Number field search results

Results (1-50 of 1011145 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
6.0.1778112.1	x^6 + 3x^4 - 2x^3 + 6x^2 + 1	$6$	[0,3]	$-\,2^{6}\cdot 3^{4}\cdot 7^{3}$	$3$	$11.0067690039$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$7.66963675212$
6.0.2177712.1	x^6 - x^5 - 4x^2 + 8	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 71^{2}$	$3$	$11.3850097631$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$17.6663598699$
6.2.2299968.1	x^6 - 2x^5 - x^4 + 4x^3 - 4x^2 + 4x + 1	$6$	[2,2]	$2^{6}\cdot 3^{3}\cdot 11^{3}$	$3$	$11.4891252931$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$8.94858785913$
6.0.2611467.1	x^6 - 3x^5 + 7x^4 - 6x^3 + 6x^2 - 7x + 5	$6$	[0,3]	$-\,3^{3}\cdot 311^{2}$	$2$	$11.7349368552$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$8.73416086387$
6.0.2725888.1	x^6 - x^5 + 2x^4 - 4x^3 + 4x^2 + 4x + 8	$6$	[0,3]	$-\,2^{11}\cdot 11^{3}$	$2$	$11.8191070971$				$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$27.7367899009$
6.2.2725888.5	x^6 - x^5 - x^4 + 2x^3 - 5x^2 - x - 3	$6$	[2,2]	$2^{11}\cdot 11^{3}$	$2$	$11.8191070971$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$18.6829042442$
6.2.3200000.1	x^6 - 2x^5 + 4x + 2	$6$	[2,2]	$2^{10}\cdot 5^{5}$	$2$	$12.1392446201$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$15.5733986742$
6.0.3421872.4	x^6 - 2x^5 + 6x^4 - 12x^3 + 14x^2 - 10x + 4	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 89^{2}$	$3$	$12.2756348091$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$5.3725526246$
6.0.3479787.1	x^6 - 3x^5 + 4x^4 - 3x^2 + 3x + 3	$6$	[0,3]	$-\,3^{3}\cdot 359^{2}$	$2$	$12.3100205204$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$9.57099207339$
6.0.3786752.3	x^6 - x^5 + 3x^4 - 4x^3 + 2x^2 - 6x + 10	$6$	[0,3]	$-\,2^{11}\cdot 43^{2}$	$2$	$12.4846913645$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$14.013439558$
6.0.3895843.1	x^6 - x^5 + x^4 - 2x^3 + 2x^2 - x + 3	$6$	[0,3]	$-\,7^{2}\cdot 43^{3}$	$2$	$12.5439286323$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$8.75310751929$
6.2.5000000.1	x^6 - 2x^5 - 8x - 4	$6$	[2,2]	$2^{6}\cdot 5^{7}$	$2$	$13.0766048601$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$22.9563447187$
6.2.5256144.1	x^6 - x^5 - 2x^4 - 2x^3 + x^2 + 5x + 4	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 23^{3}$	$3$	$13.1859434583$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$38.3435411021$
6.0.5400000.3	x^6 - 2x^5 + 5x^2 + 2x + 1	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$	$3$	$13.2454167278$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$2$	$4.93230060794$
6.0.5400000.4	x^6 - 2x^5 + 5x^4 + 6x + 3	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$	$3$	$13.2454167278$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$13.8203686028$
6.2.5778125.2	x^6 - 5x^2 - 6x - 5	$6$	[2,2]	$5^{5}\cdot 43^{2}$	$2$	$13.3956714983$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$21.401504859$
6.0.5787963.1	x^6 - x^5 + 4x^4 - 12x^3 + 15x^2 - 9x + 3	$6$	[0,3]	$-\,3^{3}\cdot 463^{2}$	$2$	$13.3994701129$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$12.1291618824$
6.0.6154544.2	x^6 - 2x^5 + 5x^4 - 2x^3 + 6x^2 + 12x + 4	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}\cdot 17^{2}$	$3$	$13.5373184967$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$34.7329016144$
6.0.6627103.2	x^6 - 2x^5 - 8x^3 + 21x^2 - 8x + 1	$6$	[0,3]	$-\,7^{3}\cdot 139^{2}$	$2$	$13.7052602488$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$10.0973990726$
6.0.6750000.1	x^6 - x^5 + 5x^2 + 3x + 2	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 5^{6}$	$3$	$13.74729637$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$42.3233145267$
6.0.7129088.4	x^6 - 3x^5 + 7x^4 - 4x^3 + 8x^2 - 4x + 4	$6$	[0,3]	$-\,2^{11}\cdot 59^{2}$	$2$	$13.8730620665$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$20.5428136872$
6.0.8108208.2	x^6 - 3x^5 + 4x^4 - 2x + 2	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 137^{2}$	$3$	$14.1738385061$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$44.1031162279$
6.0.9148592.2	x^6 - x^5 + 4x^4 + x^2 + 3x + 2	$6$	[0,3]	$-\,2^{4}\cdot 83^{3}$	$2$	$14.4619118474$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$46.6823817044$
6.2.9483264.1	x^6 - 2x^5 + x^4 - 4x^3 + 7x^2 - 2x - 5	$6$	[2,2]	$2^{10}\cdot 3^{3}\cdot 7^{3}$	$3$	$14.5487709578$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$36.4613498789$
6.0.9590832.1	x^6 - x^5 + 4x^4 + 4x^3 + x^2 + 3x + 10	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 149^{2}$	$3$	$14.5761461422$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$9.58735606627$
6.2.9800000.2	x^6 - 10x^3 - 4x + 5	$6$	[2,2]	$2^{6}\cdot 5^{5}\cdot 7^{2}$	$3$	$14.628653257$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$34.6257839335$
6.0.9834496.1	x^6 - 2x^5 + 3x^4 - 4x^3 + 5x^2 - 6x + 7	$6$	[0,3]	$-\,2^{12}\cdot 7^{4}$	$2$	$14.6372228401$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$31.6560004442$
6.0.10209375.1	x^6 - 2x^5 + 5x^4 + 9x + 12	$6$	[0,3]	$-\,3^{3}\cdot 5^{5}\cdot 11^{2}$	$3$	$14.7287715469$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$30.6381933629$
6.2.10368000.1	x^6 - 2x^5 + 4x^4 - 4x^3 + 2x^2 - 4x - 6	$6$	[2,2]	$2^{10}\cdot 3^{4}\cdot 5^{3}$	$3$	$14.7666675706$			?	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$21.9198018435$
6.0.10546875.1	x^6 - 5x^4 + 15x^2 - 11x + 5	$6$	[0,3]	$-\,3^{3}\cdot 5^{8}$	$2$	$14.8088260968$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$17.5548258232$
6.2.10731125.1	x^6 - x^5 + 2x^4 + 4x^3 - 3x^2 - 3x + 1	$6$	[2,2]	$5^{3}\cdot 293^{2}$	$2$	$14.8516330053$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$6.81902608276$
6.0.10784448.3	x^6 - 2x^5 + 4x^4 - 4x^3 + 4x^2 + 4x + 4	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 79^{2}$	$3$	$14.8639072536$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$34.1944381174$
6.0.10916416.1	x^6 - 2x^5 + 2x^4 + 7x^2 + 1	$6$	[0,3]	$-\,2^{6}\cdot 7^{2}\cdot 59^{2}$	$3$	$14.8940684767$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$5.4020629411$
6.2.11366912.2	x^6 - 2x^5 + 7x^4 - 10x^3 + 12x^2 - 8x + 1	$6$	[2,2]	$2^{9}\cdot 149^{2}$	$2$	$14.9947909805$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$11.2091815101$
6.0.12800000.1	x^6 - 2x^5 + 5x^4 + 4x + 2	$6$	[0,3]	$-\,2^{12}\cdot 5^{5}$	$2$	$15.2944898266$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$61.8109645217$
6.2.12869712.1	x^6 - x^5 - x^3 + 4x^2 + 3x - 9	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 31^{3}$	$3$	$15.3083413628$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$34.8170402258$
6.2.13203125.1	x^6 - x^5 - 4x - 1	$6$	[2,2]	$5^{7}\cdot 13^{2}$	$2$	$15.3737373026$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$18.2488150839$
6.2.13530125.1	x^6 - 2x^5 + 3x^4 - x^3 + 2x^2 + 3x - 1	$6$	[2,2]	$5^{3}\cdot 7^{2}\cdot 47^{2}$	$3$	$15.4365520444$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$20.0167357786$
6.2.13530125.2	x^6 - 3x^4 - 2x^3 + 11x^2 - 7x + 1	$6$	[2,2]	$5^{3}\cdot 7^{2}\cdot 47^{2}$	$3$	$15.4365520444$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$8.49157891171$
6.0.13687488.1	x^6 - x^5 + x^4 + x^3 + x^2 - x + 4	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 89^{2}$	$3$	$15.4663306968$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$55.9028130089$
6.0.13841712.3	x^6 - 2x^5 + 8x^4 - 12x^3 + 12x^2 - 10x + 4	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 179^{2}$	$3$	$15.4952397934$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$9.45065645161$
6.0.14625792.2	x^6 - 2x^5 + 5x^4 - 12x^3 + 15x^2 - 18x + 15	$6$	[0,3]	$-\,2^{10}\cdot 3^{3}\cdot 23^{2}$	$3$	$15.6381928835$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$39.4471392322$
6.0.14697207.1	x^6 - x^5 + 3x^4 + 6x^2 + 3	$6$	[0,3]	$-\,3^{4}\cdot 7^{3}\cdot 23^{2}$	$3$	$15.6508934626$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$38.4305857854$
6.2.14792000.2	x^6 - 3x^4 - 8x^3 - 9x^2 - 8x - 4	$6$	[2,2]	$2^{6}\cdot 5^{3}\cdot 43^{2}$	$3$	$15.6676724305$			?	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$20.0397950081$
6.2.15000633.1	x^6 - 3x^5 - 3x^4 + 4x^3 - 12x^2 + 6x - 5	$6$	[2,2]	$3^{7}\cdot 19^{3}$	$2$	$15.7042884755$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$48.9955672887$
6.0.15106608.2	x^6 - 3x^5 + 4x^4 + 6x^2 + 2x + 2	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 17^{2}$	$4$	$15.7227252981$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$52.8636670977$
6.0.15268608.1	x^6 - 2x^5 + 2x^4 + 3x^2 - 18x + 18	$6$	[0,3]	$-\,2^{8}\cdot 3^{3}\cdot 47^{2}$	$3$	$15.7507017366$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$35.9635639851$
6.0.16133283.3	x^6 - x^5 + 3x^4 + 9x^3 + 5x^2 - 2x + 1	$6$	[0,3]	$-\,3^{3}\cdot 773^{2}$	$2$	$15.8959733257$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$8.60637589824$
6.2.16200000.1	x^6 - 2x^5 - 6x - 3	$6$	[2,2]	$2^{6}\cdot 3^{4}\cdot 5^{5}$	$3$	$15.9069104351$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$77.61245252$
6.2.16200000.2	x^6 - 2x^5 + 5x^4 - 5x^2 + 8x - 1	$6$	[2,2]	$2^{6}\cdot 3^{4}\cdot 5^{5}$	$3$	$15.9069104351$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$66.4566196514$