85281056397$
4.4.2048.1	$x^{4} - 4 x^{2} + 2$	$4$	[4,0]	$2^{11}$	$1$	$6.72717132203$	$6.727171322029716$	✓	✓	$C_4$ (as 4T1)	trivial	$2$	$3$	$2.44179500662$
4.4.2225.1	$x^{4} - x^{3} - 5 x^{2} + 2 x + 4$	$4$	[4,0]	$5^{2}\cdot 89$	$2$	$6.86803506545$	$21.095023109728988$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$2.06451190313$
4.4.2304.1	$x^{4} - 4 x^{2} + 1$	$4$	[4,0]	$2^{8}\cdot 3^{2}$	$2$	$6.92820323028$	$6.928203230275509$	✓	✓	$C_2^2$ (as 4T2)	trivial	$2$	$3$	$2.66089858019$
4.4.2525.1	$x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 5$	$4$	[4,0]	$5^{2}\cdot 101$	$2$	$7.08867957419$	$22.47220505424423$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$2.09111887566$
4.4.2624.1	$x^{4} - 2 x^{3} - 3 x^{2} + 2 x + 1$	$4$	[4,0]	$2^{6}\cdot 41$	$2$	$7.15716381673$	$18.110770276274835$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$2.18595620669$
4.4.2777.1	$x^{4} - x^{3} - 4 x^{2} + x + 2$	$4$	[4,0]	$2777$	$1$	$7.25928705212$	$52.69724850502159$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$3.0387734038$
4.4.3600.1	$x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 1$	$4$	[4,0]	$2^{4}\cdot 3^{2}\cdot 5^{2}$	$3$	$7.74596669241$	$7.745966692414834$	✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$2.61534752461$
4.4.3981.1	$x^{4} - x^{3} - 4 x^{2} + 2 x + 1$	$4$	[4,0]	$3\cdot 1327$	$2$	$7.94324657916$	$63.095166217389426$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$3.18893941247$
4.4.4205.1	$x^{4} - x^{3} - 5 x^{2} - x + 1$	$4$	[4,0]	$5\cdot 29^{2}$	$2$	$8.05269963102$	$12.041594578792296$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$2.8242845114$
4.4.4225.1	$x^{4} - 9 x^{2} + 4$	$4$	[4,0]	$5^{2}\cdot 13^{2}$	$2$	$8.0622577483$	$8.06225774829855$	✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$3.19257767414$
4.4.4352.1	$x^{4} - 6 x^{2} - 4 x + 2$	$4$	[4,0]	$2^{8}\cdot 17$	$2$	$8.12217273948$	$16.492422502470642$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.18167264383$
4.4.4400.1	$x^{4} - 7 x^{2} + 11$	$4$	[4,0]	$2^{4}\cdot 5^{2}\cdot 11$	$3$	$8.14447639858$	$20.97617696340303$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.29011588515$
4.4.4525.1	$x^{4} - x^{3} - 7 x^{2} + 3 x + 9$	$4$	[4,0]	$5^{2}\cdot 181$	$2$	$8.20171446927$	$30.083217912982647$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.05516467967$
4.4.4752.1	$x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 1$	$4$	[4,0]	$2^{4}\cdot 3^{3}\cdot 11$	$3$	$8.30269545139$	$15.120539229772588$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.7053371595$
4.4.4913.1	$x^{4} - x^{3} - 6 x^{2} + x + 1$	$4$	[4,0]	$17^{3}$	$1$	$8.37214402859$	$8.37214402859269$	✓		$C_4$ (as 4T1)	trivial	$2$	$3$	$3.46198873228$
4.4.5125.1	$x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11$	$4$	[4,0]	$5^{3}\cdot 41$	$2$	$8.46103452991$	$21.410136276713814$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.09100676599$
4.4.5225.1	$x^{4} - x^{3} - 8 x^{2} + x + 11$	$4$	[4,0]	$5^{2}\cdot 11\cdot 19$	$3$	$8.50200926099$	$32.32645975048923$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.62009337972$
4.4.5725.1	$x^{4} - x^{3} - 8 x^{2} + 6 x + 11$	$4$	[4,0]	$5^{2}\cdot 229$	$2$	$8.69849008461$	$33.83784863137726$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.06647090016$
4.4.5744.1	$x^{4} - 5 x^{2} - 2 x + 1$	$4$	[4,0]	$2^{4}\cdot 359$	$2$	$8.70569820784$	$53.59104402789705$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$3.73427626648$
4.4.6125.1	$x^{4} - x^{3} - 9 x^{2} + 9 x + 11$	$4$	[4,0]	$5^{3}\cdot 7^{2}$	$2$	$8.84660269327$	$8.846602693265513$	✓	✓	$C_4$ (as 4T1)	trivial	$2$	$3$	$3.36611485007$
4.4.6224.1	$x^{4} - 6 x^{2} - 2 x + 5$	$4$	[4,0]	$2^{4}\cdot 389$	$2$	$8.88213553675$	$44.27682411416183$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$5.46622407668$
4.4.6809.1	$x^{4} - 5 x^{2} - x + 1$	$4$	[4,0]	$11\cdot 619$	$2$	$9.08386839312$	$82.516664983505$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$5.75333674058$
4.4.7053.1	$x^{4} - 2 x^{3} - 4 x^{2} + 3 x + 3$	$4$	[4,0]	$3\cdot 2351$	$2$	$9.16417704754$	$83.98214095865859$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$4.36726178292$
4.4.7056.1	$x^{4} - 5 x^{2} + 1$	$4$	[4,0]	$2^{4}\cdot 3^{2}\cdot 7^{2}$	$3$	$9.16515138991$	$9.16515138991168$	✓	✓	$C_2^2$ (as 4T2)	trivial	$2$	$3$	$5.7128756596$
4.4.7168.1	$x^{4} - 6 x^{2} + 7$	$4$	[4,0]	$2^{10}\cdot 7$	$2$	$9.20130653516$	$17.798422345016238$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$5.71497174049$
4.4.7225.1	$x^{4} - 11 x^{2} + 9$	$4$	[4,0]	$5^{2}\cdot 17^{2}$	$2$	$9.21954445729$	$9.219544457292887$	✓		$C_2^2$ (as 4T2)	trivial	$2$	$3$	$4.45404695945$
4.4.7232.1	$x^{4} - 2 x^{3} - 5 x^{2} + 4 x + 4$	$4$	[4,0]	$2^{6}\cdot 113$	$2$	$9.22177675407$	$30.066592756745816$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$8.43533741077$
4.4.7488.1	$x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 1$	$4$	[4,0]	$2^{6}\cdot 3^{2}\cdot 13$	$3$	$9.30232393605$	$17.663521732655695$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$5.73562486991$
4.4.7537.1	$x^{4} - x^{3} - 5 x^{2} + 4 x + 3$	$4$	[4,0]	$7537$	$1$	$9.31750487855$	$86.81589716175259$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$6.94332554243$
4.4.7600.1	$x^{4} - 9 x^{2} + 19$	$4$	[4,0]	$2^{4}\cdot 5^{2}\cdot 19$	$3$	$9.33691484757$	$27.568097504180443$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.08140452901$
4.4.7625.1	$x^{4} - x^{3} - 9 x^{2} + 4 x + 16$	$4$	[4,0]	$5^{3}\cdot 61$	$2$	$9.34458377794$	$26.115143751039085$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.88717250406$
4.4.8000.1	$x^{4} - 10 x^{2} + 20$	$4$	[4,0]	$2^{6}\cdot 5^{3}$	$2$	$9.45741609003$	$9.457416090031758$	✓		$C_4$ (as 4T1)	trivial	$2$	$3$	$4.50325854125$
4.4.8069.1	$x^{4} - x^{3} - 5 x^{2} + 5 x + 1$	$4$	[4,0]	$8069$	$1$	$9.4777430162$	$89.8276126811795$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$4.14172005586$
4.4.8112.1	$x^{4} - 5 x^{2} + 3$	$4$	[4,0]	$2^{4}\cdot 3\cdot 13^{2}$	$3$	$9.49034467201$	$17.663521732655695$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$5.2034416884$
4.4.8468.1	$x^{4} - x^{3} - 5 x^{2} + 3 x + 4$	$4$	[4,0]	$2^{2}\cdot 29\cdot 73$	$3$	$9.59279607636$	$73.03770071172075$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$9.39000564978$
4.4.8525.1	$x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 19$	$4$	[4,0]	$5^{2}\cdot 11\cdot 31$	$3$	$9.60889830122$	$41.291645644125154$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.41136922541$
4.4.8725.1	$x^{4} - x^{3} - 10 x^{2} + 2 x + 19$	$4$	[4,0]	$5^{2}\cdot 349$	$2$	$9.66476634282$	$41.773197148410844$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$3.76714236574$
4.4.8768.1	$x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7$	$4$	[4,0]	$2^{6}\cdot 137$	$2$	$9.67665227678$	$33.1058907144937$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.92588435923$
4.4.8789.1	$x^{4} - x^{3} - 6 x^{2} - 2 x + 1$	$4$	[4,0]	$11\cdot 17\cdot 47$	$3$	$9.68244115221$	$93.74966666607408$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$4.20025231363$
4.4.8957.1	$x^{4} - x^{3} - 5 x^{2} + x + 1$	$4$	[4,0]	$13^{2}\cdot 53$	$2$	$9.7283826282$	$26.248809496813376$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$6.0643436636$
4.4.9225.1	$x^{4} - x^{3} - 10 x^{2} + 7 x + 19$	$4$	[4,0]	$3^{2}\cdot 5^{2}\cdot 41$	$3$	$9.80035017545$	$24.79919353527449$			$D_{4}$ (as 4T3)	trivial	$2$	$3$	$5.14912489678$
4.4.9248.1	$x^{4} - 5 x^{2} + 2$	$4$	[4,0]	$2^{5}\cdot 17^{2}$	$2$	$9.80645309178$	$16.492422502470642$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$9.93835336634$
4.4.9301.1	$x^{4} - x^{3} - 5 x^{2} + x + 3$	$4$	[4,0]	$71\cdot 131$	$2$	$9.82047311635$	$96.44169222903547$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$5.65473750217$
4.4.9792.1	$x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7$	$4$	[4,0]	$2^{6}\cdot 3^{2}\cdot 17$	$3$	$9.94758940723$	$20.199009876724155$		✓	$D_{4}$ (as 4T3)	trivial	$2$	$3$	$4.9482532611$
4.4.9909.1	$x^{4} - 6 x^{2} - 3 x + 3$	$4$	[4,0]	$3^{3}\cdot 367$	$2$	$9.97717195092$	$43.66907302809774$		✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$5.73611443522$

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