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 320)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.96717311574016.1	x^12 - 6x^10 + 16x^8 - 24x^6 + 19x^4 - 6x^2 - 1	\( -\,2^{24}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.96717311574016.2	x^12 - 2x^10 - 6x^8 - 4x^6 + 3x^4 - 4x^2 - 1	\( -\,2^{24}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.2	x^12 - 2x^10 - 8x^8 - 6x^6 - 7x^4 - 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.3	x^12 + 6x^10 + 12x^8 + 8x^6 - 7x^4 - 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.4	x^12 - 2x^10 - x^8 + 8x^6 + 7x^4 - 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.5	x^12 - 6x^10 + 12x^8 - 8x^6 - 7x^4 + 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.7	x^12 + 2x^10 - x^8 - 8x^6 + 7x^4 + 14x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.677021181018112.8	x^12 - 4x^10 + 3x^8 + 8x^6 - 21x^4 + 28x^2 - 7	\( -\,2^{24}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.722204136308736.5	x^12 - 6x^10 + 12x^8 - 8x^6 - 9x^4 + 18x^2 - 9	\( -\,2^{24}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.722204136308736.6	x^12 - 3x^8 - 8x^6 + 18x^4 + 18x^2 - 9	\( -\,2^{24}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.773738492592128.7	x^12 - 6x^10 + 16x^8 - 24x^6 + 12x^4 + 8x^2 - 8	\( -\,2^{27}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.773738492592128.8	x^12 + 4x^10 + 4x^8 + 4x^6 + 20x^4 + 16x^2 - 8	\( -\,2^{27}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.3	x^12 - 6x^10 + 12x^8 - 16x^6 + 39x^4 - 36x^2 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.4	x^12 - 9x^8 - 20x^6 - 24x^4 - 18x^2 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.6	x^12 - 9x^8 + 16x^6 + 3x^4 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.7	x^12 - 6x^10 + 15x^8 - 20x^6 + 12x^4 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.10	x^12 - 9x^8 + 20x^6 - 24x^4 + 18x^2 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.2166612408926208.11	x^12 + 6x^10 + 12x^8 + 16x^6 + 39x^4 + 36x^2 - 3	\( -\,2^{24}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.4739148267126784.2	x^12 - 7x^8 + 98x^4 - 294x^2 - 49	\( -\,2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.4739148267126784.3	x^12 - 21x^8 - 98x^6 - 196x^4 - 196x^2 - 49	\( -\,2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.4739148267126784.7	x^12 - 49x^4 - 49	\( -\,2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.4739148267126784.8	x^12 + 7x^8 - 49	\( -\,2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.1	x^12 - 2x^10 + 6x^8 - 48x^6 + 28x^4 - 168x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.2	x^12 - 6x^10 - 16x^8 - 64x^6 - 84x^4 - 112x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.3	x^12 + 10x^10 + 38x^8 + 64x^6 + 28x^4 - 56x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.5	x^12 - 2x^10 - 8x^8 + 8x^6 + 28x^4 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.7	x^12 + 6x^10 - 16x^8 + 64x^6 - 84x^4 + 112x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5416169448144896.8	x^12 + 2x^10 + 6x^8 + 48x^6 + 28x^4 + 168x^2 - 56	\( -\,2^{27}\cdot 7^{9} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5777633090469888.4	x^12 - 6x^8 - 16x^6 - 24x^2 - 8	\( -\,2^{27}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.5777633090469888.9	x^12 + 6x^10 + 24x^8 + 56x^6 + 60x^4 + 24x^2 - 8	\( -\,2^{27}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.6499837226778624.1	x^12 - 6x^10 + 9x^8 + 24x^6 - 81x^4 - 162x^2 - 81	\( -\,2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.6499837226778624.2	x^12 - 6x^10 + 9x^8 + 24x^6 - 108x^4 + 162x^2 - 81	\( -\,2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.6499837226778624.7	x^12 - 9x^4 - 9	\( -\,2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.6499837226778624.8	x^12 + 9x^8 + 18x^4 - 9	\( -\,2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.13685690504052736.5	x^12 - 4x^10 - 3x^8 + 16x^6 + 30x^4 - 62x^2 - 25	\( -\,2^{24}\cdot 13^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.13685690504052736.13	x^12 - 6x^10 + 24x^8 - 56x^6 + 83x^4 - 70x^2 - 1	\( -\,2^{24}\cdot 13^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.1	x^12 + 6x^10 - 96x^6 - 324x^4 - 432x^2 - 216	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.2	x^12 - 6x^10 - 18x^8 + 96x^6 - 216x^2 - 216	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.3	x^12 + 6x^10 - 18x^8 - 96x^6 + 216x^2 - 216	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.4	x^12 - 6x^10 + 96x^6 - 324x^4 + 432x^2 - 216	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.5	x^12 + 6x^10 + 6x^8 - 32x^6 - 84x^4 - 72x^2 - 24	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.17332899271409664.7	x^12 - 6x^8 + 4x^6 + 24x^4 - 24	\( -\,2^{27}\cdot 3^{17} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.37913186137014272.1	x^12 - 28x^8 - 196x^6 - 588x^4 - 784x^2 - 392	\( -\,2^{27}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.37913186137014272.3	x^12 - 14x^8 - 392x^2 - 392	\( -\,2^{27}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.37913186137014272.7	x^12 - 14x^8 + 392x^2 - 392	\( -\,2^{27}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.37913186137014272.8	x^12 - 28x^8 + 196x^6 - 588x^4 + 784x^2 - 392	\( -\,2^{27}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.51998697814228992.7	x^12 - 6x^10 + 18x^8 - 48x^6 + 144x^4 - 216x^2 - 72	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.51998697814228992.8	x^12 - 12x^10 + 36x^8 - 60x^6 + 36x^4 - 72	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.51998697814228992.9	x^12 + 12x^10 + 36x^8 + 60x^6 + 36x^4 - 72	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial
12.2.51998697814228992.12	x^12 + 6x^10 + 18x^8 + 48x^6 + 144x^4 + 216x^2 - 72	\( -\,2^{27}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T92)	Trivial