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 1901)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.831018441984.1	x^12 - 3x^11 + 8x^10 - 16x^9 + 25x^8 - 32x^7 + 37x^6 - 32x^5 + 25x^4 - 16x^3 + 8x^2 - 3x + 1	\( 2^{8}\cdot 3\cdot 19^{6}\cdot 23 \)	12T224	Trivial
12.0.1855943480204.1	x^12 - 4x^11 + 8x^10 - 11x^9 + 18x^8 - 27x^7 + 30x^6 - 29x^5 + 33x^4 - 31x^3 + 19x^2 - 6x + 1	\( 2^{2}\cdot 11\cdot 59^{6} \)	12T224	Trivial
12.2.51889250895616.1	x^12 - 5x^11 + 12x^10 - 19x^9 + 18x^8 - 5x^7 - 7x^6 + 26x^4 - 44x^3 + 36x^2 - 16x + 4	\( -\,2^{8}\cdot 37^{6}\cdot 79 \)	12T224	Trivial
12.0.59443723108352.1	x^12 - 4x^10 + 10x^8 - 14x^6 + 12x^4 - 6x^2 + 2	\( 2^{25}\cdot 11^{6} \)	12T224	Trivial
12.0.59443723108352.2	x^12 - 2x^10 + 2x^8 - 4x^6 + 4x^4 - 2x^2 + 2	\( 2^{25}\cdot 11^{6} \)	12T224	Trivial
12.0.59443723108352.3	x^12 + 2x^10 + 2x^8 + 4x^6 + 4x^4 + 2x^2 + 2	\( 2^{25}\cdot 11^{6} \)	12T224	Trivial
12.0.59443723108352.4	x^12 + 4x^10 + 10x^8 + 14x^6 + 12x^4 + 6x^2 + 2	\( 2^{25}\cdot 11^{6} \)	12T224	Trivial
12.2.70280377795328.1	x^12 - 2x^11 - 5x^9 + 7x^8 + 2x^7 + 9x^6 - 2x^5 - 11x^4 - 13x^3 - 9x^2 - 3x - 1	\( -\,2^{8}\cdot 37^{6}\cdot 107 \)	12T224	Trivial
12.4.304767245766656.1	x^12 - 4x^11 + 3x^10 + 2x^9 + 2x^8 - 10x^7 - x^6 + 6x^5 + 18x^4 - 6x^3 - 3x^2 - 6x - 1	\( 2^{12}\cdot 29\cdot 37^{6} \)	12T224	Trivial
12.0.304767245766656.1	x^12 + 3x^10 - 2x^8 + 3x^6 + 42x^4 + 63x^2 + 29	\( 2^{12}\cdot 29\cdot 37^{6} \)	12T224	Trivial
12.0.365852060112128.1	x^12 - 5x^11 + 13x^10 - 25x^9 + 43x^8 - 64x^7 + 83x^6 - 88x^5 + 73x^4 - 45x^3 + 20x^2 - 6x + 1	\( 2^{8}\cdot 37^{6}\cdot 557 \)	12T224	Trivial
12.4.407888921597184.1	x^12 - 3x^11 + 8x^10 - 6x^9 + 11x^8 - 8x^7 + 29x^6 + 2x^5 - 15x^4 + 24x^3 - 2x^2 - 5x + 1	\( 2^{8}\cdot 3^{3}\cdot 23\cdot 37^{6} \)	12T224	Trivial
12.0.653880954191872.1	x^12 - 8x^10 + 30x^8 - 66x^6 + 88x^4 - 66x^2 + 22	\( 2^{25}\cdot 11^{7} \)	12T224	Trivial
12.0.653880954191872.2	x^12 + 4x^10 + 2x^8 - 22x^2 + 22	\( 2^{25}\cdot 11^{7} \)	12T224	Trivial
12.0.653880954191872.3	x^12 - 4x^10 + 2x^8 + 22x^2 + 22	\( 2^{25}\cdot 11^{7} \)	12T224	Trivial
12.0.653880954191872.4	x^12 + 8x^10 + 30x^8 + 66x^6 + 88x^4 + 66x^2 + 22	\( 2^{25}\cdot 11^{7} \)	12T224	Trivial
12.0.838860800000000.1	x^12 + x^10 + x^8 - 16x^6 + 18x^4 - 6x^2 + 2	\( 2^{31}\cdot 5^{8} \)	12T224	Trivial
12.0.937292452593664.2	x^12 - 7x^10 + 26x^8 - 57x^6 + 76x^4 - 57x^2 + 19	\( 2^{20}\cdot 19^{7} \)	12T224	Trivial
12.0.937292452593664.7	x^12 + 7x^10 + 26x^8 + 57x^6 + 76x^4 + 57x^2 + 19	\( 2^{20}\cdot 19^{7} \)	12T224	Trivial
12.6.3282097279493763.1	x^12 - 3x^11 - 5x^10 + 12x^9 + 10x^8 - 2x^7 + x^6 - 2x^5 + 10x^4 + 12x^3 - 5x^2 - 3x + 1	\( -\,3^{7}\cdot 107^{6} \)	12T224	Trivial
12.0.3749169810374656.4	x^12 + 2x^10 + 6x^8 - 76x^2 + 76	\( 2^{22}\cdot 19^{7} \)	12T224	Trivial
12.0.3749169810374656.12	x^12 - 2x^10 + 6x^8 + 76x^2 + 76	\( 2^{22}\cdot 19^{7} \)	12T224	Trivial
12.0.7192690496110592.5	x^12 - 6x^10 + 30x^8 - 96x^6 + 212x^4 - 330x^2 + 242	\( 2^{25}\cdot 11^{8} \)	12T224	$[2]$
12.0.7192690496110592.6	x^12 - 4x^10 + 6x^8 + 18x^6 + 100x^4 - 66x^2 + 242	\( 2^{25}\cdot 11^{8} \)	12T224	$[2]$
12.0.7192690496110592.7	x^12 + 4x^10 + 6x^8 - 18x^6 + 100x^4 + 66x^2 + 242	\( 2^{25}\cdot 11^{8} \)	12T224	$[2]$
12.0.7192690496110592.8	x^12 + 6x^10 + 30x^8 + 96x^6 + 212x^4 + 330x^2 + 242	\( 2^{25}\cdot 11^{8} \)	12T224	$[2]$
12.0.10365493399519232.1	x^12 - 7x^10 + 13x^8 + 2x^4 + 2x^2 + 2	\( 2^{31}\cdot 13^{6} \)	12T224	Trivial
12.0.10365493399519232.3	x^12 + 5x^10 + 21x^8 + 32x^6 + 42x^4 + 10x^2 + 2	\( 2^{31}\cdot 13^{6} \)	12T224	Trivial
12.0.13421772800000000.2	x^12 + 6x^10 + 21x^8 + 44x^6 + 38x^4 + 4x^2 + 2	\( 2^{35}\cdot 5^{8} \)	12T224	Trivial
12.0.13421772800000000.4	x^12 - x^10 + x^8 + 16x^6 + 18x^4 + 6x^2 + 2	\( 2^{35}\cdot 5^{8} \)	12T224	Trivial
12.0.13421772800000000.7	x^12 + 2x^10 + 9x^8 - 8x^6 + 48x^4 - 32x^2 + 8	\( 2^{35}\cdot 5^{8} \)	12T224	Trivial (GRH)
12.0.14996679241498624.3	x^12 - 4x^11 + 2x^10 + 8x^9 + 2x^8 - 4x^7 - 40x^6 - 4x^5 + 204x^4 - 272x^3 + 186x^2 - 52x + 5	\( 2^{24}\cdot 19^{7} \)	12T224	Trivial
12.0.15217593115738112.2	x^12 + 6x^10 + 16x^8 + 24x^6 + 10x^4 - 12x^2 + 2	\( 2^{33}\cdot 11^{6} \)	12T224	Trivial
12.0.15217593115738112.3	x^12 + 2x^10 + 6x^8 - 8x^6 + 18x^4 - 8x^2 + 2	\( 2^{33}\cdot 11^{6} \)	12T224	Trivial
12.0.15217593115738112.5	x^12 - 2x^10 + 6x^8 + 8x^6 + 18x^4 + 8x^2 + 2	\( 2^{33}\cdot 11^{6} \)	12T224	Trivial
12.0.15217593115738112.6	x^12 - 6x^10 + 16x^8 - 24x^6 + 10x^4 + 12x^2 + 2	\( 2^{33}\cdot 11^{6} \)	12T224	Trivial
12.0.19958958676508672.2	x^12 + 6x^10 + 22x^8 + 48x^6 + 28x^4 - 24x^2 + 8	\( 2^{25}\cdot 29^{6} \)	12T224	$[2]$
12.0.19958958676508672.3	x^12 - 6x^10 + 22x^8 - 48x^6 + 28x^4 + 24x^2 + 8	\( 2^{25}\cdot 29^{6} \)	12T224	$[2]$
12.0.20971520000000000.7	x^12 + 5x^10 + 25x^8 + 50x^4 + 50x^2 + 50	\( 2^{31}\cdot 5^{10} \)	12T224	$[2]$
12.0.23110532361879552.6	x^12 - 6x^8 - 4x^6 + 42x^4 + 8	\( 2^{29}\cdot 3^{16} \)	12T224	$[2]$
12.0.23110532361879552.7	x^12 - 6x^8 + 4x^6 + 42x^4 + 8	\( 2^{29}\cdot 3^{16} \)	12T224	$[2]$
12.4.26151583660270848.1	x^12 - 6x^11 + 20x^10 - 45x^9 + 49x^8 + 8x^7 - 141x^6 + 272x^5 - 267x^4 + 147x^3 - 35x^2 - 3x + 3	\( 2^{8}\cdot 3^{6}\cdot 13\cdot 47^{6} \)	12T224	Trivial
12.8.26151583660270848.1	x^12 - 2x^11 - 10x^10 + 30x^9 + 4x^8 - 108x^7 + 124x^6 + 48x^5 - 184x^4 + 232x^3 - 80x^2 - 240x + 144	\( 2^{8}\cdot 3^{6}\cdot 13\cdot 47^{6} \)	12T224	Trivial
12.6.29538875515443867.1	x^12 - 6x^11 + 18x^10 - 35x^9 + 24x^8 + 48x^7 - 183x^6 + 300x^5 - 261x^4 + 115x^3 - 18x^2 - 3x + 1	\( -\,3^{9}\cdot 107^{6} \)	12T224	Trivial
12.0.30814043149172736.4	x^12 - 9x^10 + 36x^8 - 72x^6 + 78x^4 - 54x^2 + 24	\( 2^{31}\cdot 3^{15} \)	12T224	$[2]$
12.0.30814043149172736.8	x^12 + 3x^10 + 12x^8 + 24x^4 + 72x^2 + 96	\( 2^{31}\cdot 3^{15} \)	12T224	$[2]$ (GRH)
12.6.33915005221435551.1	x^12 - 4x^11 + 13x^9 - 12x^8 - 33x^7 + 16x^6 + 88x^5 + 57x^4 - 25x^3 - 18x^2 + 3x + 1	\( -\,3^{6}\cdot 31\cdot 107^{6} \)	12T224	Trivial
12.6.33915005221435551.2	x^12 - 3x^11 - 4x^10 + 28x^9 - 46x^8 + 2x^7 + 161x^6 - 296x^5 + 84x^4 + 269x^3 - 227x^2 - x + 31	\( -\,3^{6}\cdot 31\cdot 107^{6} \)	12T224	Trivial
12.4.45736105295740928.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 71x^8 - 50x^7 - 49x^6 + 178x^5 - 232x^4 + 176x^3 - 80x^2 + 20x - 2	\( 2^{20}\cdot 17\cdot 37^{6} \)	12T224	Trivial
12.0.53687091200000000.4	x^12 - 6x^10 + 21x^8 - 44x^6 + 38x^4 - 4x^2 + 2	\( 2^{37}\cdot 5^{8} \)	12T224	$[2]$