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 4994)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.130563704896.1	x^12 - x^10 + x^8 - x^6 + 3x^4 - 3x^2 + 1	\( 2^{6}\cdot 31^{4}\cdot 47^{2} \)	12T226	Trivial
12.0.141863715904.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 6x^8 - 9x^7 + 9x^6 - 4x^5 + x^3 + 2x^2 - 3x + 1	\( 2^{6}\cdot 23^{4}\cdot 89^{2} \)	12T226	Trivial
12.0.413788573696.2	x^12 + x^10 + 2x^8 + 2x^6 + 2x^4 + 2x^2 + 1	\( 2^{12}\cdot 19^{2}\cdot 23^{4} \)	12T226	Trivial
12.0.800200022521.1	x^12 - x^11 + x^10 + 2x^9 - 2x^8 + 5x^7 - 2x^6 + x^5 + 5x^4 - 5x^3 + 4x^2 - 2x + 1	\( 19^{2}\cdot 23^{4}\cdot 89^{2} \)	12T226	Trivial
12.4.2792839250041.1	x^12 - 4x^11 + 6x^10 - 8x^9 + 6x^8 + 7x^7 - 8x^6 + 4x^5 - 2x^4 - 10x^3 + 3x^2 + 5x + 1	\( 31^{4}\cdot 37^{2}\cdot 47^{2} \)	12T226	Trivial
12.4.3219756519424.1	x^12 - 3x^10 + x^8 + 4x^6 - 3x^4 - 2x^2 + 1	\( 2^{12}\cdot 23^{4}\cdot 53^{2} \)	12T226	Trivial
12.4.11264239538176.1	x^12 - x^10 - 10x^8 - x^6 + 2x^4 - 5x^2 + 1	\( 2^{12}\cdot 229^{4} \)	12T226	Trivial
12.4.17868678762496.2	x^12 - 6x^11 + 15x^10 - 20x^9 + 10x^8 + 14x^7 - 29x^6 + 20x^5 - x^4 - 8x^3 + 4x^2 + 1	\( 2^{12}\cdot 257^{4} \)	12T226	Trivial
12.4.21783213228001.1	x^12 - 3x^11 + 3x^10 - 4x^9 + 5x^8 - 5x^7 + 7x^6 - 5x^5 + 5x^4 - 4x^3 + 3x^2 - 3x + 1	\( 89^{2}\cdot 229^{4} \)	12T226	Trivial
12.0.45056958152704.1	x^12 + 3x^10 + 6x^8 + 7x^6 - 5x^4 + 4	\( 2^{14}\cdot 229^{4} \)	12T226	$[2]$
12.4.45056958152704.1	x^12 + 3x^10 + 5x^8 + 2x^6 + x^4 - 5x^2 + 1	\( 2^{14}\cdot 229^{4} \)	12T226	Trivial
12.0.47464824438784.4	x^12 + x^10 + x^8 - 8x^6 + 5x^4 + x^2 + 1	\( 2^{26}\cdot 29^{4} \)	12T226	Trivial
12.0.47464824438784.11	x^12 - x^10 + x^4 + 3x^2 + 4	\( 2^{26}\cdot 29^{4} \)	12T226	Trivial
12.4.93105979932736.1	x^12 - x^11 - x^10 + 2x^9 - 2x^8 - x^7 + 2x^6 - x^5 - 2x^4 + 2x^3 - x^2 - x + 1	\( 2^{6}\cdot 23^{2}\cdot 229^{4} \)	12T226	Trivial
12.8.118034839699456.1	x^12 - 4x^11 + x^10 + 14x^9 - 20x^8 - 4x^7 + 31x^6 - 24x^5 - 12x^4 + 26x^3 + x^2 - 8x - 1	\( 2^{16}\cdot 31^{2}\cdot 37^{4} \)	12T226	Trivial
12.0.122668560941056.4	x^12 + x^10 + 6x^8 - 6x^6 + 7x^4 - 9x^2 + 4	\( 2^{32}\cdot 13^{4} \)	12T226	Trivial
12.0.122668560941056.11	x^12 - x^10 + 6x^8 + 6x^6 + 7x^4 + 9x^2 + 4	\( 2^{32}\cdot 13^{4} \)	12T226	Trivial
12.0.295862291619904.1	x^12 + 9x^10 + 35x^8 + 75x^6 + 87x^4 + 45x^2 + 4	\( 2^{6}\cdot 41^{2}\cdot 229^{4} \)	12T226	$[2]$
12.4.295862291619904.1	x^12 - 5x^9 - 5x^8 + 5x^7 - 24x^6 + 5x^5 - 5x^4 - 5x^3 + 1	\( 2^{6}\cdot 41^{2}\cdot 229^{4} \)	12T226	Trivial
12.0.323921668734976.8	x^12 + x^8 + 2x^6 - 4x^2 + 4	\( 2^{26}\cdot 13^{6} \)	12T226	Trivial
12.0.323921668734976.19	x^12 + 2x^10 - 4x^6 + 4x^4 + 16	\( 2^{26}\cdot 13^{6} \)	12T226	Trivial
12.4.334165419556864.1	x^12 - 3x^10 - 12x^9 - 2x^8 + 44x^7 + 53x^6 - 22x^5 - 60x^4 - 22x^3 + 7x^2 + 6x + 1	\( 2^{16}\cdot 7^{2}\cdot 101^{4} \)	12T226	Trivial
12.8.372423919730944.1	x^12 - 5x^10 + 3x^8 + 11x^6 - 5x^4 - 4x^2 + 1	\( 2^{8}\cdot 23^{2}\cdot 229^{4} \)	12T226	Trivial
12.0.388792267809856.1	x^12 - 3x^10 + 11x^8 - 17x^6 + 23x^4 - 15x^2 + 4	\( 2^{6}\cdot 47^{2}\cdot 229^{4} \)	12T226	$[2]$
12.0.388792267809856.2	x^12 + 4x^10 + 7x^8 + 7x^6 + 8x^4 + x^2 + 4	\( 2^{6}\cdot 47^{2}\cdot 229^{4} \)	12T226	$[2]$
12.8.413183351455744.1	x^12 - 2x^11 - 4x^10 + 12x^9 + 10x^8 - 34x^7 - 20x^6 + 48x^5 + 24x^4 - 28x^3 - 14x^2 + 4x + 2	\( 2^{18}\cdot 29^{2}\cdot 37^{4} \)	12T226	Trivial
12.8.464165997318144.1	x^12 - 4x^11 + 3x^10 + 10x^9 - 32x^8 + 46x^7 + x^6 - 102x^5 + 94x^4 + 28x^3 - 65x^2 + 22x - 1	\( 2^{12}\cdot 3^{2}\cdot 11^{2}\cdot 101^{4} \)	12T226	Trivial
12.0.472139358797824.1	x^12 + 4x^10 - 4x^9 + 11x^8 + 4x^7 + 60x^6 + 52x^5 + 111x^4 + 84x^3 + 128x^2 + 56x + 29	\( 2^{18}\cdot 31^{2}\cdot 37^{4} \)	12T226	$[2]$
12.4.490674243764224.1	x^12 + x^10 + x^8 + 2x^6 - 3x^4 - 5x^2 + 1	\( 2^{34}\cdot 13^{4} \)	12T226	Trivial
12.0.490674243764224.4	x^12 - x^10 + x^8 - 2x^6 - 3x^4 + 5x^2 + 1	\( 2^{34}\cdot 13^{4} \)	12T226	Trivial
12.0.490674243764224.6	x^12 - 7x^10 + 26x^8 - 48x^6 + 50x^4 - 22x^2 + 4	\( 2^{34}\cdot 13^{4} \)	12T226	Trivial
12.0.490674243764224.12	x^12 + 5x^10 + 10x^8 + 8x^6 + 2x^4 + 2x^2 + 4	\( 2^{34}\cdot 13^{4} \)	12T226	Trivial
12.0.559724432982016.5	x^12 - 3x^10 + 6x^8 - 8x^6 + 10x^4 - 6x^2 + 4	\( 2^{32}\cdot 19^{4} \)	12T226	Trivial
12.0.559724432982016.8	x^12 + 5x^10 + 6x^8 - 4x^6 - 2x^4 + 6x^2 + 4	\( 2^{32}\cdot 19^{4} \)	12T226	Trivial
12.0.559724432982016.13	x^12 - 6x^10 + 20x^8 - 40x^6 + 54x^4 - 44x^2 + 16	\( 2^{32}\cdot 19^{4} \)	12T226	Trivial
12.0.559724432982016.15	x^12 - 3x^10 + 10x^8 - 16x^6 + 24x^4 - 24x^2 + 16	\( 2^{32}\cdot 19^{4} \)	12T226	Trivial
12.0.759437191020544.4	x^12 - x^10 + x^8 + 8x^6 + 5x^4 - x^2 + 1	\( 2^{30}\cdot 29^{4} \)	12T226	$[2]$
12.0.759437191020544.9	x^12 + x^10 + x^4 - 3x^2 + 4	\( 2^{30}\cdot 29^{4} \)	12T226	$[2]$
12.0.759437191020544.11	x^12 + 5x^10 + 16x^8 + 26x^6 + 26x^4 + 14x^2 + 4	\( 2^{30}\cdot 29^{4} \)	12T226	Trivial
12.0.759437191020544.14	x^12 - 7x^10 + 26x^8 - 52x^6 + 64x^4 - 40x^2 + 16	\( 2^{30}\cdot 29^{4} \)	12T226	Trivial
12.0.789298907447296.8	x^12 + 2x^10 - 12x^9 + 16x^8 - 16x^7 + 12x^6 + 8x^5 + 2x^4 - 24x^3 + 14x^2 - 4x + 2	\( 2^{24}\cdot 19^{6} \)	12T226	Trivial
12.0.789298907447296.17	x^12 - 12x^9 + x^8 + 48x^6 - 8x^5 - 21x^4 - 64x^3 + 16x^2 + 84x + 31	\( 2^{24}\cdot 19^{6} \)	12T226	Trivial
12.4.914039610015744.1	x^12 - 6x^8 - 3x^6 + 3x^4 + 4	\( 2^{18}\cdot 3^{20} \)	12T226	Trivial
12.0.914039610015744.5	x^12 - 6x^8 + 3x^6 + 3x^4 + 4	\( 2^{18}\cdot 3^{20} \)	12T226	Trivial
12.0.914039610015744.7	x^12 + 3x^8 - 6x^6 + 30x^4 + 4	\( 2^{18}\cdot 3^{20} \)	12T226	Trivial
12.0.1295686674939904.15	x^12 + x^8 - 2x^6 + 4x^2 + 4	\( 2^{28}\cdot 13^{6} \)	12T226	Trivial
12.0.1295686674939904.22	x^12 - 2x^10 + 4x^6 + 4x^4 + 16	\( 2^{28}\cdot 13^{6} \)	12T226	Trivial
12.4.1336661678227456.1	x^12 - 6x^11 + 8x^10 + 6x^9 - 26x^8 + 18x^7 + 20x^6 - 36x^5 + 12x^4 + 20x^3 - 26x^2 + 12x - 2	\( 2^{18}\cdot 7^{2}\cdot 101^{4} \)	12T226	Trivial
12.4.1677721600000000.3	x^12 - 7x^10 + 10x^8 - 10x^6 + 15x^4 - 17x^2 + 4	\( 2^{32}\cdot 5^{8} \)	12T226	Trivial
12.0.1677721600000000.9	x^12 + 7x^10 + 10x^8 + 10x^6 + 15x^4 + 17x^2 + 4	\( 2^{32}\cdot 5^{8} \)	12T226	Trivial