Number field search results

Results (1-50 of 21145 matches)

 

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
6.0.16807.1	$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$	$6$	[0,3]	$-\,7^{5}$	$1$	$5.0611401848$	$5.061140184796386$	✓	✓	✓	$C_6$ (as 6T1)	trivial	$14$	$2$	$2.10181872849$
6.0.19683.1	$x^{6} - x^{3} + 1$	$6$	[0,3]	$-\,3^{9}$	$1$	$5.19615242271$	$5.196152422706632$	✓	✓	✓	$C_6$ (as 6T1)	trivial	$18$	$2$	$3.39714980258$
6.0.64827.1	$x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 7^{4}$	$2$	$6.33810341019$	$6.338103410186692$	✓	✓	?	$C_6$ (as 6T1)	trivial	$6$	$2$	$2.10181872849$
6.0.153664.1	$x^{6} + 5 x^{4} + 6 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7^{4}$	$2$	$7.31861142005$	$7.318611420045943$	✓	✓	✓	$C_6$ (as 6T1)	trivial	$4$	$2$	$2.10181872849$
6.6.300125.1	$x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1$	$6$	[6,0]	$5^{3}\cdot 7^{4}$	$2$	$8.18245631806$	$8.182456318064498$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.27756260865$
6.6.371293.1	$x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 6 x^{2} - 3 x - 1$	$6$	[6,0]	$13^{5}$	$1$	$8.47785778235$	$8.477857782354299$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.77450098008$
6.0.419904.1	$x^{6} + 6 x^{4} + 9 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 3^{8}$	$2$	$8.65349742184$	$8.65349742184445$	✓	✓	✓	$C_6$ (as 6T1)	trivial	$4$	$2$	$3.39714980258$
6.6.453789.1	$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 8 x^{2} - 8 x + 1$	$6$	[6,0]	$3^{3}\cdot 7^{5}$	$2$	$8.7661519443$	$8.766151944295878$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$4.39996237517$
6.0.771147.1	$x^{6} - x^{5} + 5 x^{4} + 6 x^{3} + 15 x^{2} + 4 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 13^{4}$	$2$	$9.5761188809$	$9.57611888089896$	✓	✓	?	$C_6$ (as 6T1)	trivial	$6$	$2$	$5.46019947038$
6.6.820125.1	$x^{6} - 9 x^{4} - 4 x^{3} + 9 x^{2} + 3 x - 1$	$6$	[6,0]	$3^{8}\cdot 5^{3}$	$2$	$9.67490423918$	$9.674904239181682$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$6.28127608708$
6.6.1075648.1	$x^{6} - 7 x^{4} + 14 x^{2} - 7$	$6$	[6,0]	$2^{6}\cdot 7^{5}$	$2$	$10.1222803696$	$10.122280369592772$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$7.70329572133$
6.0.1229312.1	$x^{6} + 10 x^{4} + 24 x^{2} + 8$	$6$	[0,3]	$-\,2^{9}\cdot 7^{4}$	$2$	$10.350079528$	$10.350079527967589$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$2.10181872849$
6.6.1229312.1	$x^{6} - 10 x^{4} + 24 x^{2} - 8$	$6$	[6,0]	$2^{9}\cdot 7^{4}$	$2$	$10.350079528$	$10.350079527967589$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$8.7234383498$
6.6.1259712.1	$x^{6} - 6 x^{4} + 9 x^{2} - 3$	$6$	[6,0]	$2^{6}\cdot 3^{9}$	$2$	$10.3923048454$	$10.392304845413264$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$10.1773563373$
6.0.1827904.1	$x^{6} + 9 x^{4} + 14 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 13^{4}$	$2$	$11.0575496274$	$11.057549627357744$	✓	✓		$C_6$ (as 6T1)	$[3]$	$4$	$2$	$5.46019947038$
6.0.2100875.1	$x^{6} - x^{5} + 8 x^{4} - 8 x^{3} + 22 x^{2} - 22 x + 29$	$6$	[0,3]	$-\,5^{3}\cdot 7^{5}$	$2$	$11.3170534969$	$11.317053496860568$	✓	✓	?	$C_6$ (as 6T1)	$[2]$	$2$	$2$	$2.10181872849$
6.0.2250423.1	$x^{6} + 9 x^{4} - 5 x^{3} + 36 x^{2} - 12 x + 8$	$6$	[0,3]	$-\,3^{8}\cdot 7^{3}$	$2$	$11.4475010746$	$11.447501074569505$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$3.39714980258$
6.0.2460375.1	$x^{6} + 6 x^{4} - 4 x^{3} + 9 x^{2} - 12 x + 19$	$6$	[0,3]	$-\,3^{9}\cdot 5^{3}$	$2$	$11.6189500386$	$11.61895003862225$	✓	✓	?	$C_6$ (as 6T1)	$[2]$	$2$	$2$	$3.39714980258$
6.0.2476099.1	$x^{6} - x^{5} + 2 x^{4} + 8 x^{3} - x^{2} - 5 x + 7$	$6$	[0,3]	$-\,19^{5}$	$1$	$11.6312931276$	$11.631293127556278$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$7.80862678603$
6.0.3195731.1	$x^{6} - x^{5} + 4 x^{4} - 3 x^{3} + 29 x^{2} - 4 x + 71$	$6$	[0,3]	$-\,7^{4}\cdot 11^{3}$	$2$	$12.1365440334$	$12.136544033351255$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$2.10181872849$
6.0.3359232.1	$x^{6} + 12 x^{4} + 36 x^{2} + 8$	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}$	$2$	$12.2378934159$	$12.237893415933033$	✓	✓	?	$C_6$ (as 6T1)	$[3]$	$2$	$2$	$3.39714980258$
6.6.3359232.1	$x^{6} - 12 x^{4} + 36 x^{2} - 8$	$6$	[6,0]	$2^{9}\cdot 3^{8}$	$2$	$12.2378934159$	$12.237893415933033$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$15.053136738$
6.0.3518667.1	$x^{6} - x^{5} + 7 x^{4} - 8 x^{3} + 43 x^{2} - 42 x + 49$	$6$	[0,3]	$-\,3^{3}\cdot 19^{4}$	$2$	$12.3328380342$	$12.332838034173273$	✓	✓	?	$C_6$ (as 6T1)	$[3]$	$6$	$2$	$7.80862678603$
6.6.3570125.1	$x^{6} - x^{5} - 12 x^{4} + 13 x^{3} + 19 x^{2} - 10 x - 5$	$6$	[6,0]	$5^{3}\cdot 13^{4}$	$2$	$12.3627163157$	$12.362716315674692$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$19.2357657825$
6.6.4148928.1	$x^{6} - 2 x^{5} - 12 x^{4} + 18 x^{3} + 23 x^{2} - 16 x + 1$	$6$	[6,0]	$2^{6}\cdot 3^{3}\cdot 7^{4}$	$3$	$12.6762068204$	$12.676206820373384$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$17.2833344396$
6.6.5274997.1	$x^{6} - x^{5} - 14 x^{4} + 9 x^{3} + 35 x^{2} - 16 x - 1$	$6$	[6,0]	$7^{4}\cdot 13^{3}$	$2$	$13.1938143701$	$13.193814370085985$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$17.5867290625$
6.6.6751269.1	$x^{6} - 12 x^{4} - 5 x^{3} + 36 x^{2} + 30 x + 1$	$6$	[6,0]	$3^{9}\cdot 7^{3}$	$2$	$13.7477270849$	$13.74772708486752$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$26.8507980102$
6.0.8103375.1	$x^{6} - x^{5} + 7 x^{4} - 5 x^{3} + 49 x^{2} - 9 x + 139$	$6$	[0,3]	$-\,3^{3}\cdot 5^{3}\cdot 7^{4}$	$3$	$14.1724300736$	$14.172430073600676$	✓	✓	?	$C_6$ (as 6T1)	$[2]$	$2$	$2$	$2.10181872849$
6.0.8340544.1	$x^{6} + 13 x^{4} + 50 x^{2} + 49$	$6$	[0,3]	$-\,2^{6}\cdot 19^{4}$	$2$	$14.2407347178$	$14.240734717803987$	✓	✓	?	$C_6$ (as 6T1)	trivial	$4$	$2$	$7.80862678603$
6.0.8605184.1	$x^{6} + 14 x^{4} + 56 x^{2} + 56$	$6$	[0,3]	$-\,2^{9}\cdot 7^{5}$	$2$	$14.3150661808$	$14.315066180821045$	✓	✓	?	$C_6$ (as 6T1)	$[4]$	$2$	$2$	$2.10181872849$
6.6.8605184.1	$x^{6} - 14 x^{4} + 56 x^{2} - 56$	$6$	[6,0]	$2^{9}\cdot 7^{5}$	$2$	$14.3150661808$	$14.315066180821045$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$28.1866403529$
6.0.8732691.1	$x^{6} - 3 x^{5} + 6 x^{4} - 5 x^{3} + 33 x^{2} - 54 x + 111$	$6$	[0,3]	$-\,3^{8}\cdot 11^{3}$	$2$	$14.3502020363$	$14.350202036282921$	✓	✓	?	$C_6$ (as 6T1)	$[3]$	$2$	$2$	$3.39714980258$
6.0.9796423.1	$x^{6} - x^{5} - 3 x^{4} + 7 x^{3} + 25 x^{2} - 55 x + 79$	$6$	[0,3]	$-\,7^{3}\cdot 13^{4}$	$2$	$14.6277632119$	$14.627763211871763$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$5.46019947038$
6.0.10024911.1	$x^{6} - x^{5} + 8 x^{4} - 9 x^{3} + 6 x^{2} + 10 x + 25$	$6$	[0,3]	$-\,3^{3}\cdot 13^{5}$	$2$	$14.6840804184$	$14.684080418380853$	✓	✓		$C_6$ (as 6T1)	$[4]$	$2$	$2$	$5.46019947038$
6.0.10077696.1	$x^{6} + 12 x^{4} + 36 x^{2} + 24$	$6$	[0,3]	$-\,2^{9}\cdot 3^{9}$	$2$	$14.6969384567$	$14.696938456699069$	✓	✓	?	$C_6$ (as 6T1)	$[2]$	$2$	$2$	$3.39714980258$
6.6.10077696.1	$x^{6} - 12 x^{4} + 36 x^{2} - 24$	$6$	[6,0]	$2^{9}\cdot 3^{9}$	$2$	$14.6969384567$	$14.696938456699069$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$34.7337150265$
6.6.11796113.1	$x^{6} - x^{5} - 17 x^{4} + 11 x^{3} + 57 x^{2} - 25 x - 13$	$6$	[6,0]	$7^{4}\cdot 17^{3}$	$2$	$15.0877039589$	$15.087703958850541$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$33.1107945948$
6.6.14414517.1	$x^{6} - 3 x^{5} - 12 x^{4} + 27 x^{3} + 21 x^{2} - 48 x + 17$	$6$	[6,0]	$3^{8}\cdot 13^{3}$	$2$	$15.6003143333$	$15.600314333277801$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$54.5168595864$
6.0.14623232.1	$x^{6} - 2 x^{5} - x^{4} - 2 x^{3} + 34 x^{2} + 28 x + 73$	$6$	[0,3]	$-\,2^{9}\cdot 13^{4}$	$2$	$15.6377366496$	$15.637736649622886$	✓	✓	?	$C_6$ (as 6T1)	trivial	$2$	$2$	$5.46019947038$
6.6.14623232.1	$x^{6} - 2 x^{5} - 13 x^{4} + 14 x^{3} + 26 x^{2} - 28 x + 1$	$6$	[6,0]	$2^{9}\cdot 13^{4}$	$2$	$15.6377366496$	$15.637736649622886$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$29.0839843952$
6.6.16290125.1	$x^{6} - x^{5} - 16 x^{4} + x^{3} + 47 x^{2} + 10 x - 11$	$6$	[6,0]	$5^{3}\cdot 19^{4}$	$2$	$15.9216254393$	$15.9216254392755$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$38.5797385191$
6.0.16468459.1	$x^{6} - x^{5} + 10 x^{4} - 7 x^{3} + 75 x^{2} - 16 x + 239$	$6$	[0,3]	$-\,7^{4}\cdot 19^{3}$	$2$	$15.9505437935$	$15.950543793511486$	✓	✓	?	$C_6$ (as 6T1)	$[3]$	$2$	$2$	$2.10181872849$
6.0.19208000.1	$x^{6} - 2 x^{5} + 12 x^{4} - 14 x^{3} + 87 x^{2} - 64 x + 281$	$6$	[0,3]	$-\,2^{6}\cdot 5^{3}\cdot 7^{4}$	$3$	$16.3649126361$	$16.364912636128995$	✓	✓	?	$C_6$ (as 6T1)	$[6]$	$2$	$2$	$2.10181872849$
6.6.22370117.1	$x^{6} - x^{5} - 20 x^{4} + 20 x^{3} + 106 x^{2} - 106 x - 83$	$6$	[6,0]	$7^{5}\cdot 11^{3}$	$2$	$16.7859030044$	$16.785903004359604$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$44.1859335662$
6.0.23762752.1	$x^{6} + 13 x^{4} + 26 x^{2} + 13$	$6$	[0,3]	$-\,2^{6}\cdot 13^{5}$	$2$	$16.9557155647$	$16.955715564708598$	✓	✓	?	$C_6$ (as 6T1)	$[2]$	$2$	$2$	$5.46019947038$
6.0.24935067.1	$x^{6} - x^{5} + 11 x^{4} - 6 x^{3} + 108 x^{2} - 80 x + 64$	$6$	[0,3]	$-\,3^{3}\cdot 31^{4}$	$2$	$17.0923491853$	$17.09234918530509$	✓	✓		$C_6$ (as 6T1)	trivial	$6$	$2$	$48.7831276503$
6.6.26198073.1	$x^{6} - 18 x^{4} - 8 x^{3} + 81 x^{2} + 72 x - 17$	$6$	[6,0]	$3^{9}\cdot 11^{3}$	$2$	$17.2336879396$	$17.233687939614086$		✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$65.1388337866$
6.0.28629151.1	$x^{6} - x^{5} + 3 x^{4} - 11 x^{3} + 44 x^{2} - 36 x + 32$	$6$	[0,3]	$-\,31^{5}$	$1$	$17.4904672465$	$17.490467246468523$	✓	✓		$C_6$ (as 6T1)	$[9]$	$2$	$2$	$48.7831276503$
6.0.29042496.1	$x^{6} + 21 x^{4} + 126 x^{2} + 189$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{5}$	$3$	$17.5323038886$	$17.532303888591755$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2]$	$2$	$2$	$2.10181872849$
6.0.29212967.1	$x^{6} - x^{5} + 13 x^{4} - 9 x^{3} + 107 x^{2} - 25 x + 377$	$6$	[0,3]	$-\,7^{4}\cdot 23^{3}$	$2$	$17.5494136776$	$17.5494136775664$	✓	✓	?	$C_6$ (as 6T1)	$[9]$	$2$	$2$	$2.10181872849$