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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.221533456000000000000.3	x^16 - 2x^15 + 4x^14 + 8x^13 + 7x^12 - 58x^11 + 214x^10 - 116x^9 - 296x^8 + 886x^7 - 268x^6 - 990x^5 + 1316x^4 + 480x^3 - 1170x^2 + 405	\( 2^{16}\cdot 5^{12}\cdot 61^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$
16.0.376145144477611196416.3	x^16 - 8x^15 + 44x^14 - 160x^13 + 448x^12 - 1008x^11 + 1784x^10 - 2664x^9 + 3292x^8 - 3248x^7 + 2900x^6 - 1728x^5 + 980x^4 - 104x^3 + 24x^2 + 104x + 17	\( 2^{52}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$
16.8.472769874482845188096.2	x^16 - 8x^14 + 8x^12 - 40x^11 + 160x^9 + 100x^8 - 128x^7 - 112x^6 + 64x^5 + 72x^4 - 8x^3 - 16x^2 + 1	\( 2^{56}\cdot 3^{8} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial
16.8.4294967296000000000000.2	x^16 - 8x^14 - 14x^12 + 116x^10 + 199x^8 - 12x^6 - 46x^4 + 4x^2 + 1	\( 2^{44}\cdot 5^{12} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.0.11574317056000000000000.7	x^16 - 6x^15 - 3x^14 + 100x^13 - 200x^12 - 374x^11 + 1876x^10 - 1520x^9 - 3801x^8 + 8020x^7 + 444x^6 - 16792x^5 + 20480x^4 - 8320x^3 - 1032x^2 + 672x + 496	\( 2^{24}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$ (GRH)
16.8.2963025166336000000000000.3	x^16 - 4x^15 - 6x^14 + 40x^13 - 82x^12 + 92x^11 + 28x^10 + 308x^9 + 227x^8 + 916x^7 - 3228x^6 - 2980x^5 - 1370x^4 + 1544x^3 + 1150x^2 + 124x + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$ (GRH)
16.0.2963025166336000000000000.4	x^16 - 8x^14 - 8x^13 - 28x^12 - 112x^11 - 386x^10 - 1084x^9 + 1550x^8 + 18704x^7 + 52532x^6 + 83536x^5 + 98107x^4 + 93808x^3 + 65772x^2 + 31856x + 16631	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2]$ (GRH)
16.8.2963025166336000000000000.4	x^16 - 2x^14 - 36x^13 + 42x^12 + 224x^11 - 684x^10 - 48x^9 + 3200x^8 - 2608x^7 - 5222x^6 + 8652x^5 + 597x^4 - 12536x^3 + 2748x^2 + 4472x - 839	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.0.20723941878730254150390625.4	x^16 - 8x^15 + 22x^14 + 16x^13 - 247x^12 + 560x^11 + 31x^10 - 2752x^9 + 5883x^8 - 2124x^7 - 13816x^6 + 26358x^5 - 2717x^4 - 55758x^3 + 94988x^2 - 78712x + 30416	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2]$ (GRH)
16.0.105910114717696000000000000.1	x^16 - 6x^15 + 3x^14 + 48x^13 + 12x^12 - 958x^11 + 2262x^10 + 3994x^9 - 18615x^8 - 26482x^7 + 177806x^6 - 36422x^5 - 772272x^4 + 778892x^3 + 1535495x^2 - 3224374x + 1637641	\( 2^{24}\cdot 5^{12}\cdot 401^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$ (GRH)
16.0.247905780760576000000000000.1	x^16 + 14x^14 + 77x^12 + 1092x^10 + 10940x^8 + 54498x^6 + 232562x^4 + 476656x^2 + 923521	\( 2^{40}\cdot 5^{12}\cdot 31^{4} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.0.247905780760576000000000000.2	x^16 + 2x^14 + 33x^12 - 356x^10 - 685x^8 - 11036x^6 + 31713x^4 + 59582x^2 + 923521	\( 2^{40}\cdot 5^{12}\cdot 31^{4} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.0.12136551081312256000000000000.1	x^16 - 4x^15 + 52x^14 - 240x^13 + 1440x^12 - 5716x^11 + 22796x^10 - 69300x^9 + 204159x^8 - 453580x^7 + 997404x^6 - 1441988x^5 + 2287980x^4 - 1475320x^3 + 2075448x^2 - 2010692x + 4536281	\( 2^{44}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2, 2, 382]$ (GRH)
16.16.12136551081312256000000000000.1	x^16 - 4x^15 - 64x^14 + 216x^13 + 1544x^12 - 3804x^11 - 19156x^10 + 26292x^9 + 128879x^8 - 50748x^7 - 431036x^6 - 108060x^5 + 647172x^4 + 456648x^3 - 284700x^2 - 382980x - 104959	\( 2^{44}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.8.12136551081312256000000000000.1	x^16 - 4x^15 - 8x^14 + 80x^13 - 440x^12 + 1844x^11 - 3324x^10 - 15060x^9 + 102439x^8 - 307740x^7 + 480604x^6 + 4492x^5 - 1910700x^4 + 4629640x^3 - 4781532x^2 + 1837308x - 229679	\( 2^{44}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2]$ (GRH)
16.0.19177071869085684350631018496.1	x^16 + 40x^14 - 32x^13 + 584x^12 - 784x^11 + 3092x^10 - 816x^9 - 838x^8 + 2656x^7 + 4472x^6 - 46480x^5 + 88892x^4 - 83632x^3 + 51880x^2 - 16464x + 3332	\( 2^{48}\cdot 13^{8}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2, 2, 42]$ (GRH)
16.16.19177071869085684350631018496.1	x^16 - 56x^14 - 8x^13 + 1112x^12 + 192x^11 - 9332x^10 - 480x^9 + 32762x^8 - 4256x^7 - 49944x^6 + 11984x^5 + 32828x^4 - 7888x^3 - 9384x^2 + 1392x + 1028	\( 2^{48}\cdot 13^{8}\cdot 17^{4} \)	$C_2^4.C_2^3$ (as 16T268)	Trivial (GRH)
16.8.28843256040984576000000000000.1	x^16 - 6x^15 + 10x^14 + 80x^13 - 511x^12 + 584x^11 - 18x^10 + 7630x^9 - 22679x^8 - 38726x^7 + 423822x^6 - 963092x^5 - 312201x^4 + 4791658x^3 - 6869654x^2 - 2933018x + 11639401	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 181^{4} \)	$C_2^4.C_2^3$ (as 16T268)	$[2, 2]$ (GRH)