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 1393)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.1242241378677.1	x^12 - 4x^11 + 5x^10 + 2x^9 - 4x^8 - 13x^7 + 24x^6 - 4x^5 - 8x^4 - 5x^3 + 12x^2 - 6x + 1	\( 3^{6}\cdot 13\cdot 107^{4} \)	12T240	Trivial
12.2.5113062984375.1	x^12 - 2x^11 + 3x^10 - x^9 + x^8 - 3x^7 + 7x^6 - 9x^5 + 4x^4 - 2x^3 - 2x^2 - x - 1	\( -\,3^{4}\cdot 5^{6}\cdot 19^{4}\cdot 31 \)	12T240	Trivial
12.0.5828978776869.1	x^12 - 3x^11 + x^10 + 8x^9 - 10x^8 - 5x^7 + 11x^6 + x^5 + 2x^4 + 5x^3 + 4x^2 + 3x + 1	\( 3^{6}\cdot 61\cdot 107^{4} \)	12T240	Trivial
12.2.10307264000000.1	x^12 - 3x^10 - 6x^9 - 7x^8 - 6x^7 - 2x^6 - 6x^5 - 7x^4 - 6x^3 - 3x^2 + 1	\( -\,2^{12}\cdot 5^{6}\cdot 11^{5} \)	12T240	Trivial
12.4.10600084000000.1	x^12 - 2x^11 - x^10 + 5x^9 - 6x^8 + x^7 + 6x^6 - 7x^5 + 8x^4 - x^3 - 7x^2 + 5x - 1	\( 2^{8}\cdot 5^{6}\cdot 11^{4}\cdot 181 \)	12T240	Trivial
12.0.12239876000000.1	x^12 - 4x^8 - 2x^7 + 3x^6 + 9x^4 + 4x^3 + 5x^2 + 2x + 1	\( 2^{8}\cdot 5^{6}\cdot 11^{5}\cdot 19 \)	12T240	Trivial
12.4.16658689078125.1	x^12 - 2x^11 - 3x^10 + 9x^9 + x^8 - 15x^7 + 20x^5 - 6x^4 - 13x^3 + 7x^2 + x - 1	\( 3^{4}\cdot 5^{6}\cdot 19^{4}\cdot 101 \)	12T240	Trivial
12.0.17803456000000.1	x^12 - 2x^11 + x^10 + 7x^8 - 6x^7 - 3x^6 + 12x^5 + 6x^4 - 4x^3 + 2x^2 + 4x + 1	\( 2^{12}\cdot 5^{6}\cdot 11^{4}\cdot 19 \)	12T240	Trivial
12.0.86029994295296.1	x^12 - 2x^11 + 2x^10 + 6x^9 - 4x^8 - 18x^7 + 4x^6 + 18x^5 - 4x^4 - 6x^3 + 2x^2 + 2x + 1	\( 2^{22}\cdot 29^{5} \)	12T240	Trivial
12.0.344119977181184.14	x^12 + 2x^10 - 8x^9 + 2x^8 - 12x^7 + 18x^6 + 8x^5 + 17x^4 - 20x^3 - 28x^2 - 16x + 40	\( 2^{24}\cdot 29^{5} \)	12T240	Trivial
12.0.361102068154368.2	x^12 - 6x^10 + 15x^8 - 18x^6 + 9x^4 + 8	\( 2^{23}\cdot 3^{16} \)	12T240	Trivial
12.2.431935667044352.1	x^12 - 4x^10 + 11x^8 - 8x^7 + 4x^6 - 11x^4 - 8x^3 - 8x^2 - 8x - 1	\( -\,2^{26}\cdot 23^{5} \)	12T240	Trivial
12.2.559724432982016.3	x^12 + 4x^10 - 36x^6 - 60x^4 - 24x^2 - 4	\( -\,2^{32}\cdot 19^{4} \)	12T240	Trivial
12.2.559724432982016.9	x^12 - 4x^10 + 36x^6 - 60x^4 + 24x^2 - 4	\( -\,2^{32}\cdot 19^{4} \)	12T240	Trivial
12.2.863871334088704.9	x^12 - 4x^11 + 16x^9 - 2x^8 - 16x^7 - 16x^6 + 48x^5 + 4x^4 - 16x^3 - 32x^2 + 32x - 8	\( -\,2^{27}\cdot 23^{5} \)	12T240	Trivial
12.2.863871334088704.10	x^12 - 4x^11 + 4x^10 + 12x^9 - 24x^8 - 32x^7 + 86x^6 + 32x^5 - 119x^4 - 4x^3 + 50x^2 - 20x + 2	\( -\,2^{27}\cdot 23^{5} \)	12T240	Trivial
12.0.1376479908724736.2	x^12 - 6x^11 + 20x^10 - 40x^9 + 62x^8 - 76x^7 + 80x^6 - 80x^5 + 81x^4 - 74x^3 + 48x^2 - 16x + 2	\( 2^{26}\cdot 29^{5} \)	12T240	Trivial
12.0.1376479908724736.9	x^12 - 4x^11 + 2x^10 + 20x^9 - 17x^8 - 96x^7 + 188x^6 + 80x^5 - 381x^4 + 36x^3 + 378x^2 - 228x + 37	\( 2^{26}\cdot 29^{5} \)	12T240	$[2]$
12.2.1727742668177408.3	x^12 - 2x^11 + 5x^10 - 6x^9 + 21x^8 + 42x^6 - 4x^5 + 20x^4 - 36x^3 - 10x^2 - 36x - 2	\( -\,2^{28}\cdot 23^{5} \)	12T240	Trivial
12.2.1727742668177408.5	x^12 - 2x^10 + 8x^8 - 8x^7 + 12x^6 + 8x^5 - 2x^4 + 16x^3 + 4x^2 + 8x + 4	\( -\,2^{28}\cdot 23^{5} \)	12T240	Trivial
12.2.1727742668177408.6	x^12 - 2x^11 + x^10 + 20x^7 - 10x^6 - 8x^5 + 2x^4 + 12x^3 + 18x^2 + 8x + 4	\( -\,2^{28}\cdot 23^{5} \)	12T240	$[2]$
12.0.1727742668177408.1	x^12 - 4x^11 + 16x^10 - 40x^9 + 63x^8 - 68x^7 + 16x^6 + 28x^5 + 17x^4 - 16x^3 - 20x^2 + 4x + 7	\( 2^{28}\cdot 23^{5} \)	12T240	$[2]$
12.4.1727742668177408.1	x^12 - 4x^11 + 6x^10 - 32x^7 + 82x^6 - 44x^5 - 95x^4 + 8x^3 + 84x^2 - 4	\( 2^{28}\cdot 23^{5} \)	12T240	Trivial
12.2.2238897731928064.8	x^12 - 10x^10 + 39x^8 - 76x^6 + 79x^4 - 34x^2 - 1	\( -\,2^{34}\cdot 19^{4} \)	12T240	Trivial
12.2.2238897731928064.11	x^12 + 2x^10 + 7x^8 - 8x^6 - 13x^4 - 2x^2 - 1	\( -\,2^{34}\cdot 19^{4} \)	12T240	Trivial
12.2.2238897731928064.12	x^12 - 2x^10 + 7x^8 + 8x^6 - 13x^4 + 2x^2 - 1	\( -\,2^{34}\cdot 19^{4} \)	12T240	Trivial
12.2.2238897731928064.15	x^12 + 10x^10 + 39x^8 + 76x^6 + 79x^4 + 34x^2 - 1	\( -\,2^{34}\cdot 19^{4} \)	12T240	Trivial
12.2.2282521714753536.12	x^12 + 6x^10 + 9x^8 - 16x^6 + 3x^4 - 6x^2 - 1	\( -\,2^{32}\cdot 3^{12} \)	12T240	Trivial
12.2.2282521714753536.16	x^12 - 6x^10 + 9x^8 + 16x^6 + 3x^4 + 6x^2 - 1	\( -\,2^{32}\cdot 3^{12} \)	12T240	Trivial
12.0.3249918613389312.1	x^12 - 6x^11 + 21x^10 - 40x^9 + 48x^8 - 18x^7 - 2x^6 - 6x^5 + 78x^4 - 48x^3 + 3x^2 + 54x + 33	\( 2^{23}\cdot 3^{18} \)	12T240	$[2]$
12.4.3455485336354816.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 13x^8 + 20x^7 - 10x^6 + 16x^5 - 30x^4 - 28x^3 - 12x^2 - 8x - 2	\( 2^{29}\cdot 23^{5} \)	12T240	Trivial
12.0.3455485336354816.1	x^12 - 4x^10 - 4x^9 + 15x^8 + 12x^7 - 28x^5 - 15x^4 + 4x^3 + 24x^2 + 16x + 7	\( 2^{29}\cdot 23^{5} \)	12T240	Trivial
12.2.4477795463856128.2	x^12 + 2x^8 - 8x^6 - 12x^4 - 16x^2 - 8	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.2.4477795463856128.3	x^12 + 2x^8 + 8x^6 - 12x^4 + 16x^2 - 8	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.2.4477795463856128.8	x^12 + 4x^10 + 6x^8 - 8x^4 - 8x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.2.4477795463856128.9	x^12 + 4x^10 + 8x^8 + 8x^6 + 2x^4 - 4x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.2.4477795463856128.15	x^12 - 4x^10 + 8x^8 - 8x^6 + 2x^4 + 4x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.2.4477795463856128.17	x^12 - 4x^10 + 6x^8 - 8x^4 + 8x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	12T240	Trivial
12.0.5505919634898944.3	x^12 - 4x^10 + 47x^8 - 120x^6 + 203x^4 - 116x^2 + 29	\( 2^{28}\cdot 29^{5} \)	12T240	Trivial
12.0.5505919634898944.15	x^12 - 4x^11 + 16x^9 + x^8 - 28x^7 - 92x^6 + 216x^5 + 8x^4 - 456x^3 + 696x^2 - 464x + 116	\( 2^{28}\cdot 29^{5} \)	12T240	$[2]$
12.0.5777633090469888.10	x^12 + 6x^10 + 15x^8 + 18x^6 + 9x^4 + 8	\( 2^{27}\cdot 3^{16} \)	12T240	Trivial
12.0.6169767367606272.11	x^12 - 9x^10 - 12x^9 + 45x^8 + 90x^7 - 123x^6 - 324x^5 + 306x^4 + 492x^3 - 486x^2 - 252x + 291	\( 2^{16}\cdot 3^{23} \)	12T240	Trivial
12.0.6847565144260608.5	x^12 - 2x^10 + 9x^8 - 8x^6 + 7x^4 - 6x^2 + 3	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.7	x^12 + 10x^10 + 29x^8 + 20x^6 + 15x^4 - 6x^2 + 3	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.9	x^12 + 2x^10 + 9x^8 + 8x^6 + 7x^4 + 6x^2 + 3	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.10	x^12 - 10x^10 + 29x^8 - 20x^6 + 15x^4 + 6x^2 + 3	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.16	x^12 + 4x^10 - 12x^9 - 2x^8 - 24x^7 - 4x^6 + 48x^5 + 62x^4 + 24x^3 - 4x^2 + 6	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.19	x^12 + 4x^10 - 20x^6 + 28x^4 - 24x^2 + 12	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.22	x^12 - 4x^10 + 20x^6 + 28x^4 + 24x^2 + 12	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial
12.0.6847565144260608.31	x^12 - 4x^10 - 4x^9 + 10x^8 + 8x^7 - 16x^6 + 122x^4 + 248x^3 + 244x^2 + 128x + 34	\( 2^{32}\cdot 3^{13} \)	12T240	Trivial