Global number field search results

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

Results (displaying all 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.8.24302560546048.1	x^12 - x^11 - 4x^10 + 10x^9 - 5x^8 - 26x^7 + 29x^6 + 10x^5 - 23x^4 + 12x^3 + 2x^2 - 5x + 1	\( 2^{8}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	Trivial
12.8.388840968736768.1	x^12 - 4x^11 + 2x^10 + 12x^9 - 27x^8 + 22x^7 + 14x^6 - 50x^5 + 25x^4 + 30x^3 - 16x^2 - 6x + 1	\( 2^{12}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	Trivial
12.0.4107132732282112.1	x^12 - 6x^11 + 22x^10 - 51x^9 + 91x^8 - 126x^7 + 165x^6 - 172x^5 + 125x^4 - 5x^3 + 3x^2 - 47x + 67	\( 2^{8}\cdot 13^{2}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	$[2]$
12.4.6221455499788288.1	x^12 - 4x^11 + 9x^10 + 2x^9 - 42x^8 + 112x^7 - 99x^6 - 84x^5 + 366x^4 - 314x^3 + 137x^2 - 16x - 1	\( 2^{16}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	$[2]$
12.4.6221455499788288.3	x^12 + 6x^10 - 13x^8 - 140x^6 - 249x^4 - 74x^2 + 37	\( 2^{16}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	Trivial
12.0.7023439997807872.1	x^12 - 3x^11 + 13x^10 - 17x^9 + 45x^8 - 12x^7 + 71x^6 + 60x^5 + 105x^4 + 139x^3 + 132x^2 + 128x + 67	\( 2^{8}\cdot 17^{2}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	$[2]$
12.12.44935434449642752.1	x^12 - 4x^11 - 20x^10 + 74x^9 + 163x^8 - 488x^7 - 724x^6 + 1364x^5 + 1747x^4 - 1292x^3 - 1712x^2 - 182x + 1	\( 2^{8}\cdot 37^{7}\cdot 43^{2} \)	$A_4:C_4$ (as 12T30)	Trivial
12.12.99543287996612608.1	x^12 - 20x^10 + 131x^8 - 384x^6 + 527x^4 - 296x^2 + 37	\( 2^{20}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	Trivial
12.8.4196371061735948288.1	x^12 - 14x^10 + 23x^8 + 156x^6 + 46x^4 - 56x^2 + 8	\( 2^{23}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.8.4196371061735948288.2	x^12 - 8x^10 - 34x^8 + 216x^6 - 143x^4 - 224x^2 + 128	\( 2^{23}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.4.67141936987775172608.7	x^12 + 14x^10 + 23x^8 - 156x^6 + 46x^4 + 56x^2 + 8	\( 2^{27}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.4.67141936987775172608.12	x^12 + 8x^10 - 34x^8 - 216x^6 - 143x^4 + 224x^2 + 128	\( 2^{27}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.8.1074270991804402761728.2	x^12 - 4x^10 - 52x^8 + 56x^6 + 69x^4 - 36x^2 + 2	\( 2^{31}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.8.1074270991804402761728.3	x^12 - 2x^10 - 99x^8 + 460x^6 - 198x^4 - 8x^2 + 8	\( 2^{31}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.4.1074270991804402761728.6	x^12 + 4x^10 - 52x^8 - 56x^6 + 69x^4 + 36x^2 + 2	\( 2^{31}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	$[10]$ (GRH)
12.4.1074270991804402761728.9	x^12 + 2x^10 - 99x^8 - 460x^6 - 198x^4 + 8x^2 + 8	\( 2^{31}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.3529148062919932510208.1	x^12 - 6x^11 + 21x^10 - 50x^9 - 461x^8 + 1904x^7 + 2954x^6 - 12132x^5 - 11974x^4 + 27384x^3 + 28760x^2 - 23264x - 6176	\( 2^{23}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.3529148062919932510208.2	x^12 - 4x^11 - 12x^10 + 168x^9 - 358x^8 - 884x^7 + 4494x^6 - 3024x^5 - 5547x^4 + 4624x^3 + 2078x^2 - 952x - 328	\( 2^{23}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.12.4297083967217611046912.1	x^12 - 44x^10 + 574x^8 - 2128x^6 + 1148x^4 - 176x^2 + 8	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.0.4297083967217611046912.8	x^12 + 44x^10 + 574x^8 + 2128x^6 + 1148x^4 + 176x^2 + 8	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	$[2, 58]$ (GRH)
12.8.4297083967217611046912.13	x^12 - 8x^10 - 90x^8 + 592x^6 - 720x^4 - 512x^2 + 512	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.8.4297083967217611046912.14	x^12 - 4x^10 - 454x^8 + 3216x^6 - 3632x^4 - 256x^2 + 512	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	Trivial (GRH)
12.4.4297083967217611046912.47	x^12 + 4x^10 - 454x^8 - 3216x^6 - 3632x^4 + 256x^2 + 512	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.4.4297083967217611046912.48	x^12 + 8x^10 - 90x^8 - 592x^6 - 720x^4 + 512x^2 + 512	\( 2^{33}\cdot 29^{8} \)	$A_4:C_4$ (as 12T30)	$[2, 2]$ (GRH)
12.4.56466369006718920163328.4	x^12 - 4x^11 + 14x^10 - 228x^9 + 392x^8 - 1828x^7 + 10442x^6 - 18732x^5 - 5363x^4 + 40568x^3 - 39796x^2 + 14048x - 1618	\( 2^{27}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.4.56466369006718920163328.5	x^12 - 4x^11 - 12x^10 - 64x^9 + 222x^8 + 740x^7 + 1014x^6 - 820x^5 + 427x^4 - 1640x^3 - 1518x^2 + 92x - 386	\( 2^{27}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.903461904107502722613248.4	x^12 - 870x^8 + 9280x^6 + 21025x^4 - 269120x^2 + 430592	\( 2^{31}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.903461904107502722613248.8	x^12 - 58x^10 - 493x^8 + 10556x^6 - 30276x^4 + 26912	\( 2^{31}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.4.903461904107502722613248.22	x^12 - 870x^8 - 9280x^6 + 21025x^4 + 269120x^2 + 430592	\( 2^{31}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2, 2]$ (GRH)
12.4.903461904107502722613248.38	x^12 + 58x^10 - 493x^8 - 10556x^6 - 30276x^4 + 26912	\( 2^{31}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2, 2]$ (GRH)
12.12.3613847616430010890452992.2	x^12 - 116x^10 + 4872x^8 - 91640x^6 + 803996x^4 - 2906496x^2 + 2179872	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.3613847616430010890452992.11	x^12 - 1044x^8 + 4176x^6 + 245572x^4 - 1695456x^2 + 2179872	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.8.3613847616430010890452992.19	x^12 - 348x^8 + 2320x^6 + 3364x^4 - 26912x^2 + 26912	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2]$ (GRH)
12.4.3613847616430010890452992.32	x^12 - 1044x^8 - 4176x^6 + 245572x^4 + 1695456x^2 + 2179872	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2, 2]$ (GRH)
12.0.3613847616430010890452992.41	x^12 + 116x^10 + 4872x^8 + 91640x^6 + 803996x^4 + 2906496x^2 + 2179872	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2, 2, 842]$ (GRH)
12.4.3613847616430010890452992.56	x^12 - 348x^8 - 2320x^6 + 3364x^4 + 26912x^2 + 26912	\( 2^{33}\cdot 29^{10} \)	$A_4:C_4$ (as 12T30)	$[2, 2, 2]$ (GRH)