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 101)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.102423828125.1	x^12 + 2x^10 - x^9 + 4x^8 - 4x^7 + 4x^6 - 7x^5 + 7x^4 - 3x^3 + 4x^2 - 3x + 1	\( 5^{9}\cdot 229^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.113439453125.1	x^12 - 2x^11 + 3x^10 - 2x^9 + 2x^8 - 4x^7 + 7x^6 - 6x^5 + 2x^4 + x^3 - 2x + 1	\( 5^{9}\cdot 241^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.246142578125.1	x^12 - 2x^11 + x^10 + 5x^9 - 5x^8 - 2x^7 + 9x^6 - 2x^5 - 5x^4 + 5x^3 + x^2 - 2x + 1	\( 5^{11}\cdot 71^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.848205078125.1	x^12 - 4x^11 + 10x^10 - 10x^9 + x^8 + 15x^7 - 21x^6 + 15x^5 + x^4 - 10x^3 + 10x^2 - 4x + 1	\( 5^{9}\cdot 659^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.11278142578125.1	x^12 - x^11 - 4x^10 + 7x^9 - 11x^7 + 7x^6 + 8x^5 - 6x^4 + 2x^3 + 17x^2 + 10x + 1	\( 3^{6}\cdot 5^{9}\cdot 89^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.16916501953125.1	x^12 - x^11 - 2x^10 + 3x^9 + x^7 + 3x^6 - x^5 - 3x^3 - 2x^2 + x + 1	\( 3^{6}\cdot 5^{9}\cdot 109^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.29418283203125.1	x^12 - x^11 + 6x^10 - 7x^9 + 18x^8 - 8x^7 + 15x^6 + 22x^5 + 41x^4 + 9x^3 + 9x^2 - 5x + 1	\( 5^{9}\cdot 3881^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.51942673828125.1	x^12 - 2x^11 - 6x^10 + 11x^9 + 15x^8 - 17x^7 - 27x^6 + 4x^5 + 29x^4 + 4x^3 - 12x^2 + 1	\( 3^{6}\cdot 5^{9}\cdot 191^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.59103517578125.1	x^12 + 14x^10 + 71x^8 + 164x^6 + 171x^4 + 65x^2 + 5	\( 5^{9}\cdot 5501^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.72705206386688.2	x^12 + 4x^10 + 10x^8 + 20x^6 + 17x^4 + 8x^2 + 8	\( 2^{37}\cdot 23^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.72705206386688.2	x^12 - 4x^10 + 10x^8 - 20x^6 + 17x^4 - 8x^2 + 8	\( 2^{37}\cdot 23^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.121433985532928.1	x^12 - 2x^11 + 2x^10 + 4x^9 - 10x^8 + 10x^7 + 10x^6 - 10x^5 - 10x^4 - 4x^3 + 2x^2 + 2x + 1	\( 2^{10}\cdot 17^{9} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.179437939453125.1	x^12 - 3x^11 - 4x^10 + 20x^9 - 5x^8 - 43x^7 + 39x^6 + 27x^5 - 55x^4 + 5x^3 + 36x^2 + 12x + 1	\( 3^{6}\cdot 5^{11}\cdot 71^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.2193401363688512.1	x^12 - 3x^11 + 2x^10 + 4x^9 - 15x^8 + 23x^7 + 11x^6 - 23x^5 - 15x^4 - 4x^3 + 2x^2 + 3x + 1	\( 2^{6}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.11479038832934912.1	x^12 - 12x^10 + 46x^8 - 52x^6 - 15x^4 - 8x^2 + 8	\( 2^{37}\cdot 17^{4} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.11479038832934912.2	x^12 + 12x^10 + 46x^8 + 52x^6 - 15x^4 + 8x^2 + 8	\( 2^{37}\cdot 17^{4} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.15911316233388032.1	x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128x + 64	\( 2^{33}\cdot 1361^{2} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.0.16169555437027328.1	x^12 + 8x^10 - 4x^8 - 4x^6 + 5x^4 - 4x^2 + 2	\( 2^{37}\cdot 7^{6} \)	$S_3^2:C_4$ (as 12T79)	$[3]$
12.4.16169555437027328.1	x^12 - 8x^10 - 4x^8 + 4x^6 + 5x^4 + 4x^2 + 2	\( 2^{37}\cdot 7^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.12.21445928455078125.1	x^12 - 3x^11 - 18x^10 + 52x^9 + 94x^8 - 279x^7 - 122x^6 + 452x^5 + 25x^4 - 228x^3 + 30x^2 + 36x - 9	\( 3^{6}\cdot 5^{9}\cdot 3881^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.12.26436901658203125.1	x^12 - 2x^11 - 17x^10 + 28x^9 + 102x^8 - 114x^7 - 268x^6 + 144x^5 + 252x^4 - 54x^3 - 55x^2 - 2x + 1	\( 3^{6}\cdot 5^{9}\cdot 31^{2}\cdot 139^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.31087100296429568.2	x^12 + 10x^10 - 5x^8 - 48x^6 - 13x^4 + 102x^2 + 17	\( 2^{18}\cdot 17^{9} \)	$S_3^2:C_4$ (as 12T79)	$[2, 2]$
12.8.35094421819016192.1	x^12 - x^11 + 4x^10 - 3x^9 - 26x^8 + 59x^7 - 116x^6 - 33x^5 + 270x^4 - 27x^3 - 140x^2 + 15x + 13	\( 2^{10}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.73040694872113152.4	x^12 - 12x^10 + 54x^8 - 116x^6 + 129x^4 - 72x^2 + 8	\( 2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.73040694872113152.5	x^12 - 12x^10 + 54x^8 - 124x^6 + 177x^4 - 144x^2 + 32	\( 2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.73040694872113152.13	x^12 + 12x^10 + 54x^8 + 116x^6 + 129x^4 + 72x^2 + 8	\( 2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.73040694872113152.24	x^12 + 12x^10 + 54x^8 + 124x^6 + 177x^4 + 144x^2 + 32	\( 2^{37}\cdot 3^{12} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.4.124348401185718272.1	x^12 - 2x^11 - 11x^10 + 32x^9 - 8x^8 - 12x^7 + 56x^6 - 368x^5 + 741x^4 - 722x^3 + 275x^2 + 120x - 118	\( 2^{20}\cdot 17^{9} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.8.126927759749414912.1	x^12 - 4x^8 - 68x^6 + 101x^4 - 28x^2 + 2	\( 2^{37}\cdot 31^{4} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.126927759749414912.2	x^12 - 4x^8 + 68x^6 + 101x^4 + 28x^2 + 2	\( 2^{37}\cdot 31^{4} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.4.207340138919886848.1	x^12 - 4x^11 - 2x^10 - 4x^9 + 9x^8 + 32x^7 + 28x^6 + 24x^5 + 12x^4 - 48x^3 - 112x^2 - 64x - 68	\( 2^{33}\cdot 17^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.207340138919886848.2	x^12 - 4x^10 + 18x^8 + 88x^6 - 24x^4 + 32x^2 + 8	\( 2^{33}\cdot 17^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.4.207340138919886848.6	x^12 + 4x^10 + 18x^8 - 88x^6 - 24x^4 - 32x^2 + 8	\( 2^{33}\cdot 17^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.497393604742873088.5	x^12 - 2x^11 + 3x^10 + 25x^8 - 66x^7 + 141x^6 - 292x^5 + 386x^4 - 32x^3 - 850x^2 + 392x + 548	\( 2^{22}\cdot 17^{9} \)	$S_3^2:C_4$ (as 12T79)	$[2, 2]$
12.8.657366253849018368.1	x^12 - 12x^10 - 16x^9 - 6x^8 + 24x^7 + 272x^6 + 624x^5 + 486x^4 + 16x^3 - 144x^2 - 48x + 4	\( 2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.657366253849018368.2	x^12 - 12x^10 + 42x^8 - 84x^6 + 225x^4 - 432x^2 + 288	\( 2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.657366253849018368.38	x^12 - 8x^9 + 12x^8 - 24x^7 + 152x^6 - 264x^5 - 141x^4 + 464x^3 + 72x^2 - 360x + 274	\( 2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.0.657366253849018368.42	x^12 + 12x^10 + 42x^8 + 84x^6 + 225x^4 + 432x^2 + 288	\( 2^{37}\cdot 3^{14} \)	$S_3^2:C_4$ (as 12T79)	$[2, 6]$
12.4.792308216414339072.7	x^12 + 4x^10 - 10x^8 - 84x^6 + 161x^4 - 280x^2 + 392	\( 2^{37}\cdot 7^{8} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.792308216414339072.10	x^12 - 4x^10 - 10x^8 + 84x^6 + 161x^4 + 280x^2 + 392	\( 2^{37}\cdot 7^{8} \)	$S_3^2:C_4$ (as 12T79)	$[2, 2]$
12.0.829360555679547392.9	x^12 - 4x^11 + 2x^10 - 4x^9 + 63x^8 - 88x^7 - 72x^6 - 56x^5 + 905x^4 - 812x^3 - 206x^2 + 196x + 103	\( 2^{35}\cdot 17^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.2246042996417036288.3	x^12 - 34x^8 + 17x^6 + 255x^4 + 289x^2 + 68	\( 2^{16}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T79)	$[2, 2]$
12.8.5086474415114289152.1	x^12 - 16x^10 + 40x^8 + 44x^6 + 40x^4 - 64x^2 + 2	\( 2^{35}\cdot 23^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.0.5086474415114289152.3	x^12 + 16x^10 + 40x^8 - 44x^6 + 40x^4 + 64x^2 + 2	\( 2^{35}\cdot 23^{6} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.5916296284641165312.2	x^12 - 12x^10 + 18x^8 + 100x^6 + 81x^4 - 72x^2 + 8	\( 2^{37}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T79)	Trivial (GRH)
12.8.5916296284641165312.3	x^12 - 12x^10 + 18x^8 + 76x^6 + 81x^4 - 288x^2 + 128	\( 2^{37}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T79)	Trivial (GRH)
12.0.5916296284641165312.21	x^12 + 12x^10 + 18x^8 - 100x^6 + 81x^4 + 72x^2 + 8	\( 2^{37}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T79)	$[3]$
12.0.5916296284641165312.53	x^12 + 12x^10 + 18x^8 - 76x^6 + 81x^4 + 288x^2 + 128	\( 2^{37}\cdot 3^{16} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.4.8984171985668145152.2	x^12 - 4x^11 - 4x^10 - 22x^9 + 127x^8 + 32x^7 - 71x^6 - 446x^5 + 372x^4 - 1128x^3 + 1959x^2 - 128x - 344	\( 2^{18}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T79)	$[2]$
12.0.8984171985668145152.3	x^12 + 17x^10 + 102x^8 + 306x^6 + 561x^4 + 629x^2 + 272	\( 2^{18}\cdot 17^{11} \)	$S_3^2:C_4$ (as 12T79)	$[2, 2]$ (GRH)