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 matches 1-50 of 92)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.5034178546849933.1	x^12 - 4x^11 + 3x^10 + x^9 - 4x^8 + 16x^7 - 38x^6 - 4x^5 - 140x^4 - 155x^3 - 4x^2 + 42x + 53	\( 13^{11}\cdot 53^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.5034178546849933.1	x^12 - x^11 + x^10 + 12x^9 - 38x^8 - 14x^7 + 40x^6 - 66x^5 + 14x^4 + 51x^3 - 25x^2 - x + 1	\( 13^{11}\cdot 53^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.7340688973975552.1	x^12 - 26x^8 - 78x^6 - 78x^4 - 13x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.7340688973975552.1	x^12 - 13x^8 + 13x^6 + 26x^4 - 39x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.7340688973975552.2	x^12 - 13x^8 - 13x^6 + 26x^4 + 39x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.7340688973975552.2	x^12 - 26x^8 + 78x^6 - 78x^4 + 13x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.11184873019184917.1	x^12 - 3x^11 + 9x^10 - 27x^9 + 42x^8 - 35x^7 + 40x^6 + 153x^5 - 407x^4 + 597x^3 - 530x^2 + 30x + 131	\( 13^{11}\cdot 79^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.11184873019184917.1	x^12 - x^11 + x^10 - x^9 - 12x^8 + 12x^7 - 90x^6 + 129x^5 + 183x^4 - 339x^3 + 92x^2 + 25x + 1	\( 13^{11}\cdot 79^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.19013029620338533.1	x^12 - 2x^11 - 9x^10 + 18x^9 - 10x^8 + 33x^7 + 25x^6 - 50x^5 - 17x^4 - 83x^3 - 16x^2 + 6x + 1	\( 13^{11}\cdot 103^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.46118408000000000.1	x^12 + 15x^10 + 70x^8 + 75x^6 - 175x^4 - 250x^2 + 125	\( 2^{12}\cdot 5^{9}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.49519263525896192.1	x^12 - 4x^10 - 22x^8 + 112x^6 - 64x^4 - 144x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.49519263525896192.4	x^12 + 12x^10 + 40x^8 - 172x^4 - 176x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.49519263525896192.4	x^12 - 12x^10 + 40x^8 - 172x^4 + 176x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.49519263525896192.12	x^12 + 4x^10 - 22x^8 - 112x^6 - 64x^4 + 144x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.0.61243533037578125.1	x^12 - x^11 + 7x^10 - 14x^9 + 62x^8 - 99x^7 + 248x^6 - 282x^5 + 513x^4 - 323x^3 + 547x^2 - 243x + 239	\( 5^{7}\cdot 13^{8}\cdot 31^{2} \)	$C_2^5.C_6$ (as 12T105)	$[2, 2]$
12.12.61243533037578125.1	x^12 - 6x^11 + 2x^10 + 45x^9 - 58x^8 - 104x^7 + 174x^6 + 97x^5 - 186x^4 - 34x^3 + 69x^2 - 5	\( 5^{7}\cdot 13^{8}\cdot 31^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.61243533037578125.1	x^12 - 3x^11 + x^10 + 5x^9 - 57x^8 + 16x^7 + 38x^6 + 55x^5 + 206x^4 - 258x^3 + 121x^2 - 255x + 155	\( 5^{7}\cdot 13^{8}\cdot 31^{2} \)	$C_2^5.C_6$ (as 12T105)	$[2]$
12.8.61243533037578125.1	x^12 - 4x^11 + 3x^10 + 14x^9 - 63x^8 + 91x^7 - 2x^6 - 171x^5 + 272x^4 - 139x^3 - 36x^2 + 30x + 5	\( 5^{7}\cdot 13^{8}\cdot 31^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.0.279621825479622925.1	x^12 - 3x^11 + 22x^10 - 53x^9 + 198x^8 - 321x^7 + 963x^6 - 731x^5 + 2739x^4 - 534x^3 + 3981x^2 + 784x + 1847	\( 5^{2}\cdot 13^{11}\cdot 79^{2} \)	$C_2^5.C_6$ (as 12T105)	$[2, 2, 6]$
12.12.279621825479622925.1	x^12 - 4x^11 - 23x^10 + 131x^9 - 4x^8 - 881x^7 + 989x^6 + 1881x^5 - 3338x^4 - 896x^3 + 3168x^2 - 270x - 675	\( 5^{2}\cdot 13^{11}\cdot 79^{2} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.369768517790072832.2	x^12 - 42x^8 + 136x^6 - 120x^4 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.369768517790072832.3	x^12 - 12x^10 + 48x^8 - 64x^6 - 12x^4 + 48x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.369768517790072832.11	x^12 + 12x^10 + 48x^8 + 64x^6 - 12x^4 - 48x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.369768517790072832.16	x^12 - 42x^8 - 136x^6 - 120x^4 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.469804094334435328.3	x^12 - 52x^8 + 104x^6 + 416x^4 - 1248x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.469804094334435328.4	x^12 - 104x^8 + 624x^6 - 1248x^4 + 416x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.469804094334435328.6	x^12 - 104x^8 - 624x^6 - 1248x^4 - 416x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.469804094334435328.7	x^12 - 52x^8 - 104x^6 + 416x^4 + 1248x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.2426443912768913408.8	x^12 - 98x^8 + 112x^6 + 2352x^4 - 5488x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.2426443912768913408.9	x^12 - 140x^8 + 280x^6 + 1372x^4 - 3136x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.2426443912768913408.33	x^12 - 140x^8 - 280x^6 + 1372x^4 + 3136x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.2426443912768913408.34	x^12 - 98x^8 - 112x^6 + 2352x^4 + 5488x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T105)	$[2]$
12.8.3327916660110655488.1	x^12 + 12x^10 - 18x^8 - 192x^6 + 540x^4 - 432x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.3327916660110655488.2	x^12 - 12x^10 + 192x^6 - 324x^4 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.3327916660110655488.34	x^12 + 12x^10 - 192x^6 - 324x^4 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.3327916660110655488.44	x^12 - 12x^10 - 18x^8 + 192x^6 + 540x^4 + 432x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.7007073538075000832.2	x^12 - 16x^10 + 22x^8 + 104x^6 - 8x^4 - 64x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.8.7007073538075000832.4	x^12 - 12x^10 + 40x^8 - 124x^4 - 16x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.7007073538075000832.12	x^12 + 12x^10 + 40x^8 - 124x^4 + 16x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.7007073538075000832.13	x^12 + 16x^10 + 22x^8 - 104x^6 - 8x^4 + 64x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial
12.4.114473097276893954048.1	x^12 - 12x^10 - 86x^8 + 16x^6 + 111x^4 + 32x^2 + 2	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.114473097276893954048.1	x^12 - 2x^11 - 13x^10 + 26x^9 + 17x^8 - 64x^7 + 110x^6 + 8x^5 - 241x^4 + 98x^3 + 67x^2 - 2x - 1	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.114473097276893954048.2	x^12 + 16x^10 + 34x^8 - 180x^6 - 289x^4 + 288x^2 + 2	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.114473097276893954048.3	x^12 - 14x^10 + 19x^8 + 216x^6 + 82x^4 - 280x^2 + 8	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.114473097276893954048.10	x^12 + 8x^10 - 36x^8 - 172x^6 + 719x^4 - 544x^2 + 32	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.114473097276893954048.15	x^12 - 22x^10 + 123x^8 - 172x^6 - 156x^4 + 288x^2 + 32	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.114473097276893954048.17	x^12 - 8x^10 - 52x^8 + 92x^6 + 503x^4 + 192x^2 + 8	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.4.114473097276893954048.19	x^12 + 14x^10 + 37x^8 - 172x^6 - 780x^4 - 736x^2 + 32	\( 2^{27}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.145887695661298614272.2	x^12 + 16x^10 - 26x^8 - 760x^6 + 872x^4 - 160x^2 + 8	\( 2^{33}\cdot 19^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)
12.8.145887695661298614272.4	x^12 - 8x^10 - 50x^8 + 232x^6 + 184x^4 - 800x^2 + 392	\( 2^{33}\cdot 19^{8} \)	$C_2^5.C_6$ (as 12T105)	Trivial (GRH)