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 468)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.819345401329.1	x^12 - x^11 - 2x^10 - x^8 + x^7 + 3x^6 + x^5 - x^4 - 2x^2 - x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.819345401329.1	x^12 - 2x^11 + 6x^10 - 7x^9 + 12x^8 - 17x^7 + 17x^6 - 19x^5 + 17x^4 - 14x^3 + 10x^2 - 4x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.819345401329.2	x^12 - 3x^11 + 3x^10 + 3x^8 - 9x^7 + 3x^6 + 3x^5 + 5x^4 - 7x^3 - x^2 + 2x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.1637716551289.1	x^12 - 2x^11 - 2x^10 + 5x^9 - 3x^8 - 3x^7 + 7x^6 - 3x^5 - 3x^4 + 5x^3 - 2x^2 - 2x + 1	\( 7^{8}\cdot 13^{2}\cdot 41^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.1801390781281.1	x^12 - 2x^11 + 2x^10 + 6x^9 - 12x^7 + 7x^6 + 12x^5 - 6x^3 + 2x^2 + 2x + 1	\( 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.1801390781281.1	x^12 - 3x^11 + x^10 + 8x^9 - 21x^8 + 27x^7 - 21x^6 + 25x^5 - 35x^4 + 27x^3 - 10x^2 - x + 1	\( 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.1801390781281.2	x^12 - 3x^11 - x^10 + 9x^9 + x^8 - 16x^7 - 7x^6 + 13x^5 + 9x^4 + 2x^3 - 11x^2 + x + 1	\( 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.3990533607424.1	x^12 + 2x^10 + 2x^8 + 3x^6 + 2x^4 + 2x^2 + 1	\( 2^{12}\cdot 7^{8}\cdot 13^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.8.40147924665121.1	x^12 - 5x^11 + 6x^10 + 9x^9 - 33x^8 + 36x^7 + 6x^6 - 51x^5 + 22x^4 + 19x^3 - 2x^2 - 8x + 1	\( 7^{10}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.8.40419192196881.1	x^12 - 6x^11 + 12x^10 - 45x^8 + 81x^7 - 25x^6 - 69x^5 + 48x^4 + 21x^3 - 18x^2 + 1	\( 3^{18}\cdot 17^{2}\cdot 19^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.218340105584896.1	x^12 + 7x^10 + 9x^8 - 2x^6 + 9x^4 + 7x^2 + 1	\( 2^{8}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.873360422339584.1	x^12 - x^11 - 4x^10 + 5x^9 + 15x^8 - 26x^7 + 40x^6 + 26x^5 + 15x^4 - 5x^3 - 4x^2 + x + 1	\( 2^{10}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.873360422339584.1	x^12 - x^11 + x^10 - 12x^9 - 4x^8 - 4x^7 + 36x^6 + 34x^5 + 31x^4 - 51x^3 - 13x^2 + 50x - 4	\( 2^{10}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.873360422339584.2	x^12 - 6x^11 + 14x^10 - 10x^9 - 22x^8 + 38x^7 + 10x^6 - 38x^5 - 22x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{10}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.873360422339584.2	x^12 - 5x^10 + 19x^8 - 31x^6 + 40x^4 + 96x^2 + 64	\( 2^{10}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.12.1377319619634049.1	x^12 - x^11 - 16x^10 + 11x^9 + 83x^8 - 19x^7 - 175x^6 - 27x^5 + 135x^4 + 60x^3 - 13x^2 - 9x - 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 41^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.3356038763843584.1	x^12 + 11x^10 + 43x^8 + 73x^6 + 53x^4 + 15x^2 + 1	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2, 2]$
12.12.3356038763843584.1	x^12 - 11x^10 + 43x^8 - 73x^6 + 53x^4 - 15x^2 + 1	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.3493441689358336.1	x^12 - 4x^10 - 2x^8 + 8x^6 - 2x^4 - 4x^2 + 1	\( 2^{12}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.3493441689358336.2	x^12 + 4x^10 - 2x^8 - 8x^6 - 2x^4 + 4x^2 + 1	\( 2^{12}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.3493441689358336.4	x^12 - 5x^11 + 15x^10 - 26x^9 + 35x^8 - 43x^7 + 115x^6 - 206x^5 + 266x^4 - 288x^3 + 296x^2 - 192x + 64	\( 2^{12}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial (GRH)
12.0.3493441689358336.7	x^12 + 5x^10 + 10x^8 + 32x^6 + 40x^4 + 80x^2 + 64	\( 2^{12}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial (GRH)
12.0.5267134544050729.1	x^12 - x^11 + 13x^10 - 2x^9 + 58x^8 - 4x^7 + 244x^6 - 161x^5 + 434x^4 - 238x^3 + 392x^2 + 98x + 49	\( 7^{8}\cdot 167^{2}\cdot 181^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[3]$
12.0.7378496640126976.1	x^12 - x^10 + 3x^8 - 7x^6 + 12x^4 - 16x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.7378496640126976.2	x^12 + x^10 + 3x^8 + 7x^6 + 12x^4 + 16x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.8.13973766757433344.3	x^12 - 6x^11 + 11x^10 - 51x^8 + 138x^7 - 165x^6 + 78x^5 + 31x^4 - 64x^3 + 17x^2 + 10x - 2	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.8.13973766757433344.4	x^12 - 11x^10 + 52x^8 - 167x^6 + 185x^4 - 68x^2 + 4	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.13973766757433344.5	x^12 - x^10 - 7x^8 + 6x^6 - 7x^4 - x^2 + 1	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial (GRH)
12.0.13973766757433344.7	x^12 - x^11 + 6x^10 - 4x^9 + 10x^8 + 11x^6 - 47x^5 + 68x^4 - 76x^3 + 8x^2 + 8x + 32	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.4.13973766757433344.8	x^12 - 9x^10 + 18x^8 - 35x^6 + 39x^4 + 74x^2 + 4	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.13973766757433344.8	x^12 - 5x^10 + 19x^8 - 62x^6 + 164x^4 - 152x^2 + 64	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.4.13973766757433344.10	x^12 - 6x^11 + 10x^10 + 4x^9 - 11x^8 - 18x^7 - 6x^6 + 12x^5 + 157x^4 - 178x^3 - 34x^2 + 36x + 4	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.4.13973766757433344.13	x^12 + x^10 + 11x^8 - 25x^6 - 16x^4 - 292x^2 + 64	\( 2^{14}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.0.27490786021543936.1	x^12 - 3x^10 + 8x^8 - 11x^6 + 32x^4 - 48x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 83^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.27490786021543936.2	x^12 + 3x^10 + 8x^8 + 11x^6 + 32x^4 + 48x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 83^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[6]$
12.0.36717844226904064.1	x^12 + 5x^8 - 7x^6 + 20x^4 + 64	\( 2^{12}\cdot 7^{8}\cdot 29^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.36717844226904064.2	x^12 + 5x^8 + 7x^6 + 20x^4 + 64	\( 2^{12}\cdot 7^{8}\cdot 29^{2}\cdot 43^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.8.55895067029733376.2	x^12 - 7x^10 + 9x^8 + 2x^6 + 9x^4 - 7x^2 + 1	\( 2^{16}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial (GRH)
12.0.55895067029733376.3	x^12 - 6x^11 + 15x^10 - 20x^9 + 32x^8 - 74x^7 + 103x^6 - 68x^5 + 41x^4 - 48x^3 + 24x^2 + 4	\( 2^{16}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$ (GRH)
12.0.55895067029733376.5	x^12 - 6x^11 + 9x^10 + 10x^9 - 19x^8 - 50x^7 + 63x^6 + 94x^5 - 55x^4 - 158x^3 + x^2 + 110x + 58	\( 2^{16}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.55895067029733376.8	x^12 + 10x^10 + 4x^8 + 16x^6 + 16x^4 + 160x^2 + 64	\( 2^{16}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.55895067029733376.16	x^12 + 6x^10 + 38x^8 + 112x^6 + 257x^4 + 306x^2 + 256	\( 2^{16}\cdot 31^{8} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$ (GRH)
12.0.77101099829039104.1	x^12 - 4x^10 + 15x^8 - 31x^6 + 60x^4 - 64x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 139^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.77101099829039104.2	x^12 + 4x^10 + 15x^8 + 31x^6 + 60x^4 + 64x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 139^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[6]$
12.0.87138619140870144.1	x^12 + 3x^8 - 9x^6 + 12x^4 + 64	\( 2^{12}\cdot 3^{16}\cdot 19^{2}\cdot 37^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.87138619140870144.2	x^12 + 3x^8 + 9x^6 + 12x^4 + 64	\( 2^{12}\cdot 3^{16}\cdot 19^{2}\cdot 37^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2]$
12.0.164445899428335616.1	x^12 - 2x^10 + 11x^8 - 15x^6 + 44x^4 - 32x^2 + 64	\( 2^{12}\cdot 7^{10}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2, 2]$
12.0.164445899428335616.2	x^12 + 2x^10 + 11x^8 + 15x^6 + 44x^4 + 32x^2 + 64	\( 2^{12}\cdot 7^{10}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2, 2, 2]$
12.0.200091517971337216.1	x^12 - x^10 + 10x^8 - 7x^6 + 40x^4 - 16x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 41^{2}\cdot 71^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2, 4]$
12.0.200091517971337216.2	x^12 + x^10 + 10x^8 + 7x^6 + 40x^4 + 16x^2 + 64	\( 2^{12}\cdot 7^{8}\cdot 41^{2}\cdot 71^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	$[2, 4]$