Number field search results

Results (1-50 of 28623 matches)

 

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
6.0.336091.1	x^6 - x^5 + x^4 + 5x^2 + 4x + 1	$6$	[0,3]	$-\,7^{2}\cdot 19^{3}$	$2$	$8.33827371165$			?	$S_3\times C_3$ (as 6T5)	trivial	$2$	$2$	$2.3409784627$
6.0.528143.1	x^6 - x^5 + 3x^4 - x^3 + 2x^2 + 2x + 1	$6$	[0,3]	$-\,7\cdot 11\cdot 19^{3}$	$3$	$8.99066718532$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$3.15256501689$
6.0.2668151.1	x^6 - x^5 + 2x^4 - 4x^3 + 5x^2 - 6x + 4	$6$	[0,3]	$-\,19^{3}\cdot 389$	$2$	$11.7770106385$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$7.22316357391$
6.0.3841040.1	x^6 - 2x^5 + 2x^4 + 2x^3 + 2x^2 - 8x + 7	$6$	[0,3]	$-\,2^{4}\cdot 5\cdot 7\cdot 19^{3}$	$4$	$12.5143454241$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$13.2942421582$
6.0.4149695.1	x^6 - 2x^5 + 4x^4 + x^3 + 3x^2 + 6x + 4	$6$	[0,3]	$-\,5\cdot 11^{2}\cdot 19^{3}$	$3$	$12.6765973591$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$10.9226578915$
6.4.5027647.1	x^6 - 3x^5 - 3x^4 + 8x^3 + 7x^2 - 3x - 2	$6$	[4,1]	$-\,19^{3}\cdot 733$	$2$	$13.0886281523$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$27.5366311582$
6.0.5377456.1	x^6 - x^5 - 5x^3 + 10x^2 - 5x + 1	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 19^{3}$	$3$	$13.2361844615$			✓	$S_3\times C_3$ (as 6T5)	$[3]$	$2$	$2$	$2.87637296087$
6.0.5377456.2	x^6 - x^5 - 2x^4 + 11x^3 + 18x^2 + 7x + 1	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 19^{3}$	$3$	$13.2361844615$			?	$S_3\times C_3$ (as 6T5)	$[3]$	$2$	$2$	$5.26788591245$
6.0.6035920.1	x^6 - x^5 + 2x^4 - 7x^3 + 16x^2 - 11x + 5	$6$	[0,3]	$-\,2^{4}\cdot 5\cdot 11\cdot 19^{3}$	$4$	$13.4934782235$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$17.1303365085$
6.0.6591499.1	x^6 - 9x^4 - 14x^3 + 25x^2 + 25x + 125	$6$	[0,3]	$-\,19^{3}\cdot 31^{2}$	$2$	$13.692960807$			?	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$7.32483413303$
6.0.6756115.1	x^6 - 3x^5 + 8x^4 - 10x^3 + 13x^2 - 9x + 5	$6$	[0,3]	$-\,5\cdot 19^{3}\cdot 197$	$3$	$13.7493712589$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$13.3230405322$
6.0.7414579.1	x^6 - 4x^4 - x^3 + 4x^2 + 2x + 5	$6$	[0,3]	$-\,19^{3}\cdot 23\cdot 47$	$3$	$13.964147134$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$9.79724125963$
6.0.8347403.1	x^6 + x^4 - 2x^3 + 5x^2 - x + 1	$6$	[0,3]	$-\,19^{3}\cdot 1217$	$2$	$14.2426859044$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$11.5959545008$
6.0.8896123.1	x^6 - x^5 - x^4 + 2x^3 + 3x + 5	$6$	[0,3]	$-\,19^{3}\cdot 1297$	$2$	$14.3946175238$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$12.6350401061$
6.0.9911255.1	x^6 - x^5 + 6x^3 + 14x^2 + 15x + 9	$6$	[0,3]	$-\,5\cdot 17^{2}\cdot 19^{3}$	$3$	$14.6562019866$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$16.8867242745$
6.0.10459975.1	x^6 - 2x^5 + 6x^4 - 11x^3 + 17x^2 - 15x + 9	$6$	[0,3]	$-\,5^{2}\cdot 19^{3}\cdot 61$	$3$	$14.7884199361$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$18.533334861$
6.4.10590296.1	x^6 - x^5 - 5x^4 + 7x^3 + 5x^2 - 10x + 1	$6$	[4,1]	$-\,2^{3}\cdot 19^{3}\cdot 193$	$3$	$14.8189699195$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$44.5947147682$
6.0.12682291.1	x^6 - 3x^5 + 6x^4 + 7x^3 + 11x^2 + 2x + 4	$6$	[0,3]	$-\,19^{3}\cdot 43^{2}$	$2$	$15.2709581042$				$S_3\times C_3$ (as 6T5)	trivial	$2$	$2$	$22.7661138895$
6.0.13368191.1	x^6 - 4x^4 - x^3 + 23x^2 - 17x + 5	$6$	[0,3]	$-\,19^{3}\cdot 1949$	$2$	$15.4056055432$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$21.4266793797$
6.0.13862039.1	x^6 - x^5 - 3x^4 - 3x^3 + 10x^2 + 28x + 17	$6$	[0,3]	$-\,19^{3}\cdot 43\cdot 47$	$3$	$15.499030018$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$18.8126717374$
6.0.15124095.1	x^6 - 2x^5 + 3x^3 + 3x^2 - x + 1	$6$	[0,3]	$-\,3^{2}\cdot 5\cdot 7^{2}\cdot 19^{3}$	$4$	$15.7257572028$			✓	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$8.86918469048$
6.0.15974611.1	x^6 + 3x^4 - 2x^3 + 7x^2 - 3x + 1	$6$	[0,3]	$-\,17\cdot 19^{3}\cdot 137$	$3$	$15.8698095615$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$13.8301860891$
6.0.16468459.1	x^6 - x^5 + 10x^4 - 7x^3 + 75x^2 - 16x + 239	$6$	[0,3]	$-\,7^{4}\cdot 19^{3}$	$2$	$15.9505437935$	✓	✓	?	$C_6$ (as 6T1)	$[3]$	$2$	$2$	$2.10181872849$
6.0.17373847.1	x^6 - 2x^5 - 4x^4 + 6x^3 + 10x^2 - 12x + 5	$6$	[0,3]	$-\,17\cdot 19^{3}\cdot 149$	$3$	$16.0934565608$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$26.9248377723$
6.0.19205200.1	x^6 - x^5 - 2x^4 - 3x^3 + 6x^2 - x + 7	$6$	[0,3]	$-\,2^{4}\cdot 5^{2}\cdot 7\cdot 19^{3}$	$4$	$16.3645150193$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$27.8462557594$
6.2.20741616.1	x^6 - x^5 - 6x^4 + 14x^2 + 16x + 4	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 7\cdot 19^{3}$	$4$	$16.5757720217$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$121.936345332$
6.2.21036553.1	x^6 - x^5 - 3x^4 + 15x^3 - 18x^2 + 13x - 3	$6$	[2,2]	$19^{3}\cdot 3067$	$2$	$16.6148246871$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$53.083313125$
6.0.21269759.1	x^6 - x^5 + 14x^3 + 10x^2 - 5x + 1	$6$	[0,3]	$-\,7\cdot 19^{3}\cdot 443$	$3$	$16.6453818142$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$28.8628556961$
6.0.21352067.1	x^6 + 7x^4 - 2x^3 + 17x^2 - 7x + 1	$6$	[0,3]	$-\,11\cdot 19^{3}\cdot 283$	$3$	$16.6561000382$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$28.8920193812$
6.0.23766435.1	x^6 - 3x^5 + 7x^4 - 6x^3 + 9x^2 + 9	$6$	[0,3]	$-\,3^{2}\cdot 5\cdot 7\cdot 11\cdot 19^{3}$	$5$	$16.9561535321$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$27.6126273408$
6.0.23793871.1	x^6 - x^5 - 3x^4 + 7x^3 + 5x^2 - 12x + 7	$6$	[0,3]	$-\,19^{3}\cdot 3469$	$2$	$16.9594143312$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$17.6989096879$
6.0.23876179.1	x^6 - x^5 + 12x^4 - 11x^3 + 73x^2 + 26x + 172	$6$	[0,3]	$-\,19^{3}\cdot 59^{2}$	$2$	$16.9691779644$				$D_{6}$ (as 6T3)	trivial	$2$	$2$	$26.5504287195$
6.0.24692400.1	x^6 - x^5 + 8x^4 - 17x^3 + 10x^2 - 9x + 9	$6$	[0,3]	$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{3}$	$4$	$17.0645124252$			?	$S_3^2$ (as 6T9)	$[3]$	$2$	$2$	$11.6203549343$
6.0.25001055.1	x^6 + 6x^4 - x^3 + 9x^2 - 3x + 5	$6$	[0,3]	$-\,3^{6}\cdot 5\cdot 19^{3}$	$3$	$17.099879733$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$35.4382566042$
6.0.25138235.1	x^6 - 3x^5 + 11x^4 - 14x^3 + 35x^2 - 16x + 35	$6$	[0,3]	$-\,5\cdot 19^{3}\cdot 733$	$3$	$17.1154818509$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$39.381790529$
6.0.25522339.1	x^6 - x^5 + 12x^4 - 10x^3 + 44x^2 - 18x + 45	$6$	[0,3]	$-\,19^{3}\cdot 61^{2}$	$2$	$17.1587934127$			?	$S_3\times C_3$ (as 6T5)	trivial	$2$	$2$	$32.2408021923$
6.0.25570352.1	x^6 - 3x^5 + 8x^4 - 9x^3 + 2x^2 + x + 1	$6$	[0,3]	$-\,2^{4}\cdot 19^{3}\cdot 233$	$3$	$17.1641690964$			✓	$C_3^2:D_4$ (as 6T13)	$[6]$	$2$	$2$	$3.80423987172$
6.0.25961315.1	x^6 - x^5 - 2x^4 + 11x^3 - x^2 - 12x + 20	$6$	[0,3]	$-\,5\cdot 19^{3}\cdot 757$	$3$	$17.2076321875$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$45.1282741559$
6.0.30179600.1	x^6 - 3x^5 + 2x^4 - x^3 + 7x + 5	$6$	[0,3]	$-\,2^{4}\cdot 5^{2}\cdot 11\cdot 19^{3}$	$4$	$17.6448882917$				$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$41.6851730474$
6.2.31112424.1	x^6 - x^5 - 2x^4 - 3x^3 + 6x^2 + 18x - 12	$6$	[2,2]	$2^{3}\cdot 3^{4}\cdot 7\cdot 19^{3}$	$4$	$17.7346371857$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$153.855276722$
6.0.31613131.1	x^6 - x^5 - 2x^4 - 7x^3 - 11x^2 + 32x + 43	$6$	[0,3]	$-\,11\cdot 19^{3}\cdot 419$	$3$	$17.7818899654$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$31.2730653286$
6.0.31695439.1	x^6 - 2x^5 + 4x^4 - 7x^3 + 11x^2 - 6x + 4	$6$	[0,3]	$-\,19^{3}\cdot 4621$	$2$	$17.7895977676$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$32.4795564412$
6.2.31853196.1	x^6 + 2x^4 - 9x^3 + x^2 - 9x + 6	$6$	[2,2]	$2^{2}\cdot 3^{3}\cdot 19^{3}\cdot 43$	$4$	$17.8043245503$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$122.469323824$
6.0.33176983.1	x^6 - 2x^5 + 8x^4 - 5x^3 + 15x^2 - 12x + 20	$6$	[0,3]	$-\,7\cdot 19^{3}\cdot 691$	$3$	$17.9255634257$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$49.9214110431$
6.0.33917755.1	x^6 - 2x^5 - x^4 + 5x^3 - 2x^2 - 3x + 45	$6$	[0,3]	$-\,5\cdot 19^{3}\cdot 23\cdot 43$	$4$	$17.9916578362$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$35.1193746553$
6.0.34349872.1	x^6 - 8x^4 - 2x^3 + 16x^2 + 8x + 20	$6$	[0,3]	$-\,2^{4}\cdot 19^{3}\cdot 313$	$3$	$18.0296593173$			?	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$13.7796618545$
6.0.35097503.1	x^6 - x^5 + 5x^4 - 3x^3 + 11x^2 + 7	$6$	[0,3]	$-\,7\cdot 17\cdot 19^{3}\cdot 43$	$4$	$18.0944770748$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$27.7287311135$
6.0.35975455.1	x^6 - 2x^5 + 5x^4 - 11x^3 + 11x^2 - 14x + 17	$6$	[0,3]	$-\,5\cdot 19^{3}\cdot 1049$	$3$	$18.16914047$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$2$	$39.6124345562$
6.2.36297828.1	x^6 - x^5 - 8x^3 + 21x^2 - 7x - 14	$6$	[2,2]	$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{3}$	$4$	$18.19617506$			?	$S_3^2$ (as 6T9)	trivial	$2$	$3$	$137.309649925$
6.2.36297828.2	x^6 - x^5 - 4x^4 - 2x^3 - 5x^2 + 15x - 12	$6$	[2,2]	$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{3}$	$4$	$18.19617506$			?	$S_3^2$ (as 6T9)	trivial	$2$	$3$	$139.723097096$