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 122)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.606355001344.1	x^12 + 3x^10 + 5x^8 + 5x^6 + 5x^4 + 3x^2 + 1	\( 2^{12}\cdot 23^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.878013976576.1	x^12 - 2x^11 + 3x^10 - 6x^7 + 11x^6 - 8x^5 - 2x^4 + 4x^3 + 5x^2 + 4x + 1	\( 2^{12}\cdot 11^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.1857616347136.2	x^12 + x^10 + 2x^8 + 3x^6 + 2x^4 + x^2 + 1	\( 2^{20}\cdot 11^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.3635215077376.3	x^12 + 3x^10 + 7x^8 + 9x^6 + 7x^4 + 3x^2 + 1	\( 2^{12}\cdot 31^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.4347792138496.1	x^12 - x^11 + x^10 + 4x^9 - x^8 - 3x^7 + 2x^6 - 3x^5 - x^4 + 4x^3 + x^2 - x + 1	\( 2^{8}\cdot 19^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.5015306502144.3	x^12 + 3x^10 - 5x^6 + 3x^2 + 1	\( 2^{20}\cdot 3^{14} \)	$S_4$ (as 12T9)	Trivial
12.0.10497600000000.1	x^12 - 2x^11 + 3x^10 - 6x^9 + 4x^8 + 4x^7 + x^6 + 4x^5 + 4x^4 - 6x^3 + 3x^2 - 2x + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	$S_4$ (as 12T9)	Trivial
12.4.10509215371264.1	x^12 + 3x^10 - 10x^8 - 25x^6 - 10x^4 + 3x^2 + 1	\( 2^{12}\cdot 37^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.12244400640000.2	x^12 - 6x^11 + 9x^10 + 10x^9 - 36x^8 + 18x^7 + 25x^6 - 30x^5 + 12x^4 - 6x^3 + 3x^2 + 3	\( 2^{12}\cdot 3^{14}\cdot 5^{4} \)	$S_4$ (as 12T9)	Trivial
12.0.12993941393521.1	x^12 - 2x^11 + 4x^10 + 3x^9 + 7x^8 + 11x^7 + 22x^6 + 3x^5 + 22x^4 - 14x^3 + 11x^2 - 5x + 1	\( 11^{4}\cdot 31^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.15608694214656.2	x^12 - 5x^10 - 2x^9 + 22x^8 - 12x^7 - 19x^6 + 22x^5 - 6x^3 + 9x^2 - 2x + 1	\( 2^{12}\cdot 3^{4}\cdot 19^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.17422409568256.1	x^12 - 2x^11 + 9x^10 - 20x^9 + 32x^8 - 50x^7 + 37x^6 - 14x^5 + 6x^4 - 6x^3 + 19x^2 - 2x + 1	\( 2^{12}\cdot 7^{4}\cdot 11^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.19292185090369.1	x^12 - 2x^11 + 9x^10 - 18x^9 + 47x^8 - 50x^7 + 119x^6 - 82x^5 + 145x^4 - 70x^3 + 61x^2 + 12x + 1	\( 19^{4}\cdot 23^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.25892303048704.1	x^12 + 3x^10 + 10x^8 + 15x^6 + 10x^4 + 3x^2 + 1	\( 2^{12}\cdot 43^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.45137758519296.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 90x^8 - 126x^7 + 141x^6 - 126x^5 + 87x^4 - 44x^3 + 12x^2 + 2	\( 2^{20}\cdot 3^{16} \)	$S_4$ (as 12T9)	Trivial
12.0.45767944570401.1	x^12 + 7x^10 + 8x^8 + 16x^6 + 8x^4 + 7x^2 + 1	\( 3^{8}\cdot 17^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.49331181715456.7	x^12 + 3x^10 + 4x^8 + 3x^6 + 4x^4 + 3x^2 + 1	\( 2^{20}\cdot 19^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.83696735582464.1	x^12 + 7x^10 + 26x^8 + 15x^6 + 26x^4 + 7x^2 + 1	\( 2^{8}\cdot 83^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.104857600000000.2	x^12 - 6x^11 + 25x^10 - 70x^9 + 162x^8 - 294x^7 + 453x^6 - 558x^5 + 535x^4 - 376x^3 + 168x^2 - 40x + 4	\( 2^{28}\cdot 5^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.104857600000000.3	x^12 - 4x^10 + 4x^8 - 4x^6 + 11x^4 - 4x^2 + 4	\( 2^{28}\cdot 5^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.128536820158464.1	x^12 - 6x^10 + 6x^8 + 10x^6 + 6x^4 - 6x^2 + 1	\( 2^{12}\cdot 3^{22} \)	$S_4$ (as 12T9)	Trivial
12.0.128536820158464.8	x^12 + 3x^10 + 15x^8 - 26x^6 + 24x^4 - 24x^2 + 16	\( 2^{12}\cdot 3^{22} \)	$S_4$ (as 12T9)	$[2]$
12.0.128536820158464.9	x^12 + 3x^10 + 6x^8 + 7x^6 - 30x^4 - 33x^2 + 49	\( 2^{12}\cdot 3^{22} \)	$S_4$ (as 12T9)	Trivial
12.4.144215816802121.1	x^12 - 2x^10 - 6x^9 - 6x^8 - 5x^7 + 8x^6 + 32x^5 - 4x^4 - 52x^3 + x^2 + 44x + 16	\( 229^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.146830437604321.1	x^12 - x^10 - 12x^9 + 14x^8 + 7x^7 + 11x^6 - 24x^5 + 7x^4 + 5x^3 + 13x^2 + 2x + 4	\( 59^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.154922431942656.1	x^12 - 2x^11 - x^10 + 6x^9 - 16x^8 + 24x^7 - x^6 - 32x^5 + 70x^4 - 132x^3 + 147x^2 - 84x + 21	\( 2^{12}\cdot 3^{8}\cdot 7^{8} \)	$S_4$ (as 12T9)	$[3]$
12.0.172771465793536.1	x^12 + 3x^10 + 14x^8 + 23x^6 + 14x^4 + 3x^2 + 1	\( 2^{12}\cdot 59^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.172771465793536.3	x^12 + 3x^10 - 5x^8 + 18x^6 + 168x^4 + 88x^2 + 16	\( 2^{12}\cdot 59^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.182401906640625.1	x^12 + 5x^10 + 13x^8 + 25x^6 + 13x^4 + 5x^2 + 1	\( 3^{4}\cdot 5^{8}\cdot 7^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.188238400000000.1	x^12 + 3x^10 + x^8 - 3x^6 + x^4 + 3x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 7^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.188238400000000.3	x^12 - 6x^9 - 8x^8 - 6x^7 + 48x^6 + 24x^5 - 36x^4 + 12x^3 + 28x^2 - 12x + 4	\( 2^{12}\cdot 5^{8}\cdot 7^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.224771578003456.1	x^12 - 4x^11 + 17x^10 - 42x^9 + 95x^8 - 156x^7 + 219x^6 - 238x^5 + 218x^4 - 152x^3 + 82x^2 - 28x + 4	\( 2^{20}\cdot 11^{8} \)	$S_4$ (as 12T9)	$[2]$
12.0.224771578003456.2	x^12 - x^10 - 8x^8 + 11x^6 + 44x^4 - 121x^2 + 121	\( 2^{20}\cdot 11^{8} \)	$S_4$ (as 12T9)	Trivial
12.4.288136807515649.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 42x^8 + 6x^7 - 108x^6 + 201x^5 - 192x^4 + 103x^3 - 10x^2 - 16x + 8	\( 257^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.320761795710976.1	x^12 - 14x^8 + 73x^4 + 4	\( 2^{12}\cdot 23^{8} \)	$S_4$ (as 12T9)	$[2]$
12.0.320761795710976.3	x^12 - 7x^10 + 41x^8 - 115x^6 + 253x^4 - 529x^2 + 529	\( 2^{12}\cdot 23^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.320761795710976.5	x^12 + 2x^10 + 24x^8 + 69x^6 + 230x^4 + 529x^2 + 529	\( 2^{12}\cdot 23^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.364679635048569.3	x^12 - 5x^11 + 15x^10 - 39x^9 + 82x^8 - 144x^7 + 225x^6 - 298x^5 + 340x^4 - 396x^3 + 396x^2 - 315x + 225	\( 3^{6}\cdot 29^{8} \)	$S_4$ (as 12T9)	$[4]$
12.0.368947264000000.2	x^12 - 3x^10 - 2x^9 + 2x^8 - 36x^7 - x^6 + 120x^5 + 100x^4 + 16x^3 - 5x^2 - 4x + 1	\( 2^{12}\cdot 5^{6}\cdot 7^{8} \)	$S_4$ (as 12T9)	$[2]$
12.4.410516225440000.1	x^12 - 9x^10 + 2x^8 - 13x^6 + 2x^4 - 9x^2 + 1	\( 2^{8}\cdot 5^{4}\cdot 37^{6} \)	$S_4$ (as 12T9)	Trivial
12.0.419430400000000.6	x^12 + 4x^10 + 14x^8 + 24x^6 + 56x^4 + 64x^2 + 64	\( 2^{30}\cdot 5^{8} \)	$S_4$ (as 12T9)	Trivial
12.0.513710701744969.1	x^12 + 2x^10 - 10x^9 + 10x^8 + x^7 + 22x^6 - 34x^5 + 24x^4 - 32x^3 + 47x^2 - 66x + 36	\( 283^{6} \)	$S_4$ (as 12T9)	$[4]$
12.0.623717458640896.1	x^12 - 6x^11 + 20x^10 - 38x^9 + 39x^8 + 24x^7 - 128x^6 + 168x^5 - 9x^4 - 130x^3 + 140x^2 - 18x + 1	\( 2^{20}\cdot 29^{6} \)	$S_4$ (as 12T9)	$[4]$
12.0.648669553496064.1	x^12 - 4x^11 + 13x^10 - 28x^9 + 62x^8 - 112x^7 + 187x^6 - 236x^5 + 218x^4 - 134x^3 + 43x^2 - 2x + 1	\( 2^{12}\cdot 3^{8}\cdot 17^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.855355656503296.9	x^12 + 10x^8 - 23x^4 + 64	\( 2^{20}\cdot 13^{8} \)	$S_4$ (as 12T9)	$[3]$
12.0.1025271882697689.1	x^12 - 3x^11 - x^9 + 24x^8 - 21x^7 - 35x^6 - 9x^5 + 195x^4 - 294x^3 + 198x^2 + 36x + 9	\( 3^{14}\cdot 11^{8} \)	$S_4$ (as 12T9)	$[4]$
12.0.1283918464548864.15	x^12 + 6x^10 - 4x^9 + 12x^8 - 24x^7 + 22x^6 + 12x^5 + 21x^4 - 24x^3 - 12x^2 + 6	\( 2^{28}\cdot 3^{14} \)	$S_4$ (as 12T9)	$[4]$
12.0.1283918464548864.31	x^12 + 12x^8 + 4x^6 + 15x^4 - 24x^2 + 16	\( 2^{28}\cdot 3^{14} \)	$S_4$ (as 12T9)	$[2]$
12.0.1295686674939904.1	x^12 - 2x^11 + 11x^10 - 2x^9 + 3x^8 + 48x^7 - 20x^6 + 16x^5 + 87x^4 - 54x^3 + 21x^2 - 6x + 1	\( 2^{28}\cdot 13^{6} \)	$S_4$ (as 12T9)	$[2]$
12.0.1295686674939904.26	x^12 + 6x^10 + 19x^8 + 48x^6 + 144x^4 + 64x^2 + 16	\( 2^{28}\cdot 13^{6} \)	$S_4$ (as 12T9)	$[2]$