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 86)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.2483630085505024.1	x^12 - 2x^10 + 8x^8 + 6x^6 + 5x^4 + 34x^2 + 25	\( 2^{24}\cdot 23^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.3011814400000000.1	x^12 - 2x^11 + 4x^10 + 10x^9 - 5x^8 - 4x^7 + 8x^6 + 4x^5 - 5x^4 - 10x^3 + 4x^2 + 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 7^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.7608796557869056.11	x^12 + 4x^10 + 5x^8 - 12x^6 - 25x^4 + 4x^2 + 49	\( 2^{32}\cdot 11^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.14889840956932096.11	x^12 + 11x^8 - 6x^6 + 38x^4 - 2x^2 + 9	\( 2^{24}\cdot 31^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.20542695432781824.4	x^12 + 3x^8 + 4x^6 + 21x^4 + 1	\( 2^{32}\cdot 3^{14} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.46221064723759104.9	x^12 - 3x^4 + 4	\( 2^{30}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.54742762016210944.33	x^12 + 6x^10 - 4x^9 - 10x^8 - 28x^7 - 72x^6 - 4x^5 + 65x^4 + 164x^3 + 282x^2 + 144x + 108	\( 2^{26}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.57541523968884736.2	x^12 + 4x^8 + 9x^4 + 4	\( 2^{28}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.82170781731127296.42	x^12 - 3x^10 + 18x^8 - 8x^6 + 120x^4 + 72x^2 + 16	\( 2^{34}\cdot 3^{14} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.131621703842267136.30	x^12 + 3x^10 + 6x^8 - 14x^6 - 12x^4 + 12x^2 + 16	\( 2^{22}\cdot 3^{22} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[8]$
12.0.131621703842267136.54	x^12 - 6x^10 + 15x^8 - 20x^6 + 51x^4 - 78x^2 + 49	\( 2^{22}\cdot 3^{22} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.184884258895036416.11	x^12 + 9x^8 + 24x^4 + 4	\( 2^{32}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.202060520306507776.25	x^12 + 4x^10 + 10x^8 + 80x^4 + 40x^2 + 36	\( 2^{32}\cdot 19^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.328683126924509184.21	x^12 + 3x^10 + 30x^8 + 84x^6 + 162x^4 + 126x^2 + 36	\( 2^{36}\cdot 3^{14} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.429496729600000000.9	x^12 + 12x^10 + 56x^8 + 128x^6 + 146x^4 + 72x^2 + 16	\( 2^{40}\cdot 5^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial
12.0.429496729600000000.14	x^12 - 6x^10 + 34x^8 - 96x^6 + 96x^4 + 64x^2 + 64	\( 2^{40}\cdot 5^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial
12.0.638686677648277504.5	x^12 + 8x^10 + 20x^8 - 104x^6 + 133x^4 - 8x^2 + 4	\( 2^{30}\cdot 29^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 2]$
12.0.808242081226031104.42	x^12 - 13x^10 + 64x^8 - 136x^6 + 200x^4 - 136x^2 + 64	\( 2^{34}\cdot 19^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$ (GRH)
12.0.875884192259375104.4	x^12 + 12x^10 - 8x^9 + 85x^8 - 136x^7 + 416x^6 - 544x^5 + 821x^4 - 528x^3 + 132x^2 + 16x + 1	\( 2^{30}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 4]$
12.0.875884192259375104.27	x^12 + 12x^8 + 61x^4 + 64	\( 2^{30}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[6]$
12.0.875884192259375104.75	x^12 - 6x^10 + 13x^8 + 117x^4 + 130x^2 + 169	\( 2^{30}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.920664383502155776.7	x^12 + x^8 + 48x^4 + 64	\( 2^{32}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 4]$
12.0.920664383502155776.26	x^12 - 16x^10 + 97x^8 - 308x^6 + 847x^4 - 2904x^2 + 5929	\( 2^{32}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.1139747622353895424.48	x^12 - 2x^10 + 33x^8 - 20x^6 + 380x^4 + 1444	\( 2^{26}\cdot 19^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[12]$
12.0.1313840315232157696.93	x^12 - 10x^10 + 25x^8 - 322x^6 + 1748x^4 + 1058x^2 + 13225	\( 2^{24}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$ (GRH)
12.0.2098185530867974144.18	x^12 - 6x^11 + 38x^10 - 126x^9 + 425x^8 - 892x^7 + 2024x^6 - 2840x^5 + 4601x^4 - 4210x^3 + 4218x^2 - 2214x + 513	\( 2^{22}\cdot 29^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.2105947261476274176.102	x^12 + 12x^10 + 60x^8 + 160x^6 + 276x^4 + 336x^2 + 256	\( 2^{26}\cdot 3^{22} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.2554746710593110016.19	x^12 - 4x^10 + 17x^8 - 88x^6 + 304x^4 + 32x^2 + 4	\( 2^{32}\cdot 29^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 4]$
12.0.3232968324904124416.20	x^12 - 6x^10 + 20x^8 + 8x^6 + 26x^4 - 12x^2 + 64	\( 2^{36}\cdot 19^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.3503536769037500416.24	x^12 - 3x^8 + 16x^4 + 64	\( 2^{32}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[12]$
12.0.3503536769037500416.87	x^12 + 2x^10 + 13x^8 - 104x^6 + 325x^4 - 390x^2 + 169	\( 2^{32}\cdot 13^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 4]$
12.0.5255361260928630784.3	x^12 + 9x^8 + 4x^4 + 4	\( 2^{26}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.5255361260928630784.5	x^12 - 2x^10 - 5x^8 - 14x^6 + 54x^4 + 28x^2 + 4	\( 2^{26}\cdot 23^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$
12.0.5307132620553846784.6	x^12 + 2x^10 + 2x^8 - 16x^6 + 58x^4 - 28x^2 + 4	\( 2^{40}\cdot 13^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.5307132620553846784.7	x^12 - 10x^10 + 74x^8 - 80x^6 + 58x^4 - 20x^2 + 4	\( 2^{40}\cdot 13^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$
12.0.8392742123471896576.63	x^12 + 18x^10 + 145x^8 + 696x^6 + 2088x^4 + 3712x^2 + 3364	\( 2^{24}\cdot 29^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$ (GRH)
12.0.11832592569282330624.2	x^12 + 6x^4 + 4	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial (GRH)
12.0.11832592569282330624.3	x^12 + 36x^8 + 6x^4 + 4	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial (GRH)
12.0.11832592569282330624.16	x^12 - 6x^8 - 6x^4 + 64	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial (GRH)
12.0.11832592569282330624.17	x^12 - 6x^8 + 48x^4 + 64	\( 2^{38}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	Trivial (GRH)
12.0.14309137159611744256.74	x^12 + 18x^10 + 143x^8 + 372x^6 + 1364x^4 - 3844x^2 + 8649	\( 2^{24}\cdot 31^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[4]$ (GRH)
12.0.47330370277129322496.54	x^12 - 12x^10 + 48x^8 - 64x^6 + 18x^4 - 72x^2 + 144	\( 2^{40}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[3]$ (GRH)
12.0.47330370277129322496.58	x^12 - 6x^10 + 18x^8 - 64x^6 + 72x^4 + 144x^2 + 144	\( 2^{40}\cdot 3^{16} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[3]$ (GRH)
12.4.56175242250280047049.1	x^12 - 3x^11 - 2x^10 + x^9 + 70x^8 - 92x^7 - 217x^6 + 260x^5 - 256x^4 + 162x^3 - 87x^2 + 2x + 1	\( 19^{6}\cdot 103^{6} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[8]$
12.0.58922520544137969664.1	x^12 + 4x^8 - 2x^4 + 4	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$ (GRH)
12.0.58922520544137969664.2	x^12 + 4x^8 + 174x^4 + 4	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$ (GRH)
12.0.58922520544137969664.12	x^12 - 10x^8 + 26x^4 + 64	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$ (GRH)
12.0.58922520544137969664.13	x^12 + 12x^8 + 136x^4 + 64	\( 2^{38}\cdot 11^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2]$ (GRH)
12.0.72943847830649307136.115	x^12 - 16x^10 + 92x^8 - 68x^6 + 25x^4 - 1508x^2 + 2500	\( 2^{32}\cdot 19^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 12]$ (GRH)
12.0.72943847830649307136.161	x^12 - 16x^10 + 26x^8 + 3724x^4 + 2888x^2 + 12996	\( 2^{32}\cdot 19^{8} \)	$C_4^2:C_3:C_2$ (as 12T65)	$[2, 4]$ (GRH)