Number field search results

Results (6 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
20.0.152...384.1	x^20 - 2x^19 + 6x^18 - 8x^17 + 16x^16 - 14x^15 + 32x^14 - 12x^13 + 32x^12 + 8x^11 + 48x^10 - 16x^9 + 48x^8 + 8x^7 + 24x^6 + 8x^5 + 32x^4 + 16x^3 + 32x^2 + 16x + 16	$20$	[0,10]	$2^{16}\cdot 3^{10}\cdot 89^{8}$	$3$	$18.1610363028$				$S_5$ (as 20T32)	$[2]$	$6$	$9$	$64033.5089322$
20.4.288...000.1	x^20 - 5x^18 - 2x^17 + 5x^16 + 8x^15 + 2x^14 - 16x^13 + 21x^12 + 28x^11 - 119x^10 - 150x^9 + 61x^8 + 164x^7 + 62x^6 - 4x^5 + 149x^4 + 396x^3 + 327x^2 + 58x - 31	$20$	[4,8]	$2^{36}\cdot 3^{16}\cdot 5^{10}$	$3$	$18.7514993051$				$S_5$ (as 20T32)	trivial	$2$	$11$	$110122.225791$
20.0.161...144.1	x^20 - 3x^19 + 12x^18 - 23x^17 + 66x^16 - 117x^15 + 222x^14 - 297x^13 + 411x^12 - 454x^11 + 456x^10 - 312x^9 + 147x^8 + 69x^7 - 150x^6 + 127x^5 - 78x^4 + 21x^3 + 16x^2 - 15x + 9	$20$	[0,10]	$2^{16}\cdot 3^{22}\cdot 23^{8}$	$3$	$20.4337704904$				$S_5$ (as 20T32)	$[2]$	$6$	$9$	$314083.885561$
20.4.163...000.1	x^20 - 10x^19 + 45x^18 - 120x^17 + 215x^16 - 292x^15 + 350x^14 - 400x^13 + 385x^12 - 230x^11 + 11x^10 + 60x^9 + 55x^8 - 140x^7 + 90x^6 - 20x^5 + 25x^4 - 50x^3 - 75x^2 + 100x - 25	$20$	[4,8]	$2^{36}\cdot 5^{22}$	$2$	$20.4513036513$				$S_5$ (as 20T32)	trivial	$2$	$11$	$331332.875442$
20.20.850...000.1	x^20 - 4x^19 - 33x^18 + 120x^17 + 468x^16 - 1392x^15 - 3799x^14 + 8012x^13 + 19008x^12 - 23720x^11 - 57969x^10 + 31228x^9 + 101057x^8 - 964x^7 - 86922x^6 - 33928x^5 + 22258x^4 + 19672x^3 + 5396x^2 + 600x + 20	$20$	[20,0]	$2^{36}\cdot 5^{10}\cdot 103^{8}$	$3$	$49.7134478267$				$S_5$ (as 20T32)	trivial	$2$	$19$	$70785617543.0$
20.20.500...841.1	x^20 - 8x^19 - 30x^18 + 396x^17 - 172x^16 - 6657x^15 + 12415x^14 + 48573x^13 - 145810x^12 - 136440x^11 + 758752x^10 - 106552x^9 - 1920339x^8 + 1396889x^7 + 2101035x^6 - 2676014x^5 - 273208x^4 + 1559242x^3 - 729758x^2 + 126529x - 7417	$20$	[20,0]	$29^{10}\cdot 431^{8}$	$2$	$60.9522731792$			?	$S_5$ (as 20T32)	trivial	$2$	$19$	$479833200273$