Global number field search results

Further refine search

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 560)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.768320000000.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 6x^8 - 10x^7 + 11x^6 - 10x^5 + 8x^4 - 2x^3 + 3x^2 + 1	\( 2^{12}\cdot 5^{7}\cdot 7^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.1093211783168.1	x^12 - 2x^9 + 4x^8 - 7x^6 + 6x^5 + 3x^4 - 8x^3 - 2x^2 + 4x + 2	\( 2^{23}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.1397239981029.1	x^12 - 4x^11 + 7x^10 - 6x^9 + 13x^7 - 22x^6 + 16x^5 + 2x^4 - 15x^3 + 14x^2 - 6x + 1	\( 3^{4}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.2034422578125.1	x^12 - 6x^10 - 7x^9 + 15x^8 + 27x^7 - 8x^6 - 39x^5 - 9x^4 + 19x^3 + 6x^2 - 3x - 1	\( 3^{12}\cdot 5^{7}\cdot 7^{2} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.2352980000000.1	x^12 - x^11 - 2x^10 + 4x^9 - 3x^8 - 2x^7 + 7x^6 + 2x^5 - 3x^4 - 4x^3 - 2x^2 + x + 1	\( 2^{8}\cdot 5^{7}\cdot 7^{6} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.4112286810112.1	x^12 - x^10 - 4x^9 - 2x^8 + 2x^7 + 8x^6 - 2x^5 - 2x^4 + 4x^3 - x^2 + 1	\( 2^{16}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.4112286810112.1	x^12 - x^11 - 4x^9 + 2x^8 - 5x^7 + 8x^6 + 6x^5 + 2x^4 - x^3 + 6x^2 - 2x + 1	\( 2^{16}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.4458050224128.1	x^12 - 6x^10 + 15x^8 - 26x^6 + 33x^4 - 24x^2 + 8	\( 2^{23}\cdot 3^{12} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.12575159829261.1	x^12 + x^10 - 3x^9 - 10x^8 - 17x^7 - 23x^6 - 25x^5 - 19x^4 - 10x^3 - 4x^2 + x + 1	\( 3^{6}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.16449147240448.1	x^12 - 2x^11 - x^10 + 4x^9 + 10x^7 + 4x^6 - 16x^5 + 19x^4 + 4x^3 + 2x^2 + 4	\( 2^{18}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.17491388530688.1	x^12 - 6x^10 + 17x^8 - 30x^6 + 31x^4 - 16x^2 + 2	\( 2^{27}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.37647680000000.1	x^12 - 2x^11 - x^10 - 4x^8 - 4x^7 + 9x^6 + 32x^5 + 46x^4 + 40x^3 + 23x^2 + 8x + 1	\( 2^{12}\cdot 5^{7}\cdot 7^{6} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.40122452017152.1	x^12 - 6x^9 + 36x^7 - 55x^6 - 6x^5 + 99x^4 - 120x^3 + 72x^2 - 24x + 4	\( 2^{23}\cdot 3^{14} \)	$C_4\times S_4$ (as 12T53)	$[2]$
12.8.47466656328125.1	x^12 - x^11 - 7x^10 + 8x^9 + 17x^8 - 15x^7 - 32x^6 - 4x^5 + 49x^4 + 26x^3 - 30x^2 - 12x - 1	\( 5^{7}\cdot 157^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.51200000000000.1	x^12 - 5x^10 + 20x^8 - 35x^6 + 40x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{11} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.61334280470528.1	x^12 - 8x^8 - 4x^6 + 13x^4 - 20x^2 + 2	\( 2^{31}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.61334280470528.8	x^12 - 8x^8 + 4x^6 + 13x^4 + 20x^2 + 2	\( 2^{31}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.65796588961792.2	x^12 - 2x^11 - 4x^10 + 11x^9 - 2x^8 - 6x^6 - 21x^5 + 20x^4 + 12x^3 + 4x^2 - 11x - 1	\( 2^{20}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.70655493361664.2	x^12 - 6x^11 + 12x^10 + x^9 - 40x^8 + 46x^7 + 24x^6 - 63x^5 - 6x^4 + 44x^3 + 22x^2 - 57x + 23	\( 2^{12}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.71328803586048.4	x^12 + 6x^10 + 15x^8 + 26x^6 + 33x^4 + 24x^2 + 8	\( 2^{27}\cdot 3^{12} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.8.97593620000000.1	x^12 - 6x^11 + 10x^10 + 5x^9 - 35x^8 + 44x^7 - 11x^6 - 34x^5 + 39x^4 - 13x^3 - 5x^2 + 5x + 1	\( 2^{8}\cdot 5^{7}\cdot 47^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.145800000000000.2	x^12 - 4x^11 + 4x^10 - 5x^8 + 16x^7 - 4x^6 - 16x^5 - 5x^4 + 4x^2 + 4x + 1	\( 2^{12}\cdot 3^{6}\cdot 5^{11} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.204800000000000.1	x^12 - 3x^11 + 11x^10 - 15x^9 + 30x^8 - 33x^7 + 69x^6 - 63x^5 + 20x^4 + 25x^3 + 21x^2 - 3x + 1	\( 2^{22}\cdot 5^{11} \)	$C_4\times S_4$ (as 12T53)	$[2]$
12.4.204800000000000.1	x^12 - 3x^11 + x^10 + 15x^9 - 50x^8 + 77x^7 - 91x^6 + 57x^5 - 20x^4 - 35x^3 + 51x^2 - 33x + 31	\( 2^{22}\cdot 5^{11} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.245337121882112.1	x^12 - 4x^10 - 16x^8 - 8x^6 + 21x^4 + 12x^2 + 2	\( 2^{33}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.245337121882112.2	x^12 + 4x^10 - 16x^8 + 8x^6 + 21x^4 - 12x^2 + 2	\( 2^{33}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.263186355847168.1	x^12 - 2x^11 + 4x^10 + 9x^9 - 15x^8 + 32x^7 + 44x^6 - 4x^5 + 23x^4 + 22x^3 - 5x - 1	\( 2^{22}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.263186355847168.2	x^12 - 2x^11 - 9x^10 + 6x^9 + 43x^8 + 16x^7 - 80x^6 - 100x^5 + 10x^4 + 104x^3 + 88x^2 + 32x + 4	\( 2^{22}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.263186355847168.3	x^12 + x^10 + 19x^8 - 2x^6 - 22x^4 + 52x^2 + 52	\( 2^{22}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.279862216491008.1	x^12 + 2x^10 - x^8 - 6x^6 + 11x^4 - 8x^2 + 2	\( 2^{31}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.279862216491008.8	x^12 - 2x^10 - x^8 + 6x^6 + 11x^4 + 8x^2 + 2	\( 2^{31}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.282621973446656.1	x^12 - 4x^11 + 4x^10 - 4x^9 + 7x^8 + 12x^7 - 21x^6 + 12x^5 - 27x^4 + 34x^3 - 16x^2 + 4x - 1	\( 2^{14}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.282621973446656.3	x^12 - 4x^11 + 13x^10 - 32x^9 + 64x^8 - 108x^7 + 160x^6 - 190x^5 + 197x^4 - 200x^3 + 182x^2 - 104x + 28	\( 2^{14}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.394649453723648.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 61x^8 - 60x^7 - 19x^6 + 198x^5 - 357x^4 + 312x^3 - 134x^2 + 28x - 2	\( 2^{23}\cdot 19^{6} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.394649453723648.2	x^12 - 4x^11 + 4x^10 + 14x^9 - 47x^8 + 32x^7 + 85x^6 - 240x^5 + 331x^4 - 312x^3 + 203x^2 - 90x + 25	\( 2^{23}\cdot 19^{6} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.427199906953125.1	x^12 - 4x^11 + x^10 + 15x^9 - 14x^8 - 28x^7 + 41x^6 + 11x^5 - 44x^4 + 30x^3 - 8x^2 - x + 1	\( 3^{2}\cdot 5^{7}\cdot 157^{4} \)	$C_4\times S_4$ (as 12T53)	$[2]$
12.4.503060929445888.3	x^12 - 4x^10 + 14x^8 - 28x^6 + 16x^4 - 8x^2 + 2	\( 2^{35}\cdot 11^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.503060929445888.12	x^12 + 4x^10 + 14x^8 + 28x^6 + 16x^4 + 8x^2 + 2	\( 2^{35}\cdot 11^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.641959232274432.1	x^12 - 6x^10 - 8x^9 - 24x^8 - 60x^7 - 58x^6 + 96x^4 + 128x^3 + 54x^2 + 12x + 1	\( 2^{27}\cdot 3^{14} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.819200000000000.3	x^12 + 5x^10 + 20x^8 + 35x^6 + 40x^4 + 25x^2 + 5	\( 2^{24}\cdot 5^{11} \)	$C_4\times S_4$ (as 12T53)	$[2]$
12.0.838860800000000.2	x^12 + 4x^10 - 4x^8 + 16x^6 + 13x^4 - 4x^2 + 2	\( 2^{31}\cdot 5^{8} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.838860800000000.2	x^12 - 4x^10 - 4x^8 - 16x^6 + 13x^4 + 4x^2 + 2	\( 2^{31}\cdot 5^{8} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.981348487528448.5	x^12 - 8x^10 + 22x^8 - 28x^6 + 17x^4 - 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.981348487528448.6	x^12 + 8x^10 + 22x^8 + 28x^6 + 17x^4 + 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.1052745423388672.5	x^12 + 4x^10 - 6x^8 + 6x^6 - 14x^4 + 13	\( 2^{24}\cdot 13^{7} \)	$C_4\times S_4$ (as 12T53)	$[2]$
12.4.1119448865964032.4	x^12 - 4x^10 + 12x^8 - 24x^6 + 24x^4 - 16x^2 + 8	\( 2^{33}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.1119448865964032.18	x^12 + 4x^10 + 12x^8 + 24x^6 + 24x^4 + 16x^2 + 8	\( 2^{33}\cdot 19^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.0.1130487893786624.2	x^12 - x^11 + 3x^10 - x^9 + 15x^8 + 4x^7 - 14x^6 + 52x^5 + 65x^4 + 17x^3 + 23x^2 + 25x + 7	\( 2^{16}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.1130487893786624.3	x^12 - 11x^10 + 34x^8 - 75x^6 + 110x^4 - 87x^2 + 29	\( 2^{16}\cdot 29^{7} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.4.1141260857376768.2	x^12 - 6x^10 + 3x^8 + 14x^6 + 3x^4 + 2	\( 2^{31}\cdot 3^{12} \)	$C_4\times S_4$ (as 12T53)	Trivial