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 1900)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.451992187175.1	x^12 - x^11 + 4x^10 + x^9 - x^8 + 12x^7 - 9x^6 + 12x^5 - x^4 + x^3 + 4x^2 - x + 1	\( -\,5^{2}\cdot 23^{5}\cdot 53^{2} \)	12T223	Trivial
12.2.1173531982847.1	x^12 - 4x^10 - 5x^9 + 8x^8 + 13x^7 - x^6 - 17x^5 - 3x^4 + 8x^3 + 6x^2 - 4x - 1	\( -\,7^{2}\cdot 23^{5}\cdot 61^{2} \)	12T223	Trivial
12.4.30673806350409.1	x^12 - x^11 - 5x^10 + 8x^8 + 20x^7 - 16x^6 - 13x^5 - 16x^4 + 28x^3 - 12x^2 + 4x - 1	\( 3^{7}\cdot 107^{5} \)	12T223	Trivial
12.0.75002423891200.1	x^12 - 3x^11 + 10x^10 - 10x^9 + 25x^8 - 20x^7 + 31x^6 - 20x^5 + 25x^4 - 10x^3 + 10x^2 - 3x + 1	\( 2^{8}\cdot 5^{2}\cdot 13^{2}\cdot 37^{5} \)	12T223	Trivial
12.4.75002423891200.1	x^12 - 5x^11 + 7x^10 + 9x^9 - 37x^8 + 26x^7 + 31x^6 - 48x^5 + 7x^4 + 7x^3 - 4x + 1	\( 2^{8}\cdot 5^{2}\cdot 13^{2}\cdot 37^{5} \)	12T223	Trivial
12.4.110790562723072.1	x^12 - x^11 + 2x^10 + x^9 + 4x^8 + x^7 - 13x^6 + 10x^5 + 6x^4 - 12x^3 - 20x^2 + 16x + 4	\( 2^{8}\cdot 37^{5}\cdot 79^{2} \)	12T223	Trivial
12.4.128403847759104.1	x^12 - 3x^11 + 4x^10 - 6x^9 + x^8 - 2x^7 + 13x^6 - 2x^5 + x^4 - 6x^3 + 4x^2 - 3x + 1	\( 2^{8}\cdot 3^{7}\cdot 47^{5} \)	12T223	Trivial
12.2.172927194497024.1	x^12 - 2x^10 - x^8 + 24x^6 + 7x^4 - 22x^2 - 11	\( -\,2^{30}\cdot 11^{5} \)	12T223	Trivial
12.2.172927194497024.2	x^12 + 2x^10 - x^8 - 24x^6 + 7x^4 + 22x^2 - 11	\( -\,2^{30}\cdot 11^{5} \)	12T223	Trivial
12.2.172927194497024.3	x^12 - 4x^11 + 8x^10 - 12x^9 + 18x^8 - 36x^7 + 64x^6 - 72x^5 + 48x^4 - 8x^3 - 8x^2 - 8x - 2	\( -\,2^{30}\cdot 11^{5} \)	12T223	Trivial
12.2.172927194497024.4	x^12 - 4x^11 + 12x^10 - 24x^9 + 30x^8 - 36x^7 + 28x^6 - 16x^5 - 6x^4 + 8x^3 - 4x^2 - 2	\( -\,2^{30}\cdot 11^{5} \)	12T223	Trivial
12.0.252259850937825.1	x^12 - 2x^11 + 5x^10 - 7x^9 + 10x^8 - 11x^7 + 9x^6 - 22x^5 + 40x^4 - 56x^3 + 80x^2 - 64x + 64	\( 3^{2}\cdot 5^{2}\cdot 257^{5} \)	12T223	$[2]$
12.4.252259850937825.1	x^12 - 4x^11 + 4x^10 + x^9 - 14x^8 + 25x^7 - 29x^5 + 30x^4 - 7x^3 - 22x^2 + 15x - 5	\( 3^{2}\cdot 5^{2}\cdot 257^{5} \)	12T223	Trivial
12.4.276064257153681.1	x^12 - 3x^11 + 8x^10 - 12x^9 + x^8 + 16x^7 - 26x^6 + 19x^5 - 14x^4 + 12x^3 + x^2 - x + 1	\( 3^{9}\cdot 107^{5} \)	12T223	Trivial
12.4.494429307838137.1	x^12 - 4x^11 + 9x^10 - 16x^9 + 16x^8 + 10x^7 - 56x^6 + 107x^5 - 150x^4 + 151x^3 - 91x^2 + 27x - 3	\( 3^{2}\cdot 7^{2}\cdot 257^{5} \)	12T223	Trivial
12.4.494429307838137.2	x^12 - 3x^11 + 9x^9 - 4x^8 - 15x^7 + 4x^6 + 12x^5 - 3x^4 - x^3 - 2x^2 + 2x + 1	\( 3^{2}\cdot 7^{2}\cdot 257^{5} \)	12T223	Trivial
12.0.601013506097152.1	x^12 - x^11 + 5x^10 - 4x^9 + 27x^8 - 23x^7 + 58x^6 - 9x^5 + 65x^4 + 2x^3 + 59x^2 + 25x + 25	\( 2^{14}\cdot 23^{2}\cdot 37^{5} \)	12T223	Trivial
12.0.601013506097152.2	x^12 - 8x^10 + 29x^8 - 62x^6 + 85x^4 - 74x^2 + 37	\( 2^{14}\cdot 23^{2}\cdot 37^{5} \)	12T223	Trivial
12.2.797345646116864.1	x^12 - 6x^10 + 9x^8 - 14x^4 + 52x^2 - 26	\( -\,2^{31}\cdot 13^{5} \)	12T223	Trivial
12.2.797345646116864.4	x^12 - 2x^11 + 2x^10 + 7x^9 - 25x^8 + 48x^7 - 68x^6 + 86x^5 - 115x^4 + 110x^3 - 58x^2 + 13x - 1	\( -\,2^{31}\cdot 13^{5} \)	12T223	Trivial
12.2.838860800000000.4	x^12 + 2x^10 + 9x^8 - 8x^6 - 22x^4 - 12x^2 - 2	\( -\,2^{31}\cdot 5^{8} \)	12T223	Trivial
12.8.955486500241408.1	x^12 - 10x^10 + 35x^8 - 10x^7 - 68x^6 + 34x^5 + 73x^4 - 40x^3 - 28x^2 + 16x - 1	\( 2^{14}\cdot 29^{2}\cdot 37^{5} \)	12T223	Trivial
12.2.1376479908724736.3	x^12 - 8x^9 - 7x^8 + 4x^7 + 32x^6 + 48x^5 - 67x^4 - 20x^3 - 12x^2 + 56x - 19	\( -\,2^{26}\cdot 29^{5} \)	12T223	Trivial
12.2.1376479908724736.4	x^12 + 4x^10 - 12x^9 + 13x^8 - 24x^7 + 62x^6 - 124x^5 + 142x^4 - 92x^3 + 32x^2 - 4x - 2	\( -\,2^{26}\cdot 29^{5} \)	12T223	Trivial
12.8.1503016511170041.1	x^12 - 3x^11 - 2x^10 + 9x^9 - 14x^8 + 31x^7 + 22x^6 - 77x^5 + 28x^4 + 21x^3 - 14x^2 + 1	\( 3^{7}\cdot 7^{2}\cdot 107^{5} \)	12T223	Trivial
12.2.1874584905187328.1	x^12 - 4x^10 + 8x^8 - 19x^4 - 76x^2 - 38	\( -\,2^{21}\cdot 19^{7} \)	12T223	Trivial
12.2.2766835111952384.1	x^12 + 6x^10 + 11x^8 + 4x^6 - 15x^4 - 22x^2 - 11	\( -\,2^{34}\cdot 11^{5} \)	12T223	Trivial
12.2.2766835111952384.2	x^12 + 2x^10 + x^8 - 9x^4 - 22x^2 - 11	\( -\,2^{34}\cdot 11^{5} \)	12T223	Trivial
12.2.2766835111952384.3	x^12 - 6x^10 + 11x^8 - 4x^6 - 15x^4 + 22x^2 - 11	\( -\,2^{34}\cdot 11^{5} \)	12T223	Trivial
12.2.2766835111952384.4	x^12 - 2x^10 + x^8 - 9x^4 + 22x^2 - 11	\( -\,2^{34}\cdot 11^{5} \)	12T223	Trivial
12.2.3355443200000000.1	x^12 + 6x^10 + 6x^8 - 16x^6 - 37x^4 - 26x^2 - 8	\( -\,2^{33}\cdot 5^{8} \)	12T223	Trivial
12.2.3355443200000000.7	x^12 - 3x^10 + 4x^8 + 2x^6 + 3x^4 + 3x^2 - 2	\( -\,2^{33}\cdot 5^{8} \)	12T223	Trivial
12.8.3821946000965632.1	x^12 - 4x^11 + 2x^10 + 16x^9 - 38x^8 + 2x^7 + 68x^6 - 50x^5 + 4x^4 + 40x^3 - 26x^2 - 4x + 2	\( 2^{16}\cdot 29^{2}\cdot 37^{5} \)	12T223	Trivial
12.2.5317382113329152.2	x^12 + 6x^10 + 21x^8 + 24x^6 - 26x^4 + 76x^2 - 38	\( -\,2^{31}\cdot 19^{5} \)	12T223	Trivial
12.2.5317382113329152.3	x^12 - 9x^10 - 6x^9 + 31x^8 + 16x^7 + 16x^6 - 48x^5 - 82x^4 + 2x^2 + 12x - 22	\( -\,2^{31}\cdot 19^{5} \)	12T223	Trivial
12.8.5327067769558425.1	x^12 - 6x^10 - 8x^9 + 72x^7 - 59x^6 - 128x^5 + 204x^4 - 56x^3 - 36x^2 + 14x + 1	\( 3^{2}\cdot 5^{2}\cdot 11^{5}\cdot 43^{5} \)	12T223	Trivial
12.2.5505919634898944.3	x^12 + 6x^10 + 5x^8 - 20x^6 - 57x^4 - 58x^2 - 29	\( -\,2^{28}\cdot 29^{5} \)	12T223	Trivial
12.2.5505919634898944.8	x^12 - 6x^10 + 5x^8 + 20x^6 - 57x^4 + 58x^2 - 29	\( -\,2^{28}\cdot 29^{5} \)	12T223	Trivial
12.2.7498339620749312.1	x^12 + 4x^10 + 8x^8 - 19x^4 + 76x^2 - 38	\( -\,2^{23}\cdot 19^{7} \)	12T223	Trivial
12.2.11555266180939776.5	x^12 - 3x^10 + 12x^8 - 28x^6 - 39x^4 - 15x^2 - 4	\( -\,2^{28}\cdot 3^{16} \)	12T223	Trivial
12.2.11555266180939776.10	x^12 + 3x^10 + 12x^8 + 28x^6 - 39x^4 + 15x^2 - 4	\( -\,2^{28}\cdot 3^{16} \)	12T223	Trivial
12.2.12757530337869824.5	x^12 + 13x^10 + 63x^8 + 128x^6 + 66x^4 - 78x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	$[2]$
12.2.12757530337869824.6	x^12 - 5x^10 + 9x^8 - 28x^6 + 74x^4 - 78x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	Trivial
12.2.12757530337869824.8	x^12 + 6x^10 + 9x^8 - 14x^4 - 52x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	Trivial
12.2.12757530337869824.9	x^12 - x^10 - x^8 - 8x^6 - 22x^4 - 26x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	Trivial
12.2.12757530337869824.12	x^12 + x^10 - x^8 + 8x^6 - 22x^4 + 26x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	Trivial
12.2.12757530337869824.14	x^12 - 13x^10 + 63x^8 - 128x^6 + 66x^4 + 78x^2 - 26	\( -\,2^{35}\cdot 13^{5} \)	12T223	Trivial
12.0.12906109962551296.1	x^12 - 6x^9 + 18x^8 - 2x^7 - 28x^6 + 4x^5 + 94x^4 + 66x^3 - 242x^2 - 82x + 439	\( 2^{22}\cdot 79^{5} \)	12T223	$[2]$
12.2.13421772800000000.5	x^12 - 6x^10 + 6x^8 + 16x^6 - 37x^4 + 26x^2 - 8	\( -\,2^{35}\cdot 5^{8} \)	12T223	Trivial
12.2.13421772800000000.10	x^12 + 3x^10 + 4x^8 - 2x^6 + 3x^4 - 3x^2 - 2	\( -\,2^{35}\cdot 5^{8} \)	12T223	Trivial