Number field search results

Results (1-50 of 1574 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
10.0.64248054784.1	x^10 - 4x^9 + 11x^8 - 22x^7 + 41x^6 - 62x^5 + 80x^4 - 78x^3 + 57x^2 - 28x + 8	$10$	[0,5]	$-\,2^{10}\cdot 89^{4}$	$2$	$12.0444229666$			?	$S_5$ (as 10T12)	trivial	$4$	$4$	$99.6060400772$
10.2.131220000000.1	x^10 - 3x^9 + 5x^8 - 17x^6 + 33x^5 - 17x^4 + 5x^2 - 3x + 1	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{7}$	$3$	$12.9359998941$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$46.2201509815$
10.0.175784940288.1	x^10 - 5x^9 + 3x^8 + 14x^7 - 5x^6 - 27x^5 - 7x^4 + 26x^3 + 25x^2 + 9x + 3	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 41^{4}$	$3$	$13.319814192$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$157.516418044$
10.2.256461670625.1	x^10 - 2x^9 + 2x^8 - 7x^6 + 13x^5 - 7x^4 + 2x^2 - 2x + 1	$10$	[2,4]	$5^{4}\cdot 17^{7}$	$2$	$13.8325499357$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$44.1229362432$
10.0.260807798403.2	x^10 - x^9 - 4x^8 + 9x^7 + 10x^6 - 25x^5 - 6x^4 + 13x^3 + 28x^2 - 33x + 9	$10$	[0,5]	$-\,3^{5}\cdot 181^{4}$	$2$	$13.8558144004$			?	$S_5$ (as 10T12)	$[2]$	$6$	$4$	$107.122533035$
10.2.262608484333.1	x^10 - 4x^9 + 3x^8 + 9x^7 - 12x^6 - 9x^5 + 17x^4 - x^3 - 4x^2 - 5x + 1	$10$	[2,4]	$13^{5}\cdot 29^{4}$	$2$	$13.8653512279$				$S_5$ (as 10T12)	trivial	$2$	$5$	$61.5059174722$
10.2.276654003125.1	x^10 - 4x^9 + 2x^8 + 8x^7 - 4x^6 - 21x^5 + 48x^4 - 58x^3 + 24x^2 - 4x - 1	$10$	[2,4]	$5^{5}\cdot 97^{4}$	$2$	$13.9377829118$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$69.6672028353$
10.2.292820000000.2	x^10 - x^9 + x^8 + 6x^7 - x^6 - 13x^5 - x^4 + 6x^3 + x^2 - x + 1	$10$	[2,4]	$2^{8}\cdot 5^{7}\cdot 11^{4}$	$3$	$14.0171613869$				$S_5$ (as 10T12)	trivial	$2$	$5$	$81.9492341533$
10.0.461008408576.1	x^10 + 6x^8 - 12x^7 + 13x^6 - 8x^5 + 13x^4 - 12x^3 + 6x^2 + 1	$10$	[0,5]	$-\,2^{12}\cdot 103^{4}$	$2$	$14.667999439$			?	$S_5$ (as 10T12)	trivial	$4$	$4$	$148.472403824$
10.2.626668503125.2	x^10 + 3x^8 + 22x^6 - 11x^5 + 9x^4 - 4x^3 + 9x^2 - 3x - 1	$10$	[2,4]	$5^{5}\cdot 7^{4}\cdot 17^{4}$	$3$	$15.1252926647$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$112.353517729$
10.2.639589548032.2	x^10 - 4x^9 + 6x^8 - 10x^7 + 23x^6 - 36x^5 + 51x^4 - 66x^3 + 56x^2 - 36x + 17	$10$	[2,4]	$2^{17}\cdot 47^{4}$	$2$	$15.1561933081$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$170.363704029$
10.0.663963962112.1	x^10 - 4x^9 + 2x^8 + 12x^7 - 22x^6 + 4x^5 + 36x^4 - 56x^3 + 44x^2 - 20x + 4	$10$	[0,5]	$-\,2^{8}\cdot 3^{11}\cdot 11^{4}$	$3$	$15.212985481$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$230.29288517$
10.2.714892578125.2	x^10 + 5x^6 - 33x^5 + 75x^4 - 115x^3 + 110x^2 - 55x + 11	$10$	[2,4]	$5^{11}\cdot 11^{4}$	$2$	$15.3258326448$				$S_5$ (as 10T12)	trivial	$2$	$5$	$140.686816299$
10.0.785877504731.1	x^10 + x^8 - 2x^7 + 21x^5 + 49x^4 - 8x^3 - 17x^2 + 11x + 11	$10$	[0,5]	$-\,11^{5}\cdot 47^{4}$	$2$	$15.471609157$			?	$S_5$ (as 10T12)	trivial	$2$	$4$	$63.7048819215$
10.0.861322076928.1	x^10 + 4x^8 - 8x^7 + 10x^6 - 22x^5 + 40x^4 - 24x^3 + 60x^2 - 36x + 36	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 61^{4}$	$3$	$15.6140856704$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$363.685858255$
10.2.946668828125.1	x^10 - 4x^9 + 6x^8 + x^7 - 21x^6 + 35x^5 - 29x^4 - 14x^3 + 16x^2 - 16x - 16	$10$	[2,4]	$5^{7}\cdot 59^{4}$	$2$	$15.7623079347$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$141.940106449$
10.0.958348132352.1	x^10 - 2x^9 + 3x^8 - x^6 + 2x^5 - x^4 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,2^{25}\cdot 13^{4}$	$2$	$15.7816471861$			?	$S_5$ (as 10T12)	trivial	$2$	$4$	$102.804149884$
10.0.964497618243.1	x^10 + x^8 - x^7 - 17x^5 - x^4 + 5x^3 - 11x^2 + 30x + 36	$10$	[0,5]	$-\,3^{5}\cdot 251^{4}$	$2$	$15.7917447606$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$464.947124584$
10.2.1015264874437.1	x^10 - 4x^9 + 11x^8 - 20x^7 + 73x^5 - 227x^4 + 454x^3 - 515x^2 + 445x - 271	$10$	[2,4]	$11^{4}\cdot 37^{5}$	$2$	$15.8729605215$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$106.466480264$
10.2.1230700078125.1	x^10 - x^8 + 16x^6 - 6x^4 + 36x^2 - 45	$10$	[2,4]	$3^{8}\cdot 5^{7}\cdot 7^{4}$	$3$	$16.181367553$				$S_5$ (as 10T12)	trivial	$2$	$5$	$240.332174864$
10.2.1343692800000.3	x^10 - x^9 + 5x^8 - 10x^7 + 9x^6 - 19x^5 - 9x^4 - 22x^3 - 5x^2 + 23x + 59	$10$	[2,4]	$2^{16}\cdot 3^{8}\cdot 5^{5}$	$3$	$16.3241282827$				$S_5$ (as 10T12)	trivial	$2$	$5$	$197.476438639$
10.0.1410076263168.1	x^10 + 2x^8 - 12x^7 + 16x^6 - 6x^5 + 12x^4 - 48x^3 + 108x^2 - 72x + 36	$10$	[0,5]	$-\,2^{8}\cdot 3^{9}\cdot 23^{4}$	$3$	$16.4030368361$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$371.012129381$
10.2.1670420000000.1	x^10 - x^9 + x^8 - 4x^7 + 14x^6 - 38x^5 + 14x^4 - 4x^3 + x^2 - x + 1	$10$	[2,4]	$2^{8}\cdot 5^{7}\cdot 17^{4}$	$3$	$16.6833233848$				$S_5$ (as 10T12)	trivial	$2$	$5$	$216.934972453$
10.2.1875781250000.1	x^10 - 5x^6 - 28x^5 - 5x^4 + 1	$10$	[2,4]	$2^{4}\cdot 5^{11}\cdot 7^{4}$	$3$	$16.877892602$				$S_5$ (as 10T12)	trivial	$2$	$5$	$245.173818245$
10.0.1912538334375.1	x^10 + 2x^8 - 3x^7 + 17x^6 - 20x^5 + 22x^4 - 26x^3 + 22x^2 - x + 1	$10$	[0,5]	$-\,3^{7}\cdot 5^{5}\cdot 23^{4}$	$3$	$16.9106777959$			?	$S_5$ (as 10T12)	$[2]$	$2$	$4$	$72.4138045125$
10.2.2339717120000.1	x^10 + 4x^8 - 2x^7 + 5x^6 + 4x^5 + 5x^4 + 10x^3 - 22x^2 - 12x + 9	$10$	[2,4]	$2^{17}\cdot 5^{4}\cdot 13^{4}$	$3$	$17.2550544976$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$344.74214707$
10.2.3116068382096.1	x^10 - 2x^9 + 7x^8 - 6x^7 + 9x^6 + 14x^5 - 14x^4 + 42x^3 + 8	$10$	[2,4]	$2^{4}\cdot 41^{7}$	$2$	$17.7566362434$				$S_5$ (as 10T12)	trivial	$2$	$5$	$810.801038138$
10.2.3200000000000.2	x^10 - 5x^9 + 15x^8 - 30x^7 + 45x^6 - 51x^5 + 45x^4 - 30x^3 + 55x^2 - 45x + 9	$10$	[2,4]	$2^{16}\cdot 5^{11}$	$2$	$17.8038939138$				$S_5$ (as 10T12)	trivial	$2$	$5$	$315.071687309$
10.0.3247296480000.1	x^10 - 2x^9 - 12x^7 + 26x^6 - 14x^5 + 32x^4 - 28x^3 + 32x^2 - 12x + 4	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 5^{4}\cdot 17^{4}$	$4$	$17.830034938$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$708.95323812$
10.0.3903069328128.1	x^10 - 2x^9 + 6x^8 + 14x^6 - 26x^5 - 4x^4 - 4x^3 + 32x^2 - 12x + 4	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 89^{4}$	$3$	$18.1610363028$			?	$S_5$ (as 10T12)	$[3]$	$6$	$4$	$291.926530312$
10.0.4129544208384.1	x^10 - 2x^9 + 2x^8 + 16x^7 + 18x^6 + 28x^5 + 36x^4 + 16x^3 + x^2 - 2x + 2	$10$	[0,5]	$-\,2^{18}\cdot 3^{8}\cdot 7^{4}$	$3$	$18.2637608589$			?	$S_5$ (as 10T12)	trivial	$4$	$4$	$474.348763482$
10.2.4415968335104.2	x^10 - 5x^9 + 13x^8 - 22x^7 + 13x^6 + 17x^5 - 69x^4 + 94x^3 - 69x^2 + 27x - 5	$10$	[2,4]	$2^{8}\cdot 29^{7}$	$2$	$18.3866494049$				$S_5$ (as 10T12)	trivial	$2$	$5$	$569.391587781$
10.2.5125781250000.1	x^10 - 5x^6 - 12x^5 - 5x^4 + 1	$10$	[2,4]	$2^{4}\cdot 3^{8}\cdot 5^{11}$	$3$	$18.66276583$				$S_5$ (as 10T12)	trivial	$2$	$5$	$507.060131124$
10.0.5910009391872.1	x^10 - x^9 + 3x^8 + 6x^7 + 9x^6 + 3x^5 + 3x^4 + 66x^3 + 75x^2 - 91x + 169	$10$	[0,5]	$-\,2^{8}\cdot 3^{11}\cdot 19^{4}$	$3$	$18.9303575613$			?	$S_5$ (as 10T12)	trivial	$6$	$4$	$1657.63006945$
10.2.6802444800000.3	x^10 - 5x^9 + 14x^8 - 17x^7 - 3x^6 + 76x^5 - 163x^4 + 207x^3 - 154x^2 + 35x + 25	$10$	[2,4]	$2^{12}\cdot 3^{12}\cdot 5^{5}$	$3$	$19.1984648343$				$S_5$ (as 10T12)	trivial	$2$	$5$	$621.394948464$
10.2.6859721385216.1	x^10 - 4x^9 - x^8 + 22x^7 - 8x^6 - 60x^5 + 30x^4 + 90x^3 - 33x^2 - 84x - 21	$10$	[2,4]	$2^{8}\cdot 3^{13}\cdot 7^{5}$	$3$	$19.2145690168$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$489.901845779$
10.0.7255941120000.1	x^10 - 4x^9 + 2x^8 + 16x^7 - 35x^6 + 12x^5 + 66x^4 - 132x^3 + 123x^2 - 60x + 12	$10$	[0,5]	$-\,2^{16}\cdot 3^{11}\cdot 5^{4}$	$3$	$19.3227695779$				$S_5$ (as 10T12)	trivial	$6$	$4$	$822.871405832$
10.2.7812500000000.2	x^10 - 10x^6 + 25x^2 - 20	$10$	[2,4]	$2^{8}\cdot 5^{15}$	$2$	$19.4661023738$				$S_5$ (as 10T12)	trivial	$2$	$5$	$589.787437562$
10.0.8174985898247.1	x^10 - 4x^9 + 5x^8 - x^7 - x^5 - x^3 + 5x^2 - 4x + 1	$10$	[0,5]	$-\,7^{4}\cdot 23^{7}$	$2$	$19.5545893995$			✓	$S_5$ (as 10T12)	$[3]$	$2$	$4$	$53.9474823266$
10.0.8649755859375.1	x^10 + 5x^8 - 5x^7 + 10x^6 - 7x^5 + 10x^4 - 5x^3 + 5x^2 + 1	$10$	[0,5]	$-\,3^{11}\cdot 5^{11}$	$2$	$19.6652913456$			?	$S_5$ (as 10T12)	$[2]$	$2$	$4$	$150.735465893$
10.2.9788549234688.1	x^10 - 2x^9 + 2x^8 - 4x^7 - 4x^6 + 84x^5 - 140x^4 + 116x^3 - 167x^2 + 170x - 74	$10$	[2,4]	$2^{24}\cdot 3^{5}\cdot 7^{4}$	$3$	$19.9100262658$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$1596.19764084$
10.2.10059713635257.1	x^10 - 3x^9 - 5x^8 + 21x^7 - 15x^6 + 12x^5 - 41x^4 + 45x^3 + 37x^2 + 12x + 3	$10$	[2,4]	$3^{7}\cdot 11^{5}\cdot 13^{4}$	$3$	$19.9645056914$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$320.322969804$
10.2.10628820000000.1	x^10 - x^9 + 5x^8 - 10x^7 + 3x^6 - 19x^5 - 3x^4 - 10x^3 - 5x^2 - x - 1	$10$	[2,4]	$2^{8}\cdot 3^{12}\cdot 5^{7}$	$3$	$20.0746741798$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$561.73872634$
10.2.10628820000000.2	x^10 - 3x^9 + 5x^8 - 2x^7 - 5x^6 + 17x^5 - 5x^4 - 2x^3 + 5x^2 - 3x + 1	$10$	[2,4]	$2^{8}\cdot 3^{12}\cdot 5^{7}$	$3$	$20.0746741798$				$S_5$ (as 10T12)	trivial	$2$	$5$	$733.915655679$
10.2.10628820000000.4	x^10 - 5x^9 + 11x^8 - 14x^7 + 33x^6 - 71x^5 + 101x^4 - 90x^3 + 107x^2 - 73x - 11	$10$	[2,4]	$2^{8}\cdot 3^{12}\cdot 5^{7}$	$3$	$20.0746741798$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$755.722725676$
10.2.11209998860288.1	x^10 - 2x^9 + 7x^8 - 8x^7 + 10x^6 - 12x^5 + 2x^4 - 24x^3 + 6x^2 - 12x + 14	$10$	[2,4]	$2^{27}\cdot 17^{4}$	$2$	$20.181830615$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$1639.94412799$
10.2.12590724022272.1	x^10 + 2x^8 - 8x^6 - 26x^4 + 8x^2 - 8	$10$	[2,4]	$2^{17}\cdot 3^{8}\cdot 11^{4}$	$3$	$20.4176178247$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$622.391254755$
10.2.12602368800000.1	x^10 - x^9 + 5x^8 - 4x^7 + 3x^6 - x^5 + 27x^4 + 62x^3 + 19x^2 + 35x + 5	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4}$	$4$	$20.4195054027$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$528.314543315$
10.2.12602368800000.2	x^10 - x^9 - x^8 + 2x^7 - 3x^6 + 5x^5 - x^4 - 42x^3 + 5x^2 + 61x + 19	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4}$	$4$	$20.4195054027$			?	$S_5$ (as 10T12)	trivial	$2$	$5$	$732.657279074$
10.2.12602368800000.3	x^10 - x^9 - 13x^8 + 14x^7 + 45x^6 - 31x^5 - 45x^4 + 86x^3 - 5x^2 - 31x + 29	$10$	[2,4]	$2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4}$	$4$	$20.4195054027$				$S_5$ (as 10T12)	trivial	$2$	$5$	$708.260442091$