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CM field	Relative class number	Regulator	$p$-adic completions	Monogenic

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
4.0.1372.1	$x^{4} - x^{3} + 3 x^{2} - 4 x + 2$	$4$	[0,2]	$2^{2}\cdot 7^{3}$	$2$	$6.08609220723$	$8.607034141317701$		✓	$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$1.48602212488$
4.0.2744.1	$x^{4} - x^{3} + 3 x^{2} + 3 x + 2$	$4$	[0,2]	$2^{3}\cdot 7^{3}$	$2$	$7.2376241554$	$12.172184414459759$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$4.76948079341$
4.0.3773.1	$x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 4$	$4$	[0,2]	$7^{3}\cdot 11$	$2$	$7.83739438281$	$14.273151402264794$		✓	$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$4.27785964575$
4.0.7889.1	$x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 11$	$4$	[0,2]	$7^{3}\cdot 23$	$2$	$9.42443859247$	$20.638942828580127$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$2.46464010781$
4.0.10976.1	$x^{4} + 7 x^{2} + 14$	$4$	[0,2]	$2^{5}\cdot 7^{3}$	$2$	$10.2355462399$	$17.214068282635402$		✓	$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$3.43186569678$
4.0.12348.1	$x^{4} - x^{3} - 4 x^{2} + 10 x + 16$	$4$	[0,2]	$2^{2}\cdot 3^{2}\cdot 7^{3}$	$3$	$10.5414209225$	$14.907820435242222$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$6.23046207204$
4.0.14749.1	$x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 18$	$4$	[0,2]	$7^{3}\cdot 43$	$2$	$11.020229626$	$28.220048629129643$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$9.52801875896$
4.2.15435.1	$x^{4} - 2 x^{3} - 2 x^{2} + 3 x - 3$	$4$	[2,1]	$-\,3^{2}\cdot 5\cdot 7^{3}$	$3$	$11.1461955593$	$16.667449944781055$		✓	$D_{4}$ (as 4T3)	trivial	$[2]$	$2$	$2$	$8.54974416098$
4.2.15435.2	$x^{4} - x^{3} - 4 x^{2} + 10 x - 5$	$4$	[2,1]	$-\,3^{2}\cdot 5\cdot 7^{3}$	$3$	$11.1461955593$	$16.667449944781055$		✓	$D_{4}$ (as 4T3)	trivial	$[2]$	$2$	$2$	$3.93108423674$
4.0.21952.1	$x^{4} + 28$	$4$	[0,2]	$2^{6}\cdot 7^{3}$	$2$	$12.1721844145$	$17.214068282635402$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$5.13966262198$
4.0.22981.1	$x^{4} - 7 x + 7$	$4$	[0,2]	$7^{3}\cdot 67$	$2$	$12.3123862348$	$35.22580538311783$		✓	$S_4$ (as 4T5)	$[2]$	$[2]$	$2$	$1$	$2.0650449598$
4.0.22981.2	$x^{4} - 2 x^{3} + 12 x^{2} - 11 x + 32$	$4$	[0,2]	$7^{3}\cdot 67$	$2$	$12.3123862348$	$35.22580538311783$		✓	$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$12.7636156373$
4.0.24353.1	$x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 32$	$4$	[0,2]	$7^{3}\cdot 71$	$2$	$12.4921766585$	$36.262079388792664$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$29.8136632009$
4.0.24696.1	$x^{4} - x^{3} - 4 x^{2} - 11 x + 37$	$4$	[0,2]	$2^{3}\cdot 3^{2}\cdot 7^{3}$	$3$	$12.5359327632$	$21.08284184494233$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$3.81612714565$
4.0.27097.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 32$	$4$	[0,2]	$7^{3}\cdot 79$	$2$	$12.8301077247$	$38.25049640225233$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$32.4284578644$
4.2.27440.1	$x^{4} - 2 x^{3} - 2 x^{2} - 4 x - 3$	$4$	[2,1]	$-\,2^{4}\cdot 5\cdot 7^{3}$	$3$	$12.8705180131$	$21.602807404215152$		✓	$S_4$ (as 4T5)	trivial	$[2]$	$2$	$2$	$12.9972049723$
4.0.30184.1	$x^{4} - x^{3} - 11 x^{2} + 3 x + 44$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 11$	$3$	$13.1808736829$	$40.37056858177486$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$11.0211740308$
4.0.30184.2	$x^{4} - x^{3} - 4 x^{2} + 17 x + 37$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 11$	$3$	$13.1808736829$	$40.37056858177486$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$3.8669927122$
4.0.33957.1	$x^{4} - 2 x^{3} + 12 x^{2} - 11 x + 46$	$4$	[0,2]	$3^{2}\cdot 7^{3}\cdot 11$	$3$	$13.57476527$	$24.72182341284559$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$7.2958004235$
4.0.34300.1	$x^{4} - x^{3} + 10 x^{2} - 18 x + 44$	$4$	[0,2]	$2^{2}\cdot 5^{2}\cdot 7^{3}$	$3$	$13.6089158927$	$19.24591342464791$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$11.5815369913$
4.0.36701.1	$x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 46$	$4$	[0,2]	$7^{3}\cdot 107$	$2$	$13.8410639247$	$44.51592672277393$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$16.1831280737$
4.0.39788.1	$x^{4} - x^{3} - 11 x^{2} - 4 x + 58$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 29$	$3$	$14.123359936$	$46.35029735162923$		✓	$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$3.4083289047$
4.0.39788.2	$x^{4} - x^{3} + 10 x^{2} + 10 x + 44$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 29$	$3$	$14.123359936$	$46.35029735162923$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$12.1965411307$
4.0.43561.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 53$	$4$	[0,2]	$7^{3}\cdot 127$	$2$	$14.4468931339$	$48.49817435261271$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$7.67153762857$
4.0.46305.1	$x^{4} - x^{3} + 3 x^{2} - 4 x + 16$	$4$	[0,2]	$3^{3}\cdot 5\cdot 7^{3}$	$3$	$14.6692183188$	$21.935597734512804$	✓		$D_{4}$ (as 4T3)	$[2, 2]$	$[2, 2]$	$2$	$1$	$3.13359847394$
4.4.46305.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 4$	$4$	[4,0]	$3^{3}\cdot 5\cdot 7^{3}$	$3$	$14.6692183188$	$21.935597734512804$			$D_{4}$ (as 4T3)	trivial	$[2, 2]$	$2$	$3$	$18.6114984751$
4.0.49392.1	$x^{4} + 7 x^{2} + 7$	$4$	[0,2]	$2^{4}\cdot 3^{2}\cdot 7^{3}$	$3$	$14.9078204352$	$21.08284184494233$	✓	✓	$D_{4}$ (as 4T3)	$[4]$	$[4]$	$2$	$1$	$3.13359847394$
4.4.49392.1	$x^{4} - 7 x^{2} + 7$	$4$	[4,0]	$2^{4}\cdot 3^{2}\cdot 7^{3}$	$3$	$14.9078204352$	$21.08284184494233$		✓	$D_{4}$ (as 4T3)	trivial	$[2, 2]$	$2$	$3$	$14.4227799942$
4.0.50764.1	$x^{4} - x^{3} + 17 x^{2} - 4 x + 58$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 37$	$3$	$15.0102857119$	$52.354544771804825$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$5.54807917018$
4.0.50764.2	$x^{4} - x^{3} - 4 x^{2} - 18 x + 72$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 37$	$3$	$15.0102857119$	$52.354544771804825$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$14.369336468$
4.0.51793.1	$x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 67$	$4$	[0,2]	$7^{3}\cdot 151$	$2$	$15.0857798903$	$52.882503115825294$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$6.25592348594$
4.2.52479.1	$x^{4} - x^{3} - 4 x^{2} - 11 x - 5$	$4$	[2,1]	$-\,3^{2}\cdot 7^{3}\cdot 17$	$3$	$15.135486593$	$30.733259151122564$			$D_{4}$ (as 4T3)	trivial	$[2]$	$2$	$2$	$16.478612882$
4.2.52479.2	$x^{4} - x^{3} - 11 x^{2} - 18 x - 12$	$4$	[2,1]	$-\,3^{2}\cdot 7^{3}\cdot 17$	$3$	$15.135486593$	$30.733259151122564$			$D_{4}$ (as 4T3)	trivial	$[2]$	$2$	$2$	$17.2734016346$
4.0.55909.1	$x^{4} - 2 x^{3} + 12 x^{2} - 11 x + 74$	$4$	[0,2]	$7^{3}\cdot 163$	$2$	$15.3769581048$	$54.943627891910246$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$20.9643187925$
4.0.60368.1	$x^{4} + 14 x^{2} + 77$	$4$	[0,2]	$2^{4}\cdot 7^{3}\cdot 11$	$3$	$15.6747887656$	$28.54630280452959$			$D_{4}$ (as 4T3)	$[2, 2]$	$[2, 2]$	$2$	$1$	$3.51214513732$
4.0.61397.1	$x^{4} - 2 x^{3} - 16 x^{2} + 17 x + 74$	$4$	[0,2]	$7^{3}\cdot 179$	$2$	$15.7411619738$	$57.57713428752713$		✓	$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$19.2078387988$
4.0.63112.1	$x^{4} - x^{3} + 17 x^{2} + 3 x + 72$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 23$	$3$	$15.8499532564$	$58.37574572244189$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$17.511716367$
4.0.63112.2	$x^{4} - x^{3} + 3 x^{2} - 25 x + 86$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 23$	$3$	$15.8499532564$	$58.37574572244189$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$15.117064862$
4.0.65513.1	$x^{4} - 2 x^{3} + 19 x^{2} - 18 x + 88$	$4$	[0,2]	$7^{3}\cdot 191$	$2$	$15.9985960066$	$59.47578921622947$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$53.2001917956$
4.0.68600.1	$x^{4} - x^{3} + 10 x^{2} + 17 x + 79$	$4$	[0,2]	$2^{3}\cdot 5^{2}\cdot 7^{3}$	$3$	$16.1838196071$	$27.217831785395497$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$4.30949805888$
4.2.68943.1	$x^{4} - x^{3} - 4 x^{2} - 11 x - 12$	$4$	[2,1]	$-\,3\cdot 7^{3}\cdot 67$	$3$	$16.204011561$	$61.01288466109334$			$S_4$ (as 4T5)	trivial	$[2]$	$2$	$2$	$34.6101014815$
4.0.71001.1	$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 88$	$4$	[0,2]	$3^{2}\cdot 7^{3}\cdot 23$	$3$	$16.323606475$	$35.7476975936101$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$28.7969050445$
4.0.72373.1	$x^{4} - 2 x^{3} - 16 x^{2} + 17 x + 88$	$4$	[0,2]	$7^{3}\cdot 211$	$2$	$16.4018993994$	$62.51219630154103$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$26.064031263$
4.0.72716.1	$x^{4} - x^{3} - 18 x^{2} + 10 x + 100$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 53$	$3$	$16.4212984864$	$62.66015436958205$			$D_{4}$ (as 4T3)	$[4]$	$[4]$	$2$	$1$	$7.92834028711$
4.0.72716.2	$x^{4} - x^{3} + 3 x^{2} + 24 x + 86$	$4$	[0,2]	$2^{2}\cdot 7^{3}\cdot 53$	$3$	$16.4212984864$	$62.66015436958205$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$5.05010618418$
4.2.73059.1	$x^{4} - x^{3} - 4 x^{2} - 4 x - 5$	$4$	[2,1]	$-\,3\cdot 7^{3}\cdot 71$	$3$	$16.4406290655$	$62.80776388948507$		✓	$S_4$ (as 4T5)	trivial	$[2]$	$2$	$2$	$12.8552877425$
4.0.79576.1	$x^{4} - x^{3} - 18 x^{2} + 17 x + 107$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 29$	$3$	$16.7956001237$	$65.54921913469981$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$6.78704036179$
4.0.79576.2	$x^{4} - x^{3} + 17 x^{2} - 25 x + 100$	$4$	[0,2]	$2^{3}\cdot 7^{3}\cdot 29$	$3$	$16.7956001237$	$65.54921913469981$			$D_{4}$ (as 4T3)	$[2]$	$[2]$	$2$	$1$	$18.616677808$
4.0.81977.1	$x^{4} - 2 x^{3} + 19 x^{2} - 18 x + 109$	$4$	[0,2]	$7^{3}\cdot 239$	$2$	$16.9208823265$	$66.5307593779829$			$D_{4}$ (as 4T3)	trivial	trivial	$2$	$1$	$8.18888408318$
4.2.85064.1	$x^{4} - 2 x^{3} - 2 x^{2} - 4 x - 24$	$4$	[2,1]	$-\,2^{3}\cdot 7^{3}\cdot 31$	$3$	$17.077978018$	$67.77185460062407$		✓	$S_4$ (as 4T5)	trivial	$[2]$	$2$	$2$	$27.4666688817$

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