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 matches 1-50 of 82)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.46411484401953.1	x^12 - 4x^9 + 17x^6 - 4x^3 + 1	\( 3^{9}\cdot 11^{9} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.58157342720000.1	x^12 - 2x^11 - 8x^9 + 10x^8 + 16x^6 + 8x^5 + 28x^4 + 8x^3 + 20x^2 + 4	\( 2^{16}\cdot 5^{4}\cdot 17^{5} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.69259433447763.2	x^12 - x^9 - x^6 - x^3 + 1	\( -\,3^{15}\cdot 13^{6} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.107567821094912.1	x^12 + 6x^10 - 2x^9 + 18x^8 - 14x^7 + 45x^6 - 20x^5 + 24x^4 - 6x^3 + x^2 + 2x + 1	\( 2^{18}\cdot 17^{7} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.117231566641875.1	x^12 - 3x^11 + 3x^10 + 3x^9 - 9x^8 + 12x^7 - 3x^6 - 33x^5 + 72x^4 - 72x^3 + 60x^2 - 45x + 15	\( -\,3^{13}\cdot 5^{4}\cdot 7^{6} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.143393766507472.1	x^12 - 5x^11 + 14x^10 - 28x^9 + 48x^8 - 69x^7 + 83x^6 - 87x^5 + 80x^4 - 61x^3 + 38x^2 - 20x + 8	\( 2^{4}\cdot 13^{5}\cdot 17^{6} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.169075682574336.1	x^12 + 4x^10 - 4x^9 + 10x^8 + 2x^6 + 16x^5 - 4x^4 + 4x^3 + 12x^2 + 3	\( 2^{33}\cdot 3^{9} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.179359981764608.2	x^12 - 4x^10 + 18x^8 - 32x^6 + 57x^4 - 28x^2 + 8	\( 2^{31}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T36)	Trivial (GRH)
12.0.503060929445888.15	x^12 + 4x^10 + 2x^8 - 4x^6 + 9x^4 + 16x^2 + 8	\( 2^{35}\cdot 11^{4} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.685529707511808.5	x^12 + 12x^10 - 2x^9 + 54x^8 - 18x^7 + 114x^6 - 54x^5 + 117x^4 - 62x^3 + 54x^2 - 24x + 4	\( 2^{16}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.1521681143169024.3	x^12 - 8x^9 + 16x^6 + 8	\( 2^{33}\cdot 3^{11} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.1721085137518592.1	x^12 - 2x^11 + 3x^10 - 14x^9 + 32x^8 - 70x^7 + 141x^6 - 162x^5 + 128x^4 - 110x^3 + 67x^2 - 14x + 3	\( 2^{22}\cdot 17^{7} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.2742118830047232.4	x^12 - 2x^9 - 2x^3 + 1	\( -\,2^{18}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.2869759708233728.1	x^12 - 4x^11 + 6x^10 - 12x^9 + x^8 - 8x^7 - 8x^5 + x^4 - 12x^3 + 6x^2 - 4x + 1	\( -\,2^{35}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.3423782572130304.4	x^12 + 6x^10 + 12x^6 + 21x^4 + 6x^2 + 6	\( 2^{31}\cdot 3^{13} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.0.3537090251849728.1	x^12 + 2x^10 - 8x^9 + 17x^8 - 16x^7 + 24x^6 - 16x^5 + 17x^4 - 8x^3 + 2x^2 + 1	\( 2^{32}\cdot 7^{7} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.2.3966492492169216.1	x^12 - 2x^10 - 29x^8 - 88x^6 - 128x^4 - 72x^2 - 4	\( -\,2^{32}\cdot 31^{4} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.6847565144260608.26	x^12 + 6x^10 - 8x^9 + 21x^8 - 48x^7 + 48x^6 - 96x^5 + 93x^4 - 104x^3 + 102x^2 + 25	\( 2^{32}\cdot 3^{13} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.0.6847565144260608.30	x^12 - 4x^11 + 24x^9 - 14x^8 - 112x^7 + 164x^6 + 64x^5 - 218x^4 + 64x^3 + 144x^2 - 128x + 32	\( 2^{32}\cdot 3^{13} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.10271347716390912.5	x^12 - 6x^10 + 24x^8 - 48x^6 + 45x^4 - 18x^2 + 18	\( 2^{31}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.2.11277990709674579.1	x^12 - 15x^9 - 16x^6 - 15x^3 + 1	\( -\,3^{14}\cdot 11^{9} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.2.14280872991653888.1	x^12 + 6x^10 + 3x^8 + 32x^6 + 23x^4 - 230x^2 - 23	\( -\,2^{22}\cdot 23^{7} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.15543550148214784.6	x^12 - 3x^11 + 9x^9 - 23x^7 + 33x^6 - 58x^5 + 168x^4 - 350x^3 + 404x^2 - 274x + 106	\( 2^{17}\cdot 17^{9} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.2.20542695432781824.21	x^12 - 6x^10 - 16x^9 - 15x^8 - 24x^7 - 24x^6 - 24x^5 - 15x^4 - 16x^3 - 6x^2 + 1	\( -\,2^{32}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.41085390865563648.27	x^12 - 24x^8 - 92x^6 - 123x^4 - 36x^2 - 2	\( -\,2^{33}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.0.43873901280755712.19	x^12 + 12x^10 - 4x^9 + 54x^8 - 36x^7 + 120x^6 - 108x^5 + 153x^4 - 148x^3 + 108x^2 - 120x + 52	\( 2^{22}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T36)	Trivial (GRH)
12.0.61628086298345472.16	x^12 - 12x^10 - 16x^9 + 36x^8 + 120x^7 + 92x^6 - 72x^5 - 102x^4 + 24x^3 + 72x^2 + 144x + 132	\( 2^{32}\cdot 3^{15} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.61628086298345472.17	x^12 + 12x^10 - 8x^9 + 54x^8 - 72x^7 + 144x^6 - 216x^5 + 297x^4 - 328x^3 + 324x^2 - 336x + 164	\( 2^{32}\cdot 3^{15} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.0.66060088129912832.2	x^12 - x^11 + 5x^10 - x^9 + 19x^8 - 11x^7 + 28x^6 + 40x^5 + 53x^4 - 35x^3 + 56x^2 + 50x + 52	\( 2^{15}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.0.92442129447518208.45	x^12 - 4x^9 + 36x^8 - 108x^7 + 200x^6 - 468x^5 + 753x^4 - 884x^3 + 1584x^2 - 2136x + 1076	\( 2^{31}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T36)	Trivial (GRH)
12.2.164341563462254592.16	x^12 - 16x^9 + 18x^8 - 48x^7 - 52x^6 + 120x^5 - 54x^4 - 224x^3 - 120x^2 - 96x - 56	\( -\,2^{35}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.164341563462254592.79	x^12 - 4x^11 + 18x^10 - 60x^9 + 169x^8 - 400x^7 + 844x^6 - 1456x^5 + 2116x^4 - 2328x^3 + 1752x^2 - 784x + 166	\( 2^{35}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.0.164341563462254592.81	x^12 - 8x^9 + 18x^8 + 4x^6 - 120x^5 + 138x^4 + 312x^2 - 288x + 264	\( 2^{35}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.2.175495605123022848.27	x^12 - 8x^9 + 6x^6 - 8x^3 + 1	\( -\,2^{24}\cdot 3^{21} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.184884258895036416.4	x^12 + 12x^10 - 8x^9 + 36x^8 - 96x^7 + 4x^6 - 144x^5 + 54x^4 + 296x^3 + 144x^2 - 240x - 100	\( -\,2^{32}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.0.221151061526708224.10	x^12 - 4x^11 + 22x^10 - 76x^9 + 239x^8 - 568x^7 + 1328x^6 - 2216x^5 + 3553x^4 - 4108x^3 + 4198x^2 - 2388x + 1103	\( 2^{35}\cdot 23^{5} \)	$S_3\wr C_2$ (as 12T36)	$[6]$
12.2.264240352519651328.8	x^12 - x^10 - 35x^8 - 81x^6 - 60x^4 - 30x^2 - 2	\( -\,2^{17}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.497393604742873088.7	x^12 - 2x^11 + 5x^10 - 14x^9 + 34x^8 - 18x^7 + 79x^6 - 58x^5 + 28x^4 + 142x^3 + 583x^2 + 974x + 919	\( 2^{22}\cdot 17^{9} \)	$S_3\wr C_2$ (as 12T36)	$[12]$
12.0.606610978192228352.4	x^12 + 2x^10 + 18x^8 + 64x^6 + 100x^4 + 200x^2 + 8	\( 2^{31}\cdot 7^{10} \)	$S_3\wr C_2$ (as 12T36)	$[3, 6]$
12.2.831979165027663872.39	x^12 + 12x^10 + 54x^8 + 68x^6 - 159x^4 - 360x^2 - 32	\( -\,2^{31}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.831979165027663872.42	x^12 + 12x^10 + 54x^8 + 100x^6 + 33x^4 - 72x^2 - 32	\( -\,2^{31}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.1479074071160291328.11	x^12 + 12x^10 + 54x^8 + 44x^6 - 303x^4 - 576x^2 - 128	\( -\,2^{35}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T36)	$[2]$
12.0.1479074071160291328.68	x^12 - 12x^10 - 16x^9 + 54x^8 + 144x^7 - 24x^6 - 432x^5 - 423x^4 + 328x^3 + 756x^2 + 312x + 38	\( 2^{35}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.12.2036127821347749888.1	x^12 - 6x^11 - 9x^10 + 74x^9 + 48x^8 - 270x^7 - 117x^6 + 360x^5 + 84x^4 - 172x^3 - 9x^2 + 12x + 1	\( 2^{16}\cdot 3^{13}\cdot 11^{7} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.2.3327916660110655488.128	x^12 - 16x^9 + 56x^6 + 160x^3 - 8	\( -\,2^{33}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T36)	$[3]$
12.0.3524782361638076416.19	x^12 - 4x^11 + 6x^10 - 4x^9 + 25x^8 - 72x^7 + 8x^6 + 240x^5 - 218x^4 - 528x^3 + 1400x^2 - 1184x + 392	\( 2^{33}\cdot 17^{7} \)	$S_3\wr C_2$ (as 12T36)	$[4]$
12.0.4991874990165983232.27	x^12 - 12x^10 - 8x^9 + 90x^8 + 120x^7 - 272x^6 - 648x^5 + 81x^4 + 1704x^3 + 2268x^2 + 1296x + 396	\( 2^{32}\cdot 3^{19} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.4991874990165983232.41	x^12 + 24x^10 - 8x^9 + 252x^8 - 96x^7 + 1312x^6 - 432x^5 + 3204x^4 + 192x^3 + 2592x^2 + 1728x + 288	\( 2^{32}\cdot 3^{19} \)	$S_3\wr C_2$ (as 12T36)	Trivial
12.0.5086474415114289152.15	x^12 + 16x^10 + 108x^8 + 448x^6 + 1252x^4 + 2112x^2 + 1568	\( 2^{35}\cdot 23^{6} \)	$S_3\wr C_2$ (as 12T36)	$[6]$ (GRH)
12.0.5429855677795401728.3	x^12 - 20x^10 + 113x^8 - 124x^6 + 264x^4 - 122x^2 + 32	\( 2^{17}\cdot 23^{10} \)	$S_3\wr C_2$ (as 12T36)	$[3]$