Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.2497515382702158081163264.1	x^20 + 2x^18 + x^16 - 18x^12 + 12x^10 - 2x^8 + 81x^4 - 14x^2 + 1	\( 2^{42}\cdot 7^{6}\cdot 13^{6} \)	20T199	$[2]$
20.0.93695850529185649263640576.1	x^20 - 4x^19 + 13x^18 - 40x^17 + 96x^16 - 172x^15 + 242x^14 - 272x^13 + 197x^12 + 96x^11 - 421x^10 + 384x^9 + 2x^8 - 680x^7 + 1546x^6 - 1352x^5 + 140x^4 + 296x^3 + 16x^2 - 32x + 8	\( 2^{36}\cdot 7^{10}\cdot 13^{6} \)	20T199	Trivial (GRH)
20.4.159840984492938117194448896.2	x^20 - 4x^18 - 2x^16 + 24x^14 - 7x^12 + 8x^10 + 20x^8 - 228x^6 + 248x^4 - 80x^2 + 4	\( 2^{48}\cdot 7^{6}\cdot 13^{6} \)	20T199	Trivial (GRH)
20.0.722591325711766930119983104.1	x^20 - 4x^18 - 14x^16 + 70x^14 + 21x^12 - 262x^10 + x^8 + 304x^6 + 60x^4 + 4	\( 2^{32}\cdot 743^{6} \)	20T199	$[2]$ (GRH)
20.4.1114555263208692764939124736.1	x^20 - 4x^19 - 3x^18 + 22x^17 - 6x^16 - 44x^15 + 13x^14 + 94x^13 + 46x^12 - 180x^11 - 103x^10 + 230x^9 + 81x^8 - 296x^7 - 410x^6 - 316x^5 - 122x^4 - 8x^3 - 12x^2 - 16x - 4	\( 2^{36}\cdot 7^{6}\cdot 13^{10} \)	20T199	Trivial (GRH)
20.8.5796813598572716138681640625.1	x^20 - 2x^19 + 2x^18 + 20x^17 - 11x^16 - 18x^15 + 136x^14 + 112x^13 - 141x^12 + 23x^11 + 144x^10 - 437x^9 - 620x^8 - 56x^7 + 282x^6 + 470x^5 + 467x^4 - 29x^3 - 265x^2 - 78x + 11	\( 5^{10}\cdot 13^{6}\cdot 223^{6} \)	20T199	Trivial (GRH)
20.0.15398252078750514273032991801.1	x^20 + 9x^18 - 2x^17 + 52x^16 - 17x^15 + 184x^14 - 94x^13 + 480x^12 - 313x^11 + 848x^10 - 753x^9 + 1155x^8 - 964x^7 + 1139x^6 - 808x^5 + 717x^4 - 354x^3 + 189x^2 - 30x + 4	\( 3^{10}\cdot 7993^{6} \)	20T199	$[2]$ (GRH)
20.8.44980292500311338198447265625.1	x^20 - 4x^19 - 3x^18 + 16x^17 + 8x^16 - 12x^15 + 52x^14 + 2x^13 - 389x^12 - 8x^11 + 608x^10 - 448x^9 - 840x^8 + 1126x^7 + 1072x^6 - 1335x^5 - 544x^4 + 901x^3 + 13x^2 - 256x + 29	\( 5^{10}\cdot 4079^{6} \)	20T199	Trivial (GRH)
20.0.1131118633456222501419144127184896.1	x^20 + 28x^18 + 320x^16 + 1928x^14 + 6624x^12 + 13196x^10 + 14960x^8 + 9056x^6 + 2592x^4 + 336x^2 + 16	\( 2^{28}\cdot 71^{6}\cdot 179^{6} \)	20T199	$[2, 20]$ (GRH)
20.0.16306500045643672482006601944858624.1	x^20 - 2x^19 + 16x^18 - 24x^17 + 152x^16 - 214x^15 + 836x^14 - 964x^13 + 3032x^12 - 3320x^11 + 6696x^10 - 5712x^9 + 8920x^8 - 6720x^7 + 7176x^6 - 3128x^5 + 1776x^4 - 448x^3 + 240x^2 - 48x + 16	\( 2^{16}\cdot 3^{10}\cdot 71^{6}\cdot 179^{6} \)	20T199	$[2, 264]$ (GRH)
20.20.1158265480659171841453203586237333504.1	x^20 - 38x^18 + 604x^16 - 5200x^14 + 26240x^12 - 78512x^10 + 134768x^8 - 122944x^6 + 51584x^4 - 6784x^2 + 64	\( 2^{38}\cdot 71^{6}\cdot 179^{6} \)	20T199	Trivial (GRH)
20.20.2696796973839336637065754240000000000.1	x^20 - 6x^19 - 23x^18 + 180x^17 + 137x^16 - 2048x^15 + 356x^14 + 11414x^13 - 6429x^12 - 34356x^11 + 25401x^10 + 57758x^9 - 46797x^8 - 53802x^7 + 44480x^6 + 25646x^5 - 21265x^4 - 4808x^3 + 4381x^2 + 52x - 211	\( 2^{16}\cdot 5^{10}\cdot 71^{6}\cdot 179^{6} \)	20T199	Trivial (GRH)