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 52)

Label	Polynomial	Discriminant	Galois group	Class group
12.8.44804009850925.1	x^12 - 4x^11 + 3x^10 + x^9 - 4x^8 + 3x^7 + x^6 + 9x^5 + 3x^4 - 12x^3 - 4x^2 + 3x + 1	\( 5^{2}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.1120100246273125.1	x^12 - 3x^11 - 4x^10 + 12x^9 + 3x^8 + 4x^7 + 27x^6 - 81x^5 - 82x^4 + 77x^3 + 81x^2 + 17x + 1	\( 5^{4}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.1593224064453125.1	x^12 - 2x^11 - 8x^10 + 15x^9 + 26x^8 - 25x^7 - 72x^6 - 21x^5 + 151x^4 + 45x^3 - 90x^2 - 30x + 5	\( 5^{9}\cdot 13^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.4.1722266138669557.1	x^12 - 2x^11 + 4x^10 - 21x^9 + 55x^8 - 58x^7 - 27x^6 + 145x^5 - 212x^4 + 190x^3 - 107x^2 + 32x + 1	\( 13^{11}\cdot 31^{2} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.12.3958882310427733.1	x^12 - 4x^11 - 10x^10 + 53x^9 + 9x^8 - 205x^7 + 105x^6 + 204x^5 - 101x^4 - 90x^3 + 22x^2 + 16x + 1	\( 13^{11}\cdot 47^{2} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.4.7340688973975552.3	x^12 - 26x^8 + 78x^4 + 65x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.7340688973975552.3	x^12 - 26x^8 + 78x^4 - 65x^2 + 13	\( 2^{12}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.12.11184873019184917.1	x^12 - 4x^11 - 10x^10 + 40x^9 + 48x^8 - 140x^7 - 129x^6 + 191x^5 + 146x^4 - 103x^3 - 56x^2 + 16x + 1	\( 13^{11}\cdot 79^{2} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.49519263525896192.3	x^12 - 4x^10 - 22x^8 + 56x^6 - 8x^4 - 32x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.49519263525896192.10	x^12 + 4x^10 - 22x^8 - 56x^6 - 8x^4 + 32x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.0.125854463671248325.1	x^12 - 2x^11 + 17x^10 - 34x^9 + 159x^8 - 305x^7 + 909x^6 - 1493x^5 + 2869x^4 - 3385x^3 + 3910x^2 - 2646x + 1171	\( 5^{2}\cdot 13^{11}\cdot 53^{2} \)	$C_4\times A_4$ (as 12T29)	$[2, 2, 4]$
12.0.180092405836384093.1	x^12 - 4x^11 + 29x^10 - 51x^9 + 256x^8 - 166x^7 + 963x^6 + 126x^5 + 1810x^4 + 1054x^3 + 2336x^2 + 1472x + 1223	\( 13^{11}\cdot 317^{2} \)	$C_4\times A_4$ (as 12T29)	$[3, 6]$
12.8.369768517790072832.1	x^12 - 36x^8 + 40x^6 + 36x^4 - 48x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.4.369768517790072832.27	x^12 - 36x^8 - 40x^6 + 36x^4 + 48x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.469804094334435328.2	x^12 - 104x^8 + 1248x^4 - 2080x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.469804094334435328.8	x^12 - 104x^8 + 1248x^4 + 2080x^2 + 832	\( 2^{18}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.2426443912768913408.11	x^12 - 84x^8 + 280x^6 + 196x^4 - 784x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.2426443912768913408.31	x^12 - 84x^8 - 280x^6 + 196x^4 + 784x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.3327916660110655488.3	x^12 - 12x^10 + 18x^8 + 120x^6 - 216x^4 + 72	\( 2^{33}\cdot 3^{18} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.3327916660110655488.35	x^12 + 12x^10 + 18x^8 - 120x^6 - 216x^4 + 72	\( 2^{33}\cdot 3^{18} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.7007073538075000832.3	x^12 + 4x^10 - 46x^8 + 8x^6 + 88x^4 - 64x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.4.7007073538075000832.14	x^12 - 4x^10 - 46x^8 - 8x^6 + 88x^4 + 64x^2 + 8	\( 2^{33}\cdot 13^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.145887695661298614272.3	x^12 + 8x^10 - 52x^8 - 40x^6 + 148x^4 - 80x^2 + 8	\( 2^{33}\cdot 19^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.145887695661298614272.14	x^12 - 8x^10 - 52x^8 + 40x^6 + 148x^4 + 80x^2 + 8	\( 2^{33}\cdot 19^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.8.1184195427934675140608.4	x^12 - 156x^8 + 520x^6 + 676x^4 - 2704x^2 + 1352	\( 2^{33}\cdot 13^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.1184195427934675140608.18	x^12 - 156x^8 - 520x^6 + 676x^4 + 2704x^2 + 1352	\( 2^{33}\cdot 13^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.8.7326278225721213059072.1	x^12 - 8x^10 - 100x^8 + 224x^6 + 228x^4 - 288x^2 + 32	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.12.7326278225721213059072.2	x^12 - 44x^10 + 602x^8 - 3280x^6 + 7824x^4 - 7680x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.8.7326278225721213059072.2	x^12 - 4x^10 - 118x^8 + 400x^6 + 208x^4 - 1280x^2 + 512	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.8.7326278225721213059072.3	x^12 - 16x^10 - 28x^8 + 800x^6 - 1436x^4 - 1280x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.8.7326278225721213059072.4	x^12 - 28x^10 + 170x^8 + 304x^6 - 2544x^4 + 1536x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.7326278225721213059072.12	x^12 + 8x^10 - 100x^8 - 224x^6 + 228x^4 + 288x^2 + 32	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.7326278225721213059072.39	x^12 + 4x^10 - 118x^8 - 400x^6 + 208x^4 + 1280x^2 + 512	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.7326278225721213059072.45	x^12 + 28x^10 + 170x^8 - 304x^6 - 2544x^4 - 1536x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.7326278225721213059072.50	x^12 + 16x^10 - 28x^8 - 800x^6 - 1436x^4 + 1280x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.0.7326278225721213059072.91	x^12 + 44x^10 + 602x^8 + 3280x^6 + 7824x^4 + 7680x^2 + 2048	\( 2^{33}\cdot 31^{8} \)	$C_4\times A_4$ (as 12T29)	$[2, 58]$ (GRH)
12.8.15394540563150776827904.3	x^12 - 364x^8 + 1768x^6 + 18148x^4 - 114608x^2 + 65000	\( 2^{33}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.8.15394540563150776827904.8	x^12 - 572x^8 + 3432x^6 - 988x^4 - 6448x^2 + 2600	\( 2^{33}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.15394540563150776827904.14	x^12 - 364x^8 - 1768x^6 + 18148x^4 + 114608x^2 + 65000	\( 2^{33}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.15394540563150776827904.31	x^12 - 572x^8 - 3432x^6 - 988x^4 + 6448x^2 + 2600	\( 2^{33}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.8.52665458133728799752192.4	x^12 - 228x^8 + 760x^6 + 1444x^4 - 5776x^2 + 2888	\( 2^{33}\cdot 19^{10} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.4.52665458133728799752192.19	x^12 - 228x^8 - 760x^6 + 1444x^4 + 5776x^2 + 2888	\( 2^{33}\cdot 19^{10} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.12.7040553374918085749768192.2	x^12 - 124x^10 + 4898x^8 - 66464x^6 + 338272x^4 - 492032x^2 + 123008	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	Trivial (GRH)
12.0.7040553374918085749768192.5	x^12 + 124x^10 + 4898x^8 + 66464x^6 + 338272x^4 + 492032x^2 + 123008	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2, 2, 4, 212]$ (GRH)
12.8.7040553374918085749768192.12	x^12 - 1116x^8 + 4960x^6 + 34596x^4 - 184512x^2 + 123008	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.8.7040553374918085749768192.13	x^12 - 2604x^8 + 9920x^6 + 188356x^4 - 861056x^2 + 492032	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.8.7040553374918085749768192.14	x^12 - 2604x^8 + 39680x^6 + 188356x^4 - 3444224x^2 + 7872512	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.7040553374918085749768192.16	x^12 - 1116x^8 - 4960x^6 + 34596x^4 + 184512x^2 + 123008	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2, 2]$ (GRH)
12.8.7040553374918085749768192.24	x^12 - 372x^8 + 2480x^6 + 3844x^4 - 30752x^2 + 30752	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2]$ (GRH)
12.4.7040553374918085749768192.26	x^12 - 2604x^8 - 9920x^6 + 188356x^4 + 861056x^2 + 492032	\( 2^{33}\cdot 31^{10} \)	$C_4\times A_4$ (as 12T29)	$[2, 2]$ (GRH)