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 )

Label	Polynomial	Discriminant	Galois group	Class group
12.0.7086244000000.1	x^12 - x^11 + 5x^10 - 10x^9 + 9x^8 - 9x^7 + 14x^6 + 9x^5 + 9x^4 + 10x^3 + 5x^2 + x + 1	\( 2^{8}\cdot 5^{6}\cdot 11^{6} \)	$D_6$ (as 12T3)	$[2]$
12.0.8067775586689.1	x^12 - 5x^11 + 18x^10 - 48x^9 + 100x^8 - 178x^7 + 267x^6 - 336x^5 + 364x^4 - 329x^3 + 245x^2 - 147x + 49	\( 7^{10}\cdot 13^{4} \)	$A_4 \times C_2$ (as 12T7)	$[2]$
12.0.8916100448256.2	x^12 - 4x^11 + 4x^10 + 12x^9 - 37x^8 + 32x^7 + 22x^6 - 80x^5 + 88x^4 - 48x^3 + 10x^2 + 1	\( 2^{24}\cdot 3^{12} \)	$C_6\times S_3$ (as 12T18)	$[2]$
12.0.11709207984384.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 22x^8 - 34x^7 + 47x^6 - 40x^5 + 38x^4 - 42x^3 + 27x^2 - 8x + 1	\( 2^{8}\cdot 3^{6}\cdot 89^{4} \)	$S_5$ (as 12T74)	$[2]$
12.0.12745792515625.1	x^12 - 5x^11 + 12x^10 - 24x^9 + 48x^8 - 66x^7 + 53x^6 - 36x^5 + 42x^4 - 41x^3 + 23x^2 - 7x + 1	\( 5^{6}\cdot 13^{8} \)	$A_4$ (as 12T4)	$[2]$
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)	$[2]$
12.0.13867245015625.1	x^12 - 3x^11 + 12x^10 - 15x^9 + 17x^8 - 12x^7 + 21x^6 + 12x^5 + 17x^4 + 15x^3 + 12x^2 + 3x + 1	\( 5^{6}\cdot 31^{6} \)	$D_6$ (as 12T3)	$[2]$
12.0.14412774445056.1	x^12 - x^11 - x^10 - 4x^9 + 7x^8 - 3x^7 + 2x^6 + 3x^5 + 7x^4 + 4x^3 - x^2 + x + 1	\( 2^{12}\cdot 3^{6}\cdot 13^{6} \)	$S_3 \times C_2^2$ (as 12T10)	$[2]$
12.0.14512627712000.1	x^12 - 4x^11 + 7x^10 - 2x^9 - 16x^8 + 20x^7 + x^6 - 40x^5 + 18x^4 + 74x^3 + 49x^2 + 12x + 1	\( 2^{16}\cdot 5^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
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)	$[2]$
12.0.23086477815921.1	x^12 - 3x^11 - x^9 + 33x^8 - 66x^7 + 81x^6 - 66x^5 + 33x^4 - x^3 - 3x + 1	\( 3^{14}\cdot 13^{6} \)	$D_6$ (as 12T3)	$[2]$
12.0.27825593350009.1	x^12 - 3x^11 + 5x^10 - 13x^9 + 36x^8 - 72x^7 + 115x^6 - 150x^5 + 144x^4 - 92x^3 + 38x^2 - 9x + 1	\( 7^{8}\cdot 13^{6} \)	$A_4$ (as 12T4)	$[2]$
12.0.29721861554176.5	x^12 - 4x^11 + 12x^10 - 32x^9 + 49x^8 - 52x^7 + 38x^6 + 8x^5 + 15x^4 + 12x^3 + 26x^2 + 8x + 1	\( 2^{24}\cdot 11^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.29721861554176.8	x^12 - 4x^11 + 6x^10 - 4x^9 + 6x^8 - 12x^7 + 30x^6 - 88x^5 + 184x^4 - 236x^3 + 180x^2 - 76x + 14	\( 2^{24}\cdot 11^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.30667140235264.4	x^12 - 9x^8 + 23x^4 + 1	\( 2^{30}\cdot 13^{4} \)	$C_2^2\times S_4$ (as 12T48)	$[2]$
12.0.32357746661769.1	x^12 - 6x^11 + 12x^10 - 3x^9 - 18x^8 - 3x^7 + 67x^6 - 39x^5 - 39x^4 - 12x^3 + 36x^2 + 12x + 1	\( 3^{18}\cdot 17^{4} \)	$A_4 \times C_2$ (as 12T7)	$[2]$
12.0.38806720086016.1	x^12 - 4x^11 + 6x^10 + 2x^9 + 9x^8 - 30x^7 - 32x^5 + 22x^4 + 46x^3 + 24x^2 + 4x + 1	\( 2^{18}\cdot 23^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.38806720086016.3	x^12 - 2x^11 + 2x^10 + 9x^8 - 24x^7 + 30x^6 - 4x^5 + 6x^4 - 46x^3 + 98x^2 - 70x + 25	\( 2^{18}\cdot 23^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.38806720086016.10	x^12 + 2x^10 + 20x^8 + 72x^6 + 80x^4 + 32x^2 + 64	\( 2^{18}\cdot 23^{6} \)	$D_6$ (as 12T3)	$[2]$
12.0.40060837890625.1	x^12 - 4x^11 + 8x^10 - 12x^9 + 7x^8 + x^7 - x^6 + 7x^5 + 8x^4 - x^3 + 4x^2 + x + 1	\( 5^{9}\cdot 29^{5} \)	$C_3:S_3.D_4$ (as 12T82)	$[2]$
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)	$[2]$
12.0.40400838383661.1	x^12 - 2x^11 + 5x^10 - 3x^9 + 5x^8 + 4x^7 + x^6 + 4x^5 + 5x^4 - 3x^3 + 5x^2 - 2x + 1	\( 3^{3}\cdot 7^{3}\cdot 257^{4} \)	12T221	$[2]$
12.0.41326975008000.1	x^12 - 4x^11 + 2x^10 + 13x^9 - 19x^8 - 12x^7 + 39x^6 - 24x^5 + 41x^4 - 59x^3 - 73x^2 + 77x + 121	\( 2^{8}\cdot 3^{6}\cdot 5^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.45056958152704.1	x^12 + 3x^10 + 6x^8 + 7x^6 - 5x^4 + 4	\( 2^{14}\cdot 229^{4} \)	12T226	$[2]$
12.0.47464824438784.2	x^12 - x^10 + 11x^8 - 6x^6 + 11x^4 - x^2 + 1	\( 2^{26}\cdot 29^{4} \)	$C_2^2\times C_2^2:S_4$ (as 12T139)	$[2]$
12.0.47464824438784.6	x^12 - x^10 - 2x^9 - 4x^8 + 8x^7 - 10x^6 + 4x^5 + 38x^4 - 64x^3 + 50x^2 - 20x + 4	\( 2^{26}\cdot 29^{4} \)	$C_2^2\times C_2^2:S_4$ (as 12T139)	$[2]$
12.0.47464824438784.7	x^12 + 9x^8 - 28x^6 + 52x^4 - 24x^2 + 4	\( 2^{26}\cdot 29^{4} \)	$C_2^2\times S_4$ (as 12T48)	$[2]$
12.0.47464824438784.13	x^12 + 9x^8 + 28x^6 + 52x^4 + 24x^2 + 4	\( 2^{26}\cdot 29^{4} \)	$C_2^2\times S_4$ (as 12T48)	$[2]$
12.0.52716660869376.1	x^12 - 3x^11 + 7x^10 - 8x^9 + 3x^8 + 21x^7 - 20x^6 + 21x^5 + 19x^4 - 22x^3 + 21x^2 - 5x + 1	\( 2^{8}\cdot 3^{6}\cdot 7^{10} \)	$D_6$ (as 12T3)	$[3]$
12.0.54203275126125.1	x^12 - x^11 + x^10 - 3x^9 + 9x^8 - x^7 + 13x^6 - x^5 + 9x^4 - 3x^3 + x^2 - x + 1	\( 3^{6}\cdot 5^{3}\cdot 29^{6} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.56192894500864.1	x^12 - 6x^9 - 5x^8 - 14x^7 + 18x^6 + 26x^5 + 7x^4 + 30x^3 + 32x^2 - 8x + 1	\( 2^{18}\cdot 11^{8} \)	$C_2 \times S_4$ (as 12T23)	$[2]$
12.0.56192894500864.2	x^12 - 2x^11 + 8x^10 - 4x^9 + 5x^8 + 10x^7 - 14x^6 - 10x^5 + 5x^4 + 4x^3 + 8x^2 + 2x + 1	\( 2^{18}\cdot 11^{8} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.60236288000000.1	x^12 - 5x^11 + 9x^10 - 3x^9 - 14x^8 + 36x^7 - 26x^6 - 4x^5 + 46x^4 - 54x^3 + 40x^2 - 16x + 4	\( 2^{15}\cdot 5^{6}\cdot 7^{6} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.64793042714624.1	x^12 - 14x^10 + 77x^8 - 203x^6 + 280x^4 - 196x^2 + 56	\( 2^{15}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.0.67834724548608.1	x^12 - 6x^11 + 20x^10 - 44x^9 + 66x^8 - 56x^7 + 4x^6 + 40x^5 - 16x^4 - 40x^3 + 52x^2 - 24x + 4	\( 2^{16}\cdot 3^{6}\cdot 17^{5} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.70955197267968.1	x^12 - 2x^10 - 2x^9 + 6x^8 + 10x^7 - 23x^6 - 10x^5 + 63x^4 - 72x^3 + 39x^2 - 10x + 1	\( 2^{18}\cdot 3^{6}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.72964670628096.1	x^12 - x^11 - x^10 + 12x^9 - 5x^8 - 5x^7 + 52x^6 - 35x^5 + 37x^4 + 24x^3 + 23x^2 + 5x + 1	\( 2^{8}\cdot 3^{10}\cdot 13^{6} \)	$S_3^2$ (as 12T16)	$[2]$
12.0.74049191673856.2	x^12 + 2x^10 + 4x^8 + 8x^6 + 16x^4 + 32x^2 + 64	\( 2^{18}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.74049191673856.3	x^12 - 6x^11 + 18x^10 - 28x^9 + 26x^8 - 16x^7 + 20x^6 - 22x^5 + 17x^4 - 14x^3 + 2x^2 + 2x + 1	\( 2^{18}\cdot 7^{10} \)	$C_2^2 \times A_4$ (as 12T25)	$[2]$
12.0.74049191673856.4	x^12 - 4x^11 + 6x^10 - 12x^9 + 30x^8 - 56x^7 + 120x^6 - 224x^5 + 284x^4 - 240x^3 + 136x^2 - 48x + 8	\( 2^{18}\cdot 7^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.0.80244904034304.3	x^12 - 8x^9 + 15x^8 + 24x^7 + 32x^6 - 24x^5 + 15x^4 + 8x^3 + 1	\( 2^{24}\cdot 3^{14} \)	$D_6$ (as 12T3)	$[2]$
12.0.80244904034304.5	x^12 + 9x^8 - 20x^6 - 12x^4 + 24x^2 + 4	\( 2^{24}\cdot 3^{14} \)	$D_6$ (as 12T3)	$[2]$
12.0.80244904034304.6	x^12 + 32x^6 + 48x^4 + 24x^2 + 4	\( 2^{24}\cdot 3^{14} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.80244904034304.7	x^12 + 12x^8 + 36x^4 + 36	\( 2^{24}\cdot 3^{14} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.80873772931125.1	x^12 - x^11 + 2x^10 + 2x^9 - 2x^8 + 4x^7 - 49x^6 - 59x^5 + 40x^4 + 51x^3 + 78x^2 + 144x + 72	\( 3^{6}\cdot 5^{3}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.80980417183744.2	x^12 + 8x^10 + 24x^8 + 38x^6 + 24x^4 + 8x^2 + 1	\( 2^{24}\cdot 13^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.80980417183744.5	x^12 + x^8 + 4x^6 + 36x^4 - 24x^2 + 4	\( 2^{24}\cdot 13^{6} \)	$S_3 \times C_2^2$ (as 12T10)	$[2]$
12.0.80980417183744.6	x^12 - 2x^10 + 6x^8 + 2x^6 + x^4 + 4x^2 + 4	\( 2^{24}\cdot 13^{6} \)	$C_2 \times S_4$ (as 12T24)	$[2]$
12.0.80980417183744.7	x^12 + x^8 - 4x^6 + 36x^4 + 24x^2 + 4	\( 2^{24}\cdot 13^{6} \)	$D_6$ (as 12T3)	$[2]$
12.0.80980417183744.8	x^12 - 4x^9 - 7x^8 - 36x^7 + 8x^6 + 144x^5 + 276x^4 + 248x^3 + 128x^2 + 32x + 4	\( 2^{24}\cdot 13^{6} \)	$D_6$ (as 12T3)	$[2]$

In order to download results, .