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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
4.4.6125.1	$x^{4} - x^{3} - 9 x^{2} + 9 x + 11$	$4$	[4,0]	$5^{3}\cdot 7^{2}$	$2$	$8.84660269327$	$8.846602693265513$		✓	✓	$C_4$ (as 4T1)	trivial	$2$	$3$	$3.36611485007$
4.2.8624.1	$x^{4} - 2 x^{3} + 2 x^{2} + 6 x + 2$	$4$	[2,1]	$-\,2^{4}\cdot 7^{2}\cdot 11$	$3$	$9.63667443312$	$19.699129000227927$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$6.39904749595$
4.2.10339.1	$x^{4} - x^{3} - 2 x^{2} + 2 x - 3$	$4$	[2,1]	$-\,7^{2}\cdot 211$	$2$	$10.0836934366$	$38.43175770115127$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$5.58382041386$
4.2.12103.1	$x^{4} - x^{3} + 7 x^{2} - 6 x + 1$	$4$	[2,1]	$-\,7^{2}\cdot 13\cdot 19$	$3$	$10.4887385094$	$41.58124577258358$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$6.77715534445$
4.0.13328.1	$x^{4} - 3 x^{2} - 14 x + 53$	$4$	[0,2]	$2^{4}\cdot 7^{2}\cdot 17$	$3$	$10.7446245871$	$21.817424229271428$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$3.29189154683$
4.2.13475.1	$x^{4} - x^{3} - 2 x^{2} - 12 x - 31$	$4$	[2,1]	$-\,5^{2}\cdot 7^{2}\cdot 11$	$3$	$10.7741295547$	$19.621416870348583$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$4.21276710093$
4.0.15680.1	$x^{4} - 2 x^{3} - 12 x^{2} + 6 x + 65$	$4$	[0,2]	$2^{6}\cdot 5\cdot 7^{2}$	$3$	$11.1901656261$	$16.73320053068151$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$6.01244231173$
4.0.15729.1	$x^{4} - x^{3} + x + 8$	$4$	[0,2]	$3\cdot 7^{2}\cdot 107$	$3$	$11.1988977167$	$47.40253157796533$				$S_4$ (as 4T5)	$[2]$	$2$	$1$	$5.70891048014$
4.2.17199.1	$x^{4} - 3 x^{2} - 7 x - 3$	$4$	[2,1]	$-\,3^{3}\cdot 7^{2}\cdot 13$	$3$	$11.4518539096$	$34.368625199180826$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$12.2956373849$
4.2.19600.1	$x^{4} - 7 x^{2} - 49$	$4$	[2,1]	$-\,2^{4}\cdot 5^{2}\cdot 7^{2}$	$3$	$11.8321595662$	$16.73320053068151$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$5.78651667578$
4.4.19796.1	$x^{4} - x^{3} - 7 x^{2} + x + 8$	$4$	[4,0]	$2^{2}\cdot 7^{2}\cdot 101$	$3$	$11.8616296813$	$42.20815519009746$			✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$17.1354827341$
4.2.21119.1	$x^{4} - 5 x^{2} - 14 x - 13$	$4$	[2,1]	$-\,7^{2}\cdot 431$	$2$	$12.0550311673$	$54.92722457943783$				$S_4$ (as 4T5)	trivial	$2$	$2$	$8.68982104024$
4.2.26803.1	$x^{4} - x^{3} + 4 x^{2} + 6 x + 1$	$4$	[2,1]	$-\,7^{2}\cdot 547$	$2$	$12.7951638477$	$61.87891401761993$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$3.24270063503$
4.2.28175.1	$x^{4} - x^{3} - 3 x^{2} + 6 x + 1$	$4$	[2,1]	$-\,5^{2}\cdot 7^{2}\cdot 23$	$3$	$12.9558520876$	$28.372521918222215$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$2$	$5.57717436936$
4.0.29645.1	$x^{4} - x^{3} + 7 x^{2} - 13 x + 15$	$4$	[0,2]	$5\cdot 7^{2}\cdot 11^{2}$	$3$	$13.1216323019$	$19.621416870348583$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$4.37724810732$
4.2.31752.1	$x^{4} - x^{3} - 3 x^{2} + 6 x - 6$	$4$	[2,1]	$-\,2^{3}\cdot 3^{4}\cdot 7^{2}$	$3$	$13.3488167588$	$32.37842254987355$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$18.456350868$
4.0.32144.1	$x^{4} - 17 x^{2} - 14 x + 130$	$4$	[0,2]	$2^{4}\cdot 7^{2}\cdot 41$	$3$	$13.3898274316$	$33.88214869219483$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$17.9900916552$
4.2.33320.1	$x^{4} - x^{3} - 7 x^{2} + 8 x + 8$	$4$	[2,1]	$-\,2^{3}\cdot 5\cdot 7^{2}\cdot 17$	$4$	$13.5106501452$	$68.99275324264136$				$S_4$ (as 4T5)	trivial	$2$	$2$	$15.7378428517$
4.2.33663.1	$x^{4} - 2 x^{3} - x^{2} - 5 x + 1$	$4$	[2,1]	$-\,3\cdot 7^{2}\cdot 229$	$3$	$13.5452867784$	$69.34695379034324$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$12.9952834137$
4.2.34055.1	$x^{4} - x^{3} - 2 x^{2} + 16 x - 24$	$4$	[2,1]	$-\,5\cdot 7^{2}\cdot 139$	$3$	$13.5845488909$	$69.74955196988724$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$17.6601583058$
4.0.35917.1	$x^{4} + 2 x^{2} - 7 x + 15$	$4$	[0,2]	$7^{2}\cdot 733$	$2$	$13.7665467416$	$71.63099887618489$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$1$	$3.0449273733$
4.2.39200.1	$x^{4} + x^{2} - 14 x + 2$	$4$	[2,1]	$-\,2^{5}\cdot 5^{2}\cdot 7^{2}$	$3$	$14.070888342$	$30.944895057811237$				$S_4$ (as 4T5)	trivial	$2$	$2$	$27.8341464737$
4.0.40768.1	$x^{4} - 2 x^{3} - 12 x^{2} - 8 x + 170$	$4$	[0,2]	$2^{6}\cdot 7^{2}\cdot 13$	$3$	$14.2095345253$	$26.981475126464083$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$10.3592428674$
4.2.45668.1	$x^{4} - x^{3} + 5 x^{2} - 12 x + 4$	$4$	[2,1]	$-\,2^{2}\cdot 7^{2}\cdot 233$	$3$	$14.6185062614$	$80.77128202523468$				$S_4$ (as 4T5)	trivial	$2$	$2$	$16.5334991868$
4.0.48265.1	$x^{4} - x^{3} + 4 x^{2} - x + 8$	$4$	[0,2]	$5\cdot 7^{2}\cdot 197$	$3$	$14.8220432994$	$83.03613671167511$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$1$	$8.29921969309$
4.4.48657.1	$x^{4} - x^{3} - 7 x^{2} + 8 x + 1$	$4$	[4,0]	$3\cdot 7^{2}\cdot 331$	$3$	$14.8520475892$	$83.37265738837884$			✓	$S_4$ (as 4T5)	trivial	$2$	$3$	$21.9620623142$
4.4.50225.1	$x^{4} - x^{3} - 23 x^{2} + 16 x + 116$	$4$	[4,0]	$5^{2}\cdot 7^{2}\cdot 41$	$3$	$14.970282172$	$37.881393849751625$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$12.5499126082$
4.2.52528.1	$x^{4} - 2 x^{3} - 6 x + 2$	$4$	[2,1]	$-\,2^{4}\cdot 7^{2}\cdot 67$	$3$	$15.1390183834$	$48.616991778623884$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$14.4202908609$
4.0.53312.1	$x^{4} - 2 x^{3} + 13 x^{2} + 2 x + 43$	$4$	[0,2]	$2^{6}\cdot 7^{2}\cdot 17$	$3$	$15.1951938137$	$30.854497241083024$				$D_{4}$ (as 4T3)	$[2]$	$2$	$1$	$5.43565288549$
4.0.55125.1	$x^{4} - x^{3} + 26 x^{2} - 26 x + 151$	$4$	[0,2]	$3^{2}\cdot 5^{3}\cdot 7^{2}$	$3$	$15.3227653391$	$15.322765339111537$	✓	✓		$C_4$ (as 4T1)	$[2, 2]$	$2$	$1$	$0.962423650119$
4.2.55615.1	$x^{4} + x^{2} - 21 x + 9$	$4$	[2,1]	$-\,5\cdot 7^{2}\cdot 227$	$3$	$15.3567030117$	$89.13472948295743$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$25.3987371275$
4.2.56644.1	$x^{4} - x^{3} + 15 x - 13$	$4$	[2,1]	$-\,2^{2}\cdot 7^{2}\cdot 17^{2}$	$3$	$15.4272486205$	$21.817424229271428$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$13.7911330547$
4.2.57036.1	$x^{4} - x^{3} - 7 x^{2} + 15 x - 6$	$4$	[2,1]	$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 97$	$4$	$15.4538703738$	$71.64438817710507$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$32.2885005502$
4.0.57232.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 221$	$4$	[0,2]	$2^{4}\cdot 7^{2}\cdot 73$	$3$	$15.46712982$	$45.21061822182926$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$7.61762975205$
4.0.62720.1	$x^{4} - 28 x^{2} + 245$	$4$	[0,2]	$2^{8}\cdot 5\cdot 7^{2}$	$3$	$15.8252839937$	$23.664319132398465$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$7.66404996111$
4.2.63504.1	$x^{4} - 2 x^{3} + 6 x^{2} + 16 x - 20$	$4$	[2,1]	$-\,2^{4}\cdot 3^{4}\cdot 7^{2}$	$3$	$15.8745078664$	$32.37842254987355$				$S_4$ (as 4T5)	trivial	$2$	$2$	$18.398457302$
4.0.63700.1	$x^{4} - x^{3} + 5 x^{2} + 9 x + 4$	$4$	[0,2]	$2^{2}\cdot 5^{2}\cdot 7^{2}\cdot 13$	$4$	$15.8867425636$	$44.27793545242387$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$1$	$13.6249803166$
4.2.68012.1	$x^{4} - x^{3} - 3 x^{2} + 13 x - 6$	$4$	[2,1]	$-\,2^{2}\cdot 7^{2}\cdot 347$	$3$	$16.1490279628$	$78.23488007525349$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$38.3536701585$
4.0.69776.1	$x^{4} - 17 x^{2} - 28 x + 277$	$4$	[0,2]	$2^{4}\cdot 7^{2}\cdot 89$	$3$	$16.2527373601$	$49.91993589739474$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$4.87542810648$
4.2.70168.1	$x^{4} - x^{3} - 9 x^{2} + 2 x + 18$	$4$	[2,1]	$-\,2^{3}\cdot 7^{2}\cdot 179$	$3$	$16.2755163051$	$100.11992808627062$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$30.0846402389$
4.2.71736.1	$x^{4} - x^{3} + 7 x^{2} - 6 x - 6$	$4$	[2,1]	$-\,2^{3}\cdot 3\cdot 7^{2}\cdot 61$	$4$	$16.3656888207$	$101.23240587875011$				$S_4$ (as 4T5)	trivial	$2$	$2$	$25.3878410182$
4.2.72128.1	$x^{4} - 2 x^{3} + 2 x^{2} + 6 x - 5$	$4$	[2,1]	$-\,2^{6}\cdot 7^{2}\cdot 23$	$3$	$16.38800065$	$35.888716889852724$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$22.1680601772$
4.0.72961.1	$x^{4} - 2 x^{3} + 7 x^{2} + x + 2$	$4$	[0,2]	$7^{2}\cdot 1489$	$2$	$16.4351130006$	$102.0930947713899$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$1$	$7.97179411057$
4.0.74676.1	$x^{4} - x^{3} + 5 x^{2} - 5 x + 18$	$4$	[0,2]	$2^{2}\cdot 3\cdot 7^{2}\cdot 127$	$4$	$16.5308529164$	$81.97816099510437$				$S_4$ (as 4T5)	$[2]$	$2$	$1$	$22.7830941858$
4.4.74725.1	$x^{4} - x^{3} - 30 x^{2} + 2 x + 179$	$4$	[4,0]	$5^{2}\cdot 7^{2}\cdot 61$	$3$	$16.5335640035$	$46.20606020859169$				$D_{4}$ (as 4T3)	trivial	$2$	$3$	$10.8105222739$
4.2.75852.1	$x^{4} - x^{3} - 2 x^{2} - 12 x - 24$	$4$	[2,1]	$-\,2^{2}\cdot 3^{2}\cdot 7^{2}\cdot 43$	$4$	$16.5955541643$	$47.70133557994095$			✓	$S_4$ (as 4T5)	$[2]$	$2$	$2$	$21.707310971$
4.0.76048.1	$x^{4} - 31 x^{2} - 14 x + 305$	$4$	[0,2]	$2^{4}\cdot 7^{2}\cdot 97$	$3$	$16.606264434$	$52.11525688318153$				$D_{4}$ (as 4T3)	$[2]$	$4$	$1$	$8.80809812599$
4.2.76587.1	$x^{4} - 2 x^{3} - 13 x + 23$	$4$	[2,1]	$-\,3\cdot 7^{2}\cdot 521$	$3$	$16.6356113086$	$104.59923517884822$				$S_4$ (as 4T5)	trivial	$2$	$2$	$19.4161603292$
4.2.77567.1	$x^{4} - x^{3} + 5 x^{2} + 2 x - 3$	$4$	[2,1]	$-\,7^{2}\cdot 1583$	$2$	$16.6885747653$	$105.26632889960588$			✓	$S_4$ (as 4T5)	trivial	$2$	$2$	$17.8502398917$
4.2.78400.1	$x^{4} - 14 x^{2} - 196$	$4$	[2,1]	$-\,2^{6}\cdot 5^{2}\cdot 7^{2}$	$3$	$16.7332005307$	$23.664319132398465$				$D_{4}$ (as 4T3)	trivial	$2$	$2$	$7.37606293827$

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