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 all 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.82497731821568.1	x^12 + 4x^8 - 4x^6 + 5x^4 - 12x^2 + 2	\( 2^{35}\cdot 7^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.0.117128000000000.1	x^12 - x^11 + 2x^10 - 10x^9 + 9x^8 - 22x^7 + 41x^6 + 9x^5 - 9x^4 - 49x^3 + 11x^2 + 8x + 11	\( 2^{12}\cdot 5^{9}\cdot 11^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.0.265720500000000.1	x^12 - 9x^10 - 6x^9 + 36x^8 + 48x^7 - 38x^6 - 108x^5 + 9x^4 + 200x^3 + 216x^2 + 96x + 16	\( 2^{8}\cdot 3^{12}\cdot 5^{9} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.756680642578125.2	x^12 - 3x^9 - x^6 + 3x^3 + 1	\( 3^{18}\cdot 5^{9} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.4565043429507072.1	x^12 - 4x^9 - 18x^6 - 12x^3 - 1	\( 2^{33}\cdot 3^{12} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.4565043429507072.4	x^12 - 4x^9 - 6x^6 + 4x^3 + 1	\( 2^{33}\cdot 3^{12} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.0.15196929064453125.3	x^12 - 21x^9 + 211x^6 - 891x^3 + 1331	\( 3^{12}\cdot 5^{9}\cdot 11^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[2]$
12.0.18260173718028288.43	x^12 - 12x^10 - 8x^9 + 18x^8 + 48x^7 + 148x^6 + 72x^5 + 105x^4 - 40x^3 - 24x + 14	\( 2^{35}\cdot 3^{12} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.0.18260173718028288.64	x^12 - 12x^10 - 8x^9 + 54x^8 + 72x^7 - 64x^6 - 216x^5 - 183x^4 + 104x^3 + 396x^2 + 336x + 98	\( 2^{35}\cdot 3^{12} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.49519263525896192.13	x^12 - 4x^11 - 2x^10 + 20x^9 - 27x^8 - 40x^7 + 116x^6 + 120x^5 - 342x^4 - 64x^3 + 216x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.0.71228826095703125.1	x^12 - x^11 + 7x^10 - 8x^9 + 50x^8 + 43x^7 + 267x^6 + 246x^5 + 1546x^4 + 30x^3 + 360x^2 - 150x + 25	\( 5^{9}\cdot 19^{4}\cdot 23^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[3]$
12.4.164341563462254592.2	x^12 - 24x^9 - 12x^8 + 72x^7 + 188x^6 - 312x^5 - 123x^4 + 264x^3 - 204x^2 + 192x - 14	\( 2^{35}\cdot 3^{14} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.164341563462254592.4	x^12 - 24x^8 + 12x^6 + 189x^4 - 324x^2 + 18	\( 2^{35}\cdot 3^{14} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.198077054103584768.4	x^12 - 12x^10 + 26x^8 - 140x^6 + 129x^4 - 328x^2 + 8	\( 2^{35}\cdot 7^{8} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[3]$
12.0.198077054103584768.12	x^12 - 4x^10 - 16x^9 + 4x^8 + 112x^7 + 156x^6 - 104x^5 + 86x^4 - 624x^3 + 144x^2 + 432x + 324	\( 2^{35}\cdot 7^{8} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[2, 2]$
12.12.778836347115798528.1	x^12 - 24x^10 + 180x^8 - 476x^6 + 309x^4 - 60x^2 + 2	\( 2^{35}\cdot 3^{4}\cdot 23^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.1479074071160291328.1	x^12 + 12x^10 - 16x^9 - 54x^8 - 72x^7 - 32x^6 + 288x^5 + 129x^4 - 312x^3 + 36x^2 + 144x - 62	\( 2^{35}\cdot 3^{16} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.1479074071160291328.29	x^12 + 12x^10 + 18x^8 - 124x^6 + 81x^4 - 144x^2 + 32	\( 2^{35}\cdot 3^{16} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.2426443912768913408.36	x^12 - 4x^11 + 6x^10 - 12x^9 - 33x^8 + 168x^7 - 412x^6 + 1120x^5 - 738x^4 + 208x^3 + 976x^2 - 3520x + 736	\( 2^{33}\cdot 7^{10} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[3]$
12.4.3327916660110655488.4	x^12 - 8x^9 - 16x^6 + 32x^3 - 8	\( 2^{33}\cdot 3^{18} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial
12.4.3327916660110655488.5	x^12 - 12x^9 + 26x^6 + 12x^3 + 1	\( 2^{33}\cdot 3^{18} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial (GRH)
12.0.9705775651075653632.23	x^12 - 4x^11 - 2x^10 + 52x^9 - 95x^8 - 24x^7 + 504x^6 - 488x^5 + 2337x^4 - 2524x^3 + 5998x^2 - 4180x + 6497	\( 2^{35}\cdot 7^{10} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[2, 6]$ (GRH)
12.0.13311666640442621952.65	x^12 + 12x^10 + 18x^8 - 24x^7 - 52x^6 - 144x^5 - 87x^4 + 48x^3 + 288x^2 + 264x + 142	\( 2^{35}\cdot 3^{18} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[2]$
12.0.13311666640442621952.87	x^12 + 12x^10 + 54x^8 + 204x^6 + 657x^4 + 864x^2 + 1152	\( 2^{35}\cdot 3^{18} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[2]$ (GRH)
12.12.16479838152000000000.1	x^12 - 4x^11 - 36x^10 + 203x^9 + 101x^8 - 2222x^7 + 3079x^6 + 4734x^5 - 13511x^4 + 6255x^3 + 4833x^2 - 2673x - 729	\( 2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 41^{4} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	Trivial (GRH)
12.0.735093969631029552528.1	x^12 - 3x^9 + 14x^6 - 24x^3 + 64	\( 2^{4}\cdot 3^{18}\cdot 17^{9} \)	$C_2\times C_3:S_3.C_2$ (as 12T41)	$[110]$ (GRH)