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 66)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.15203947802176.1	x^12 - 4x^11 + 9x^10 - 22x^9 + 32x^8 - 30x^7 + 57x^6 - 56x^5 - 14x^3 + 14x^2 + 14x + 7	\( 2^{6}\cdot 7^{10}\cdot 29^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.0.15203947802176.3	x^12 - 4x^11 + 6x^10 - 12x^9 + 44x^8 - 98x^7 + 134x^6 - 168x^5 + 249x^4 - 310x^3 + 262x^2 - 146x + 43	\( 2^{6}\cdot 7^{10}\cdot 29^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.75753088140625.1	x^12 - x^11 - 2x^10 - 8x^8 + x^7 - 11x^6 + x^5 - 8x^4 - 2x^2 - x + 1	\( 5^{6}\cdot 7^{8}\cdot 29^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.151416101265625.1	x^12 - 2x^11 - 4x^10 + 3x^9 + 10x^8 + 13x^7 - 21x^6 - 27x^5 + 25x^4 + 20x^3 - 10x^2 - 8x - 1	\( 5^{6}\cdot 7^{8}\cdot 41^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.242810410640625.2	x^12 - 3x^11 - 6x^8 + 3x^7 - 9x^6 + 3x^5 - 6x^4 - 3x + 1	\( 3^{16}\cdot 5^{6}\cdot 19^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.368947264000000.2	x^12 - 5x^10 + 2x^8 + 17x^6 - 19x^4 + 2x^2 + 1	\( 2^{12}\cdot 5^{6}\cdot 7^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.564668382613504.2	x^12 + 2x^10 - 7x^8 - 19x^6 - 8x^4 + 5x^2 + 1	\( 2^{12}\cdot 13^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.564668382613504.3	x^12 - 5x^10 + 5x^8 + 6x^6 - 7x^4 - 2x^2 + 1	\( 2^{12}\cdot 13^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.860374847629609.1	x^12 - 3x^11 + 2x^10 + 10x^9 - 48x^8 + 109x^7 - 193x^6 + 245x^5 - 250x^4 + 250x^3 - 202x^2 + 105x - 25	\( 13^{10}\cdot 79^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.2950947586890625.1	x^12 - 3x^11 + x^10 + 19x^9 - 36x^8 + 28x^7 + 3x^6 - 14x^5 + 96x^4 - 163x^3 + 81x^2 - 41x + 29	\( 5^{6}\cdot 7^{8}\cdot 181^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.4739148267126784.5	x^12 - 6x^10 + 8x^8 + 8x^6 - 13x^4 - 6x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.4739148267126784.13	x^12 + 2x^10 - 10x^8 - 20x^6 - 5x^4 + 4x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.12.5674816059390625.1	x^12 - 3x^11 - 14x^10 + 34x^9 + 88x^8 - 114x^7 - 301x^6 + 26x^5 + 408x^4 + 340x^3 + 117x^2 + 18x + 1	\( 5^{6}\cdot 7^{8}\cdot 251^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.6189907940737024.2	x^12 - 2x^10 - 9x^8 + 14x^6 + 10x^4 - 8x^2 + 1	\( 2^{30}\cdot 7^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.6189907940737024.6	x^12 - 4x^10 - 8x^8 + 14x^6 + 27x^4 + 10x^2 + 1	\( 2^{30}\cdot 7^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.6499837226778624.3	x^12 - 15x^8 - 2x^6 + 36x^4 - 12x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.6499837226778624.29	x^12 - 12x^8 - 14x^6 + 9x^4 + 12x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.12.26635831223765625.1	x^12 - 3x^11 - 15x^10 + 55x^9 + 48x^8 - 303x^7 + 90x^6 + 516x^5 - 312x^4 - 278x^3 + 153x^2 + 48x - 19	\( 3^{16}\cdot 5^{6}\cdot 199^{2} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.46221064723759104.2	x^12 - 6x^10 + 3x^8 + 30x^6 - 42x^4 + 12x^2 + 1	\( 2^{30}\cdot 3^{16} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.4.46221064723759104.12	x^12 - 6x^10 - 3x^8 + 30x^6 + 36x^4 + 12x^2 + 1	\( 2^{30}\cdot 3^{16} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.0.52456210366771264.2	x^12 - 5x^11 + 10x^10 - 14x^9 + 4x^8 + 34x^7 - 47x^6 + 45x^5 + 32x^4 - 68x^3 + 20x^2 + 36x + 16	\( 2^{6}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[9]$
12.4.303305489096114176.2	x^12 + 16x^10 + 88x^8 + 190x^6 + 121x^4 - 38x^2 + 1	\( 2^{30}\cdot 7^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.8.303305489096114176.3	x^12 - 6x^10 - 13x^8 + 106x^6 - 104x^4 + 8x^2 + 1	\( 2^{30}\cdot 7^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.415989582513831936.6	x^12 - 6x^10 - 9x^8 + 78x^6 - 18x^4 - 108x^2 + 9	\( 2^{30}\cdot 3^{18} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.415989582513831936.19	x^12 + 6x^10 - 21x^8 - 188x^6 - 285x^4 + 30x^2 + 1	\( 2^{30}\cdot 3^{18} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.0.839299365868340224.2	x^12 - 3x^10 + 27x^8 - 49x^6 + 92x^4 - 68x^2 + 16	\( 2^{10}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[9]$
12.8.875884192259375104.1	x^12 - 2x^10 - 13x^8 + 14x^6 + 26x^4 - 28x^2 + 1	\( 2^{30}\cdot 13^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.875884192259375104.12	x^12 + 8x^10 - 38x^6 - 39x^4 - 6x^2 + 1	\( 2^{30}\cdot 13^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.0.3357197463473360896.10	x^12 - 12x^10 + 60x^8 - 98x^6 + 147x^4 - 130x^2 + 64	\( 2^{12}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[18]$
12.0.3357197463473360896.14	x^12 - 6x^10 + 15x^8 - 82x^6 + 480x^4 - 1184x^2 + 1024	\( 2^{12}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[18]$
12.0.3357197463473360896.16	x^12 + 5x^10 - 18x^8 - 20x^6 + 344x^4 - 960x^2 + 1024	\( 2^{12}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[2, 18]$ (GRH)
12.0.13428789853893443584.22	x^12 - 6x^10 + 15x^8 + 42x^6 - 140x^4 + 56x^2 + 1024	\( 2^{14}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[18]$ (GRH)
12.0.13428789853893443584.38	x^12 + 9x^10 + 26x^8 + 52x^6 + 136x^4 + 32x^2 + 256	\( 2^{14}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[18]$ (GRH)
12.8.18235961957662326784.2	x^12 - 10x^10 + 23x^8 + 22x^6 - 94x^4 + 16x^2 + 49	\( 2^{30}\cdot 19^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.18235961957662326784.21	x^12 + 6x^10 - 13x^8 - 92x^6 - 69x^4 + 62x^2 + 49	\( 2^{30}\cdot 19^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial
12.0.53715159415573774336.46	x^12 + 14x^10 + 61x^8 + 52x^6 + 308x^4 - 192x^2 + 256	\( 2^{16}\cdot 31^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[2, 18]$ (GRH)
12.8.102862222917439062016.3	x^12 - 6x^10 - 4x^8 + 56x^6 - 61x^4 - 6x^2 + 1	\( 2^{24}\cdot 19^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.102862222917439062016.8	x^12 - 4x^10 - 25x^8 - 20x^6 + 10x^4 + 10x^2 + 1	\( 2^{24}\cdot 19^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.148024428491834392576.4	x^12 - 8x^10 - 8x^8 + 202x^6 - 449x^4 - 50x^2 + 625	\( 2^{30}\cdot 13^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[2]$ (GRH)
12.4.148024428491834392576.24	x^12 + 6x^10 - 37x^8 - 266x^6 - 284x^4 + 500x^2 + 625	\( 2^{30}\cdot 13^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	$[2]$ (GRH)
12.8.3663139112860606529536.1	x^12 - 10x^10 + 15x^8 + 76x^6 - 164x^4 - 16x^2 + 4	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.3663139112860606529536.4	x^12 - 14x^10 - 107x^8 + 1516x^6 - 1910x^4 + 592x^2 + 16	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.3663139112860606529536.5	x^12 + 6x^10 - 131x^8 + 428x^6 - 462x^4 + 96x^2 + 64	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.3663139112860606529536.7	x^12 - 10x^10 - 33x^8 + 396x^6 - 4x^4 - 2768x^2 + 2116	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.3663139112860606529536.12	x^12 - 14x^10 + 17x^8 + 152x^6 + 198x^4 + 96x^2 + 16	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.3663139112860606529536.16	x^12 + 16x^10 - 100x^8 - 1320x^6 - 1028x^4 + 656x^2 + 16	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.3663139112860606529536.17	x^12 + 30x^10 + 135x^8 + 56x^6 - 512x^4 - 576x^2 + 64	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.3663139112860606529536.39	x^12 - 4x^10 - 134x^8 - 136x^6 + 1608x^4 + 1408x^2 + 256	\( 2^{32}\cdot 31^{8} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.8.6583182266716099969024.4	x^12 - 26x^10 + 231x^8 - 790x^6 + 620x^4 + 876x^2 + 121	\( 2^{30}\cdot 19^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)
12.4.6583182266716099969024.14	x^12 + 8x^10 - 100x^8 - 1018x^6 - 2101x^4 - 662x^2 + 121	\( 2^{30}\cdot 19^{10} \)	$C_2^2\wr C_2:C_3$ (as 12T58)	Trivial (GRH)