Number field search results

Results (13 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
20.2.627...672.1	x^20 - 2x^19 + 5x^17 - x^16 - 6x^15 - 8x^14 + 22x^13 + 4x^12 - 32x^11 + 16x^10 + 10x^9 + 3x^8 - 30x^7 + 22x^6 + 5x^5 - 12x^4 + 4x^3 - 2x^2 + 3x - 1	$20$	[2,9]	$-\,2^{16}\cdot 3^{5}\cdot 13^{14}$	$3$	$13.7995414981$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$10$	$1516.67926689$
20.2.640...000.1	x^20 - 5x^18 + 5x^16 - 10x^14 + 45x^12 + x^10 - 45x^8 - 10x^6 - 5x^4 - 5x^2 - 1	$20$	[2,9]	$-\,2^{28}\cdot 5^{22}$	$2$	$15.4991898755$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$10$	$6343.32708051$
20.4.320...000.1	x^20 - 72x^15 - 712x^10 + 288x^5 + 16	$20$	[4,8]	$2^{16}\cdot 5^{22}\cdot 29^{5}$	$3$	$23.729604547$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$11$	$527936.193913$
20.0.160...000.1	x^20 - 5x^19 + 10x^18 - 25x^17 + 70x^16 - 51x^15 - 50x^14 - 235x^13 + 895x^12 - 180x^11 - 384x^10 - 1430x^9 + 2595x^8 + 2575x^7 + 5100x^6 + 3749x^5 + 5420x^4 + 2385x^3 + 1760x^2 + 445x + 431	$20$	[0,10]	$2^{16}\cdot 5^{23}\cdot 29^{5}$	$3$	$25.7181071259$				$D_{10}:C_4$ (as 20T22)	$[2]$	$2$	$9$	$615825.309667$
20.4.191...125.1	x^20 - 4x^15 - 183x^10 + 104x^5 + 1	$20$	[4,8]	$5^{30}\cdot 29^{5}$	$2$	$25.9450496413$				$D_{10}:C_4$ (as 20T22)	trivial	$2$	$11$	$1748237.43405$
20.0.955...625.1	x^20 - 6x^15 - 439x^10 + 5344x^5 + 161051	$20$	[0,10]	$5^{31}\cdot 29^{5}$	$2$	$28.119202945$				$D_{10}:C_4$ (as 20T22)	$[2]$	$2$	$9$	$2039278.36661$
20.10.368...000.1	x^20 - 5x^18 - 115x^16 - 250x^14 + 525x^12 + 1201x^10 - 525x^8 - 250x^6 + 115x^4 - 5x^2 - 1	$20$	[10,5]	$-\,2^{28}\cdot 5^{22}\cdot 7^{8}$	$3$	$33.7557852041$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$14$	$79536181.4047$
20.10.184...000.1	x^20 - 160x^16 + 2360x^12 - 4240x^8 + 1520x^4 - 80	$20$	[10,5]	$-\,2^{28}\cdot 5^{23}\cdot 7^{8}$	$3$	$36.5844655471$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$14$	$291170226.718$
20.2.190...000.1	x^20 - 5	$20$	[2,9]	$-\,2^{20}\cdot 5^{39}$	$2$	$46.1340417295$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$10$	$745710353.59$
20.20.184...000.1	x^20 - 5x^19 - 30x^18 + 160x^17 + 330x^16 - 1933x^15 - 1700x^14 + 11500x^13 + 4245x^12 - 36760x^11 - 5160x^10 + 65020x^9 + 4050x^8 - 63410x^7 - 3400x^6 + 31774x^5 + 1655x^4 - 6755x^3 + 100x^2 + 460x - 41	$20$	[20,0]	$2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 29^{5}$	$4$	$51.6808581933$			?	$D_{10}:C_4$ (as 20T22)	trivial	$2$	$19$	$49401883665.9$
20.0.193...712.1	x^20 - 5x^19 - 11x^18 + 83x^17 + 56x^16 - 700x^15 + 105x^14 + 2882x^13 - 1781x^12 - 5757x^11 + 7777x^10 + 3940x^9 - 13469x^8 - 7812x^7 + 52825x^6 - 87721x^5 + 99762x^4 - 30932x^3 + 54617x^2 - 18028x + 20591	$20$	[0,10]	$2^{15}\cdot 17^{14}\cdot 37^{8}$	$3$	$51.8044934332$	✓		?	$D_{10}:C_4$ (as 20T22)	$[4, 20]$	$2$	$9$	$7343104.2357$
20.20.128...288.1	x^20 - 3x^19 - 38x^18 + 109x^17 + 461x^16 - 1366x^15 - 2392x^14 + 7958x^13 + 5346x^12 - 23708x^11 - 2958x^10 + 37354x^9 - 7565x^8 - 29683x^7 + 13316x^6 + 9335x^5 - 6991x^4 + 252x^3 + 780x^2 - 208x + 16	$20$	[20,0]	$2^{16}\cdot 17^{5}\cdot 53^{14}$	$3$	$56.9415566526$				$D_{10}:C_4$ (as 20T22)	trivial	$2$	$19$	$576057394786$
20.0.185...616.1	x^20 - 3x^19 - 8x^18 + 28x^17 - x^16 - 28x^15 + 212x^14 - 658x^13 + 2547x^12 - 587x^11 + 12252x^10 + 10456x^9 + 54982x^8 + 70259x^7 + 186965x^6 + 205103x^5 + 344870x^4 + 251547x^3 + 274509x^2 + 116534x + 141499	$20$	[0,10]	$2^{16}\cdot 29^{5}\cdot 53^{14}$	$3$	$65.0753638061$	✓		?	$D_{10}:C_4$ (as 20T22)	$[2, 410]$	$2$	$9$	$7826958.70528$