Number field search results

Results (1-50 of 224027 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
12.0.41223887921.1	x^12 - 2x^11 + 2x^10 - x^9 + 2x^8 - 5x^7 + 8x^6 - 7x^5 + 4x^4 - 3x^3 + 4x^2 - 3x + 1	$12$	[0,6]	$37^{2}\cdot 41\cdot 857^{2}$	$3$	$7.66647538703$			✓	12T293	trivial	$2$	$5$	$1.16313281573$
12.0.41479432225.1	x^12 - 4x^11 + 8x^10 - 11x^9 + 12x^8 - 9x^7 + 3x^6 + 2x^5 - 3x^4 + 2x^3 - x + 1	$12$	[0,6]	$5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 23^{4}$	$4$	$7.67042451285$			✓	$C_2^2\times C_2^2:S_4$ (as 12T139)	trivial	$2$	$5$	$1.16804069437$
12.0.42058512657.1	x^12 + 2x^10 - x^9 + x^8 - 5x^7 + 6x^6 - 10x^5 + 13x^4 - 10x^3 + 7x^2 - 4x + 1	$12$	[0,6]	$3^{6}\cdot 7^{2}\cdot 73\cdot 127^{2}$	$4$	$7.67929160277$			✓	12T260	trivial	$6$	$5$	$3.53470566706$
12.0.42194001221.1	x^12 - 3x^11 + 7x^10 - 12x^9 + 17x^8 - 21x^7 + 24x^6 - 24x^5 + 22x^4 - 17x^3 + 10x^2 - 4x + 1	$12$	[0,6]	$41\cdot 1029121981$	$2$	$7.68135009037$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$5$	$1.18014639216$
12.0.42553255797.1	x^12 - x^9 + 5x^8 - 2x^7 - x^6 - 7x^5 + 8x^4 - 4x^3 + 5x^2 - 4x + 1	$12$	[0,6]	$3^{6}\cdot 13^{3}\cdot 163^{2}$	$3$	$7.68677907982$			✓	$C_3^4:D_4$ (as 12T167)	trivial	$6$	$5$	$3.5586949501$
12.0.42925852301.1	x^12 - x^11 - 2x^10 + 3x^9 + x^8 - x^7 - x^6 - 2x^5 + 3x^4 + 2x^3 - 2x^2 - x + 1	$12$	[0,6]	$79\cdot 543365219$	$2$	$7.69236548534$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$5$	$1.19267939797$
12.0.44223092609.1	x^12 - x^11 + x^9 - 2x^8 + x^7 + 3x^4 - x^3 - 2x^2 + 1	$12$	[0,6]	$89\cdot 22291^{2}$	$2$	$7.7114744831$			not computed	12T293	trivial	$2$	$5$	$1.21605234252$
12.0.44533203125.1	x^12 - 2x^11 + 7x^10 - 7x^9 + 14x^8 - 6x^7 + 13x^6 - 2x^5 + 10x^4 - 2x^3 + 5x^2 - x + 1	$12$	[0,6]	$5^{9}\cdot 151^{2}$	$2$	$7.71596640012$			✓	$C_3\times C_3^2:(C_3:C_4)$ (as 12T131)	trivial	$10$	$5$	$6.10223070288$
12.0.45425463296.1	x^12 - 2x^11 + 2x^9 - 2x^8 + 3x^6 - 2x^4 - 2x^3 + 2x + 1	$12$	[0,6]	$2^{12}\cdot 89\cdot 353^{2}$	$3$	$7.7287325766$			✓	12T260	trivial	$4$	$5$	$2.47334952808$
12.0.45539379833.1	x^12 - x^11 - x^9 + 3x^8 - 2x^7 + x^6 - 2x^5 + 3x^4 - x^3 - x + 1	$12$	[0,6]	$17\cdot 73^{2}\cdot 709^{2}$	$3$	$7.730345879$			✓	12T293	trivial	$2$	$5$	$1.24111898861$
12.0.46060985097.1	x^12 - 5x^11 + 12x^10 - 19x^9 + 24x^8 - 27x^7 + 28x^6 - 24x^5 + 15x^4 - 5x^3 + x^2 - x + 1	$12$	[0,6]	$3^{6}\cdot 337\cdot 433^{2}$	$3$	$7.73768600028$			not computed	12T260	trivial	$6$	$5$	$3.73838590524$
12.0.46110822453.1	x^12 - 2x^11 + x^10 + x^9 + x^8 - 5x^7 + 6x^6 - 4x^5 + 4x^4 - 5x^3 + 5x^2 - 3x + 1	$12$	[0,6]	$3^{6}\cdot 63252157$	$2$	$7.73838332708$			✓	$S_6\wr C_2$ (as 12T299)	trivial	$6$	$5$	$3.74818062756$
12.0.46574387721.1	x^12 - x^11 - x^10 + x^9 + 2x^8 - 3x^6 + 2x^4 + x^3 - x^2 - x + 1	$12$	[0,6]	$3^{6}\cdot 7993^{2}$	$2$	$7.74483666021$			✓	$S_6\times C_2$ (as 12T219)	trivial	$6$	$5$	$3.77072282107$
12.0.46580196393.1	x^12 - 3x^10 - x^9 + 5x^8 + x^7 - 7x^6 - x^5 + 8x^4 + 2x^3 - 4x^2 - x + 1	$12$	[0,6]	$3^{6}\cdot 157\cdot 406981$	$3$	$7.74491714909$			✓	$S_6\wr C_2$ (as 12T299)	trivial	$6$	$5$	$3.77092097525$
12.0.46716936381.1	x^12 - 4x^11 + 9x^10 - 15x^9 + 23x^8 - 33x^7 + 44x^6 - 50x^5 + 45x^4 - 29x^3 + 13x^2 - 4x + 1	$12$	[0,6]	$3^{6}\cdot 23^{4}\cdot 229$	$3$	$7.74680925796$			not computed	12T193	trivial	$6$	$5$	$3.77207610108$
12.0.46779109213.1	x^12 - 4x^11 + 8x^10 - 10x^9 + 8x^8 - 3x^7 - 2x^6 + 4x^5 - 2x^4 - x^3 + 2x^2 - x + 1	$12$	[0,6]	$31^{4}\cdot 37^{3}$	$2$	$7.74766788221$			not computed	$C_4^2.(C_4\times S_3)$ (as 12T150)	trivial	$2$	$5$	$1.25722954293$
12.0.46911328256.1	x^12 - 2x^9 + 4x^8 - 4x^7 + x^6 + 4x^4 - 8x^3 + 8x^2 - 4x + 1	$12$	[0,6]	$2^{12}\cdot 13^{4}\cdot 401$	$3$	$7.74949039193$			not computed	12T208	trivial	$4$	$5$	$2.52000020832$
12.0.47724987301.1	x^12 - 3x^11 + 7x^10 - 11x^9 + 16x^8 - 19x^7 + 20x^6 - 18x^5 + 15x^4 - 11x^3 + 6x^2 - 3x + 1	$12$	[0,6]	$61\cdot 83^{2}\cdot 337^{2}$	$3$	$7.76060331827$			✓	12T293	trivial	$2$	$5$	$1.27712868376$
12.0.47738317081.1	x^12 - 3x^11 + x^10 + 7x^9 - 8x^8 - 4x^7 + 13x^6 - 4x^5 - 8x^4 + 7x^3 + x^2 - 3x + 1	$12$	[0,6]	$7^{10}\cdot 13^{2}$	$2$	$7.76078392578$			✓	$C_2^2 \times A_4$ (as 12T25)	trivial	$14$	$5$	$8.9159604909$
12.0.48737056617.1	x^12 - 2x^11 + 5x^10 - 10x^9 + 16x^8 - 22x^7 + 30x^6 - 31x^5 + 28x^4 - 27x^3 + 19x^2 - 7x + 1	$12$	[0,6]	$3^{9}\cdot 19^{5}$	$2$	$7.77418625735$			✓	$C_3\times C_3:D_4$ (as 12T42)	trivial	$6$	$5$	$3.8758756969$
12.0.50551744653.1	x^12 - 4x^11 + 11x^10 - 21x^9 + 32x^8 - 40x^7 + 45x^6 - 46x^5 + 40x^4 - 26x^3 + 12x^2 - 4x + 1	$12$	[0,6]	$3^{6}\cdot 37^{5}$	$2$	$7.79790630012$			not computed	$C_3\times C_3:D_4$ (as 12T42)	trivial	$6$	$5$	$3.95685086216$
12.0.51067940737.1	x^12 - 3x^11 + 6x^10 - 10x^9 + 15x^8 - 18x^7 + 20x^6 - 19x^5 + 16x^4 - 12x^3 + 7x^2 - 3x + 1	$12$	[0,6]	$11^{2}\cdot 31^{4}\cdot 457$	$3$	$7.80451097147$			✓	12T250	trivial	$2$	$5$	$1.32924669226$
12.0.51514924901.1	x^12 - 2x^11 - x^10 + 2x^9 + 4x^8 - x^7 - 7x^6 + x^5 + 4x^4 - 2x^3 - x^2 + 2x + 1	$12$	[0,6]	$11^{2}\cdot 31^{4}\cdot 461$	$3$	$7.81018082983$			✓	12T250	trivial	$2$	$5$	$1.33838343414$
12.0.53440955929.1	x^12 - x^11 + x^10 - 3x^9 + 4x^8 - 2x^7 + x^6 - 2x^5 + 4x^4 - 3x^3 + x^2 - x + 1	$12$	[0,6]	$19^{2}\cdot 23^{6}$	$2$	$7.83410734676$			not computed	$C_2\times S_4$ (as 12T21)	trivial	$2$	$5$	$1.36801263468$
12.0.54507773961.1	x^12 - x^11 - 2x^10 + 5x^9 - x^8 - 4x^7 + 5x^6 - 4x^5 - x^4 + 5x^3 - 2x^2 - x + 1	$12$	[0,6]	$3^{6}\cdot 8647^{2}$	$2$	$7.84702200576$			not computed	$S_6\times C_2$ (as 12T219)	trivial	$6$	$5$	$4.14786100391$
12.0.55358453125.1	x^12 - 4x^11 + 11x^10 - 22x^9 + 35x^8 - 45x^7 + 49x^6 - 44x^5 + 33x^4 - 21x^3 + 11x^2 - 4x + 1	$12$	[0,6]	$5^{6}\cdot 61\cdot 241^{2}$	$3$	$7.8571551481$			✓	12T260	trivial	$2$	$5$	$1.40064596697$
12.0.56689952000.1	x^12 - 5x^11 + 13x^10 - 25x^9 + 39x^8 - 50x^7 + 53x^6 - 48x^5 + 37x^4 - 23x^3 + 12x^2 - 4x + 1	$12$	[0,6]	$2^{8}\cdot 5^{3}\cdot 11^{6}$	$3$	$7.87273272153$			✓	$(C_6\times C_2):C_2$ (as 12T15)	trivial	$2$	$5$	$1.4199505274$
12.0.58300115053.1	x^12 - x^11 + 4x^10 - 4x^9 + 9x^8 - 6x^7 + 11x^6 - 6x^5 + 8x^4 - 3x^3 + 4x^2 - x + 1	$12$	[0,6]	$23^{4}\cdot 208333$	$2$	$7.8911285384$			✓	12T294	trivial	$2$	$5$	$1.44906493339$
12.0.59081901957.1	x^12 - 3x^11 + 5x^10 - 6x^9 + 5x^8 - 2x^7 - x^6 + 4x^5 - 4x^4 + 2x^3 - x + 1	$12$	[0,6]	$3^{6}\cdot 13^{3}\cdot 37\cdot 997$	$4$	$7.89989293816$			✓	12T274	trivial	$6$	$5$	$4.38856707636$
12.0.59182215273.1	x^12 - 5x^11 + 14x^10 - 31x^9 + 53x^8 - 72x^7 + 81x^6 - 72x^5 + 53x^4 - 31x^3 + 14x^2 - 5x + 1	$12$	[0,6]	$3^{6}\cdot 433^{3}$	$2$	$7.90100981774$			✓	$S_3\wr C_2$ (as 12T35)	trivial	$6$	$5$	$4.35580546019$
12.0.59767578125.1	x^12 - 5x^11 + 13x^10 - 21x^9 + 24x^8 - 21x^7 + 18x^6 - 17x^5 + 15x^4 - 9x^3 + 4x^2 - 2x + 1	$12$	[0,6]	$5^{9}\cdot 71\cdot 431$	$3$	$7.90749279408$			✓	12T264	trivial	$10$	$5$	$7.40729189233$
12.0.60454515625.1	x^12 - x^11 - 2x^10 + 2x^9 + 4x^8 - 3x^7 - 5x^6 + 3x^5 + 5x^4 - x^3 - 3x^2 + 1	$12$	[0,6]	$5^{6}\cdot 7^{2}\cdot 281^{2}$	$3$	$7.91502690536$			✓	12T236	trivial	$2$	$5$	$1.47630310859$
12.0.63518590021.1	x^12 - 2x^11 + 3x^10 - 2x^9 + 2x^8 - 4x^7 + 4x^6 - 2x^5 - x^4 + 2x^2 - x + 1	$12$	[0,6]	$23^{4}\cdot 61^{3}$	$2$	$7.94770497569$			not computed	$C_4^2.(C_4\times S_3)$ (as 12T150)	trivial	$2$	$5$	$1.51948050623$
12.0.63568613376.1	x^12 - 4x^11 + 9x^10 - 14x^9 + 16x^8 - 14x^7 + 10x^6 - 6x^5 + 6x^4 - 6x^3 + 6x^2 - 4x + 1	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 61\cdot 349$	$4$	$7.94822638136$			not computed	12T261	trivial	$12$	$5$	$9.18542221354$
12.0.63853279857.1	x^12 - 4x^11 + 9x^10 - 13x^9 + 17x^8 - 21x^7 + 25x^6 - 27x^5 + 26x^4 - 20x^3 + 12x^2 - 5x + 1	$12$	[0,6]	$3^{6}\cdot 23^{4}\cdot 313$	$3$	$7.95118638902$			not computed	12T193	trivial	$6$	$5$	$4.5780204292$
12.0.63995902381.1	x^12 - x^11 + 2x^9 - x^8 - 4x^7 + 5x^6 - x^5 - x^4 - x^3 + 4x^2 - 3x + 1	$12$	[0,6]	$73^{2}\cdot 229^{3}$	$2$	$7.95266485522$			not computed	$C_3^3.(C_3\times S_4)$ (as 12T231)	trivial	$2$	$5$	$1.54183330651$
12.0.66468114161.1	x^12 - x^11 - 2x^10 + 4x^9 + x^8 - 5x^7 + x^6 + 5x^5 + x^4 - 4x^3 - 2x^2 + x + 1	$12$	[0,6]	$23^{6}\cdot 449$	$2$	$7.9778239152$			not computed	$C_2^4:C_3.D_4$ (as 12T135)	trivial	$2$	$5$	$1.56137956029$
12.0.66699927001.1	x^12 - x^9 + x^7 - x^4 - x^3 + x + 1	$12$	[0,6]	$47\cdot 1117\cdot 1270499$	$3$	$7.9801388252$			not computed	$S_{12}$ (as 12T301)	trivial	$2$	$5$	$1.58972306672$
12.0.67030763409.1	x^12 - x^11 - 2x^10 + 6x^8 - x^7 - 5x^6 - x^5 + 6x^4 - 2x^2 - x + 1	$12$	[0,6]	$3^{6}\cdot 43^{2}\cdot 223^{2}$	$3$	$7.98342985511$			not computed	$S_6\times C_2$ (as 12T219)	trivial	$6$	$5$	$4.81968495903$
12.0.69637938597.1	x^12 - 2x^11 + 3x^10 - 2x^9 + 4x^6 - 11x^5 + 17x^4 - 16x^3 + 11x^2 - 5x + 1	$12$	[0,6]	$3^{6}\cdot 19^{4}\cdot 733$	$3$	$8.00885613193$			not computed	12T208	trivial	$6$	$5$	$4.89240598709$
12.0.70127513856.1	x^12 + x^10 - 3x^8 - 3x^6 + 2x^4 + 2x^2 + 1	$12$	[0,6]	$2^{8}\cdot 3^{6}\cdot 613^{2}$	$3$	$8.01353313251$			not computed	12T236	trivial	$6$	$5$	$4.86613553287$
12.0.70516271401.1	x^12 - 3x^11 + 4x^10 - x^9 - 3x^8 + 4x^7 - 3x^6 + 4x^5 - 3x^4 - x^3 + 4x^2 - 3x + 1	$12$	[0,6]	$37^{2}\cdot 7177^{2}$	$2$	$8.01722573211$			✓	12T285	trivial	$2$	$5$	$1.65463443861$
12.0.71939651121.1	x^12 - x^11 - 3x^10 + x^9 + 5x^8 + 3x^7 - 3x^6 - 7x^5 - 2x^4 + 3x^3 + 2x^2 + x + 1	$12$	[0,6]	$3^{6}\cdot 13^{3}\cdot 44917$	$3$	$8.03058827935$			not computed	12T274	trivial	$6$	$5$	$4.93206182745$
12.0.72509192309.1	x^12 - x^10 - x^9 + x^7 + x^6 + x^5 - 2x^3 - x^2 + x + 1	$12$	[0,6]	$72509192309$	$1$	$8.03586728509$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$5$	$1.66307418431$
12.0.73358639104.1	x^12 - 2x^11 + 2x^10 - 2x^9 + 6x^8 - 10x^7 + 10x^6 - 12x^5 + 17x^4 - 14x^3 + 8x^2 - 4x + 1	$12$	[0,6]	$2^{18}\cdot 23^{4}$	$2$	$8.04367050498$			not computed	$C_2 \times S_4$ (as 12T23)	trivial	$4$	$5$	$3.42242551816$
12.0.73645476129.1	x^12 - x^11 - x^10 + 2x^9 - 2x^7 + 3x^5 - 2x^4 + 2x^2 - 2x + 1	$12$	[0,6]	$3^{6}\cdot 19^{2}\cdot 23^{4}$	$3$	$8.046286759$			not computed	$C_2^2\times S_4$ (as 12T48)	trivial	$6$	$5$	$4.99030501888$
12.0.74733890625.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 93x^8 - 138x^7 + 164x^6 - 153x^5 + 111x^4 - 61x^3 + 24x^2 - 6x + 1	$12$	[0,6]	$3^{14}\cdot 5^{6}$	$2$	$8.0561300054$		✓	not computed	$D_6$ (as 12T3)	trivial	$6$	$5$	$5.15894342496$
12.0.74880094208.1	x^12 - 2x^11 + 2x^10 - 2x^9 + 5x^8 - 10x^7 + 14x^6 - 16x^5 + 17x^4 - 14x^3 + 9x^2 - 4x + 1	$12$	[0,6]	$2^{12}\cdot 17^{3}\cdot 61^{2}$	$3$	$8.05744219486$			not computed	$C_3^4:D_4$ (as 12T167)	trivial	$4$	$5$	$3.38131432466$
12.0.74948100349.1	x^12 - x^11 - x^10 + 2x^9 + 2x^8 - 5x^7 + 3x^6 + 2x^4 - 6x^3 + 7x^2 - 4x + 1	$12$	[0,6]	$79^{2}\cdot 229^{3}$	$2$	$8.0580517556$			✓	$C_3^3.(C_3\times S_4)$ (as 12T231)	trivial	$2$	$5$	$1.67713762237$
12.0.75794375168.1	x^12 - 4x^11 + 9x^10 - 12x^9 + 14x^8 - 19x^7 + 30x^6 - 39x^5 + 37x^4 - 26x^3 + 14x^2 - 5x + 1	$12$	[0,6]	$2^{9}\cdot 23^{6}$	$2$	$8.06559507223$			not computed	$(C_6\times C_2):C_2$ (as 12T15)	trivial	$2$	$5$	$1.74341488875$