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 559)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.73358639104.1	x^12 - 2x^11 + 2x^10 - 2x^9 + 6x^8 - 10x^7 + 10x^6 - 12x^5 + 17x^4 - 14x^3 + 8x^2 - 4x + 1	\( 2^{18}\cdot 23^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.194389282816.1	x^12 + x^10 + 4x^8 + 4x^6 + 4x^4 + x^2 + 1	\( 2^{12}\cdot 83^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.242095489024.1	x^12 - 4x^11 + 8x^10 - 12x^9 + 17x^8 - 30x^7 + 56x^6 - 74x^5 + 66x^4 - 40x^3 + 18x^2 - 6x + 1	\( 2^{18}\cdot 31^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.245635219456.1	x^12 - 4x^4 + 4	\( 2^{24}\cdot 11^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.389136420864.3	x^12 - x^10 - 4x^9 + 2x^7 + 5x^6 + 2x^5 - 4x^3 - x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.491300061184.1	x^12 - 2x^11 + 2x^10 - x^8 + 2x^7 - 2x^6 + 2x^5 - x^4 + 2x^2 - 2x + 1	\( 2^{18}\cdot 37^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.517110562816.1	x^12 - x^10 - x^8 + 6x^6 - x^4 - x^2 + 1	\( 2^{16}\cdot 53^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.741637881856.2	x^12 - 2x^10 + 4x^8 - 2x^6 + 4x^4 - 2x^2 + 1	\( 2^{20}\cdot 29^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.794123370496.1	x^12 - x^10 + 7x^8 + 2x^6 + 7x^4 - x^2 + 1	\( 2^{16}\cdot 59^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.860013262161.1	x^12 - x^11 + 2x^10 + 3x^9 + x^8 - 2x^7 + x^6 - 2x^5 + x^4 + 3x^3 + 2x^2 - x + 1	\( 3^{8}\cdot 107^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.896218169344.1	x^12 - 2x^9 - x^8 - 2x^7 + 2x^6 + 2x^5 - x^4 + 2x^3 + 1	\( 2^{18}\cdot 43^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.907401035776.1	x^12 + 4x^8 - 6x^6 + 4x^4 + 1	\( 2^{16}\cdot 61^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.1636073786281.1	x^12 - 7x^10 - 5x^9 + 20x^8 + 21x^7 - 16x^6 - 22x^5 + 10x^4 + 11x^3 + 7x^2 + 2x + 1	\( 11^{6}\cdot 31^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.1916696264704.3	x^12 + 2x^8 + x^4 + 4	\( 2^{26}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.2186423566336.2	x^12 + 4x^8 + 4x^4 + 4	\( 2^{24}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.2244531326976.1	x^12 - x^10 + 2x^8 - 6x^7 + 11x^6 - 6x^5 + 2x^4 - x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 17^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.3176493481984.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 25x^8 - 46x^7 + 59x^6 - 34x^5 + 20x^4 - 30x^3 + 24x^2 - 8x + 1	\( 2^{18}\cdot 59^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.3841600000000.1	x^12 - 2x^11 + x^10 - 6x^9 + 16x^8 - 18x^7 + 13x^6 - 6x^5 - 6x^4 + 12x^3 + x^2 - 4x - 1	\( 2^{12}\cdot 5^{8}\cdot 7^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.3930163511296.1	x^12 - 2x^10 - 5x^8 - 8x^6 + 23x^4 - 14x^2 + 1	\( 2^{28}\cdot 11^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.3930163511296.5	x^12 + 2x^10 - 5x^8 + 8x^6 + 23x^4 + 14x^2 + 1	\( 2^{28}\cdot 11^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.4694952902656.3	x^12 - x^8 - 8x^6 - x^4 + 1	\( 2^{24}\cdot 23^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.4694952902656.4	x^12 - x^8 + 8x^6 - x^4 + 1	\( 2^{24}\cdot 23^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.7055355940864.1	x^12 + x^10 + 11x^8 + 11x^6 + 20x^4 - 4x^2 + 4	\( 2^{12}\cdot 7^{6}\cdot 11^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.7496644000000.1	x^12 - x^11 - x^10 - 4x^9 - 3x^8 - 11x^7 + 10x^6 + 11x^5 - 3x^4 + 4x^3 - x^2 + x + 1	\( 2^{8}\cdot 5^{6}\cdot 37^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.7666785058816.2	x^12 + 2x^8 + 2x^6 + 2x^4 + 1	\( 2^{28}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.7666785058816.4	x^12 - 2x^10 + 11x^8 - 24x^6 + 30x^4 - 16x^2 + 4	\( 2^{28}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.8745694265344.6	x^12 + 10x^8 - 7x^4 + 4	\( 2^{26}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.8916100448256.3	x^12 - 12x^8 + 36x^4 + 4	\( 2^{24}\cdot 3^{12} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.11866206109696.2	x^12 - 6x^11 + 11x^10 - 2x^9 - 7x^8 - 12x^7 + 14x^6 + 28x^5 - 38x^4 + 24x^3 - 34x^2 + 20x + 2	\( 2^{24}\cdot 29^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.11866206109696.5	x^12 - 6x^11 + 19x^10 - 38x^9 + 53x^8 - 52x^7 + 38x^6 - 28x^5 + 34x^4 - 40x^3 + 30x^2 - 12x + 2	\( 2^{24}\cdot 29^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.13165366384921.1	x^12 - 3x^11 + 10x^10 - 11x^9 + 20x^8 - 3x^7 + 34x^6 - 2x^5 + 15x^4 + 53x^3 + 79x^2 + 5x + 1	\( 19^{6}\cdot 23^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.13763268972544.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 97x^8 - 154x^7 + 209x^6 - 232x^5 + 218x^4 - 162x^3 + 100x^2 - 42x + 14	\( 2^{12}\cdot 7^{6}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.14757890560000.1	x^12 + 2x^10 - x^8 + 24x^6 - x^4 + 2x^2 + 1	\( 2^{12}\cdot 5^{4}\cdot 7^{8} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.15494111297536.3	x^12 - 6x^10 + 17x^8 - 26x^6 + 14x^4 - 2x^2 + 1	\( 2^{24}\cdot 31^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.15494111297536.6	x^12 + 6x^10 + 17x^8 + 26x^6 + 14x^4 + 2x^2 + 1	\( 2^{24}\cdot 31^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.23533413765625.2	x^12 - 2x^11 - 6x^10 + 3x^9 + 13x^8 - x^7 - 15x^6 - x^5 + 13x^4 + 3x^3 - 6x^2 - 2x + 1	\( 5^{6}\cdot 197^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.25389989167104.4	x^12 + 6x^10 + 12x^8 + 10x^6 + 12x^4 + 6x^2 + 1	\( 2^{16}\cdot 3^{18} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.26214400000000.2	x^12 + 2x^8 + 33x^4 + 4	\( 2^{26}\cdot 5^{8} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.29721861554176.1	x^12 - 4x^11 + 2x^10 + 16x^9 - 44x^8 + 48x^7 - 6x^6 - 24x^5 + 6x^4 + 12x^3 - 4x^2 - 12x - 2	\( 2^{24}\cdot 11^{6} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.30667140235264.1	x^12 - 2x^10 - 3x^8 + 16x^6 + 13x^4 - 18x^2 + 1	\( 2^{30}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.30667140235264.3	x^12 - 6x^10 + 17x^8 - 28x^6 + 36x^4 - 32x^2 + 4	\( 2^{30}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.30667140235264.7	x^12 - 2x^10 - x^8 + 12x^6 + 2x^4 - 8x^2 + 4	\( 2^{30}\cdot 13^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.34012224000000.1	x^12 - 3x^10 - 8x^9 + 12x^7 + 21x^6 - 36x^5 + 16x^3 - 3x^2 - 1	\( 2^{12}\cdot 3^{12}\cdot 5^{6} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.34982777061376.1	x^12 - 4x^10 + 6x^8 - 10x^6 + 6x^4 - 4x^2 + 1	\( 2^{28}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.34982777061376.2	x^12 - 2x^10 - x^8 - 28x^6 - x^4 - 2x^2 + 1	\( 2^{28}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.34982777061376.3	x^12 - 10x^10 + 39x^8 - 72x^6 + 58x^4 - 16x^2 + 4	\( 2^{28}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.34982777061376.4	x^12 + 2x^10 - x^8 + 28x^6 - x^4 + 2x^2 + 1	\( 2^{28}\cdot 19^{4} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.0.35664401793024.7	x^12 - 6x^8 + 9x^4 + 4	\( 2^{26}\cdot 3^{12} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.38806720086016.2	x^12 - 4x^11 + 2x^10 + 8x^9 - 21x^8 + 56x^7 - 44x^6 - 64x^5 + 19x^4 + 148x^3 - 126x^2 + 32x + 1	\( 2^{18}\cdot 23^{6} \)	$C_2 \times S_4$ (as 12T23)	Trivial
12.4.38982341165056.1	x^12 + x^10 - 8x^8 - 17x^6 - 8x^4 + x^2 + 1	\( 2^{16}\cdot 29^{6} \)	$C_2 \times S_4$ (as 12T23)	Trivial