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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 184)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.188900999168000.1	x^12 - 2x^11 + 2x^10 + 4x^9 - 4x^8 + 6x^7 + 12x^6 - 6x^5 + 27x^4 + 20x^3 + 12x^2 + 28x + 13	\( 2^{18}\cdot 5^{3}\cdot 7^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.188900999168000.2	x^12 - 4x^11 + 16x^9 - 18x^8 + 2x^7 + 24x^6 - 48x^5 - x^4 + 38x^3 - 24x^2 + 14x + 29	\( 2^{18}\cdot 5^{3}\cdot 7^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.284512575791808.1	x^12 + 4x^10 - 11x^9 - x^8 - 27x^7 + 24x^6 + 23x^5 + 24x^4 + 16x^3 + 7x^2 + 3x + 1	\( 2^{6}\cdot 3^{3}\cdot 7^{8}\cdot 13^{4} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	$[2]$
12.4.284512575791808.1	x^12 - 4x^10 - 9x^9 - 18x^8 - 18x^7 - 7x^6 + 12x^5 + 20x^4 + 22x^3 + 7x^2 - 7x - 7	\( 2^{6}\cdot 3^{3}\cdot 7^{8}\cdot 13^{4} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.284512575791808.2	x^12 - 4x^11 + 9x^9 - 11x^8 + 2x^7 + 10x^6 + x^5 - 8x^4 - 11x^3 + 4x^2 + 7x + 1	\( 2^{6}\cdot 3^{3}\cdot 7^{8}\cdot 13^{4} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.285618310742016.1	x^12 - 4x^11 + 10x^10 - 12x^9 - 2x^8 + 56x^7 - 160x^6 + 224x^5 - 128x^4 - 40x^3 + 96x^2 - 48x + 8	\( 2^{18}\cdot 3^{3}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.285618310742016.1	x^12 - 2x^11 + 4x^10 - 14x^9 + 32x^8 - 84x^7 + 160x^6 - 216x^5 + 235x^4 - 172x^3 + 108x^2 - 38x + 13	\( 2^{18}\cdot 3^{3}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.677021181018112.1	x^12 - 6x^10 + 19x^8 - 36x^6 + 42x^4 - 28x^2 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.677021181018112.1	x^12 + 2x^10 - x^8 + 6x^6 + 14x^4 + 14x^2 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.677021181018112.3	x^12 - 2x^10 - x^8 + 8x^6 - 14x^4 + 14x^2 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.677021181018112.3	x^12 - 2x^10 - x^8 - 6x^6 + 14x^4 - 14x^2 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.677021181018112.4	x^12 + 6x^10 + 19x^8 + 36x^6 + 42x^4 + 28x^2 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.677021181018112.4	x^12 - 4x^10 + 3x^8 - 6x^6 - 14x^4 + 7	\( 2^{24}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.773738492592128.3	x^12 + 2x^10 - 2x^8 - 4x^4 + 8x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.773738492592128.4	x^12 + 4x^10 + 6x^8 - 8x^4 - 24x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.2166612408926208.1	x^12 - 6x^8 - 4x^6 - 3x^4 - 18x^2 + 3	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.2166612408926208.2	x^12 + 6x^10 + 6x^8 + 4x^6 - 3x^4 + 3	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.2166612408926208.2	x^12 - 6x^10 + 18x^8 - 32x^6 + 33x^4 - 18x^2 + 3	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.2166612408926208.3	x^12 - 6x^8 + 4x^6 - 3x^4 + 18x^2 + 3	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.2166612408926208.5	x^12 - 3x^8 - 8x^6 - 9x^4 + 27	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.2166612408926208.8	x^12 - 3x^8 + 8x^6 - 9x^4 + 27	\( 2^{24}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.2779905883635712.2	x^12 - 4x^11 + 8x^10 - 8x^9 + 23x^8 - 86x^7 + 180x^6 - 226x^5 + 192x^4 - 124x^3 + 62x^2 - 22x + 5	\( 2^{18}\cdot 13^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.2779905883635712.2	x^12 - 2x^11 + 20x^9 - 46x^8 + 98x^7 - 124x^6 + 122x^5 - 11x^4 - 20x^3 - 8x + 1	\( 2^{18}\cdot 13^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.5416169448144896.1	x^12 - 16x^10 + 90x^8 - 244x^6 + 336x^4 - 224x^2 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.5416169448144896.2	x^12 - 2x^10 + 6x^8 + 8x^6 + 56x^2 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.5416169448144896.2	x^12 - 6x^10 - 2x^8 + 48x^6 - 168x^2 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.5416169448144896.3	x^12 + 6x^10 - 2x^8 - 48x^6 + 168x^2 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.5416169448144896.4	x^12 - 4x^10 + 10x^8 - 20x^6 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.5416169448144896.4	x^12 + 16x^10 + 90x^8 + 244x^6 + 336x^4 + 224x^2 + 56	\( 2^{27}\cdot 7^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.5777633090469888.2	x^12 + 6x^10 + 12x^8 - 36x^4 - 48x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.5777633090469888.14	x^12 + 6x^10 + 6x^8 + 12x^4 + 24x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.17332899271409664.1	x^12 - 6x^10 - 24x^8 + 56x^6 + 84x^4 - 216x^2 + 24	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.4.17332899271409664.2	x^12 - 6x^10 + 24x^8 - 56x^6 + 84x^4 - 72x^2 + 24	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.17332899271409664.4	x^12 + 6x^10 + 12x^8 + 16x^6 + 12x^4 + 24	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.17332899271409664.4	x^12 - 6x^10 + 18x^8 - 48x^6 + 108x^4 - 216x^2 + 216	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.0.17332899271409664.7	x^12 + 6x^10 - 24x^8 - 56x^6 + 84x^4 + 216x^2 + 24	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.17332899271409664.12	x^12 + 6x^10 + 18x^8 + 48x^6 + 108x^4 + 216x^2 + 216	\( 2^{27}\cdot 3^{17} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.37913186137014272.11	x^12 + 14x^10 + 56x^8 + 112x^6 + 196x^4 + 392x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	$[2]$
12.0.37913186137014272.12	x^12 + 14x^10 + 84x^8 + 280x^6 + 588x^4 + 784x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	$[2]$
12.4.37913186137014272.25	x^12 - 14x^10 + 84x^8 - 280x^6 + 588x^4 - 784x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.4.37913186137014272.27	x^12 - 14x^10 + 56x^8 - 112x^6 + 196x^4 - 392x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.4.51998697814228992.9	x^12 - 18x^8 + 72x^4 - 216x^2 + 72	\( 2^{27}\cdot 3^{18} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.0.51998697814228992.12	x^12 - 18x^8 + 108x^6 - 144x^4 + 72	\( 2^{27}\cdot 3^{18} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	$[2]$
12.4.51998697814228992.13	x^12 - 18x^8 - 108x^6 - 144x^4 + 72	\( 2^{27}\cdot 3^{18} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial (GRH)
12.0.51998697814228992.16	x^12 - 18x^8 + 72x^4 + 216x^2 + 72	\( 2^{27}\cdot 3^{18} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	$[2]$
12.6.108296692370108416.2	x^12 - 5x^11 + 4x^10 + 3x^9 + 37x^8 - 68x^7 - 105x^6 + 219x^5 + 62x^4 - 195x^3 - 23x^2 + 58x + 4	\( -\,2^{12}\cdot 31^{9} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.4.109485524032421888.5	x^12 - 8x^10 + 22x^8 - 36x^6 + 80x^4 - 80x^2 + 8	\( 2^{27}\cdot 13^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.0.109485524032421888.7	x^12 + 2x^10 - 10x^8 + 16x^6 - 20x^4 + 8x^2 + 8	\( 2^{27}\cdot 13^{8} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.6.116905326643474432.2	x^12 - 6x^11 + 15x^10 - 20x^9 - 74x^8 + 350x^7 - 617x^6 + 608x^5 - 223x^4 - 152x^3 + 160x^2 - 42x - 1	\( -\,2^{12}\cdot 7^{9}\cdot 29^{4} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial
12.8.136736192768500125.1	x^12 - 3x^11 - 3x^10 + 4x^9 + 15x^8 + 75x^7 - 191x^6 - 48x^5 + 240x^4 - 31x^3 - 39x^2 + 3x + 1	\( 3^{16}\cdot 5^{3}\cdot 71^{4} \)	$C_2\times C_2^2\wr C_2:C_3$ (as 12T88)	Trivial