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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.104976000000000000.2	x^16 - 7x^14 + 21x^12 - 36x^10 + 39x^8 - 28x^6 + 14x^4 - 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial
16.0.1479302070556640625.2	x^16 - 12x^14 - 2x^13 + 68x^12 + 38x^11 - 205x^10 - 210x^9 + 321x^8 + 562x^7 - 105x^6 - 676x^5 - 305x^4 + 230x^3 + 252x^2 + 88x + 16	\( 3^{8}\cdot 5^{12}\cdot 31^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial
16.8.26873856000000000000.2	x^16 - 2x^15 - 6x^14 + 16x^13 + 17x^12 - 60x^11 - 28x^10 + 136x^9 + 27x^8 - 196x^7 - 20x^6 + 170x^5 + 15x^4 - 72x^3 - 6x^2 + 8x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial (GRH)
16.0.376145144477611196416.4	x^16 - 8x^15 + 28x^14 - 32x^13 - 16x^12 + 56x^11 + 112x^10 - 48x^9 - 140x^8 + 160x^7 + 796x^6 + 1088x^5 + 812x^4 + 368x^3 + 104x^2 + 16x + 1	\( 2^{52}\cdot 17^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.0.1504580577910444785664.2	x^16 - 8x^15 + 12x^14 + 40x^13 - 84x^12 - 136x^11 + 296x^10 + 440x^9 - 558x^8 - 872x^7 + 840x^6 + 1776x^5 + 396x^4 - 640x^3 - 176x^2 + 224x + 98	\( 2^{54}\cdot 17^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$
16.8.4294967296000000000000.3	x^16 - 18x^12 + 79x^8 - 22x^4 + 1	\( 2^{44}\cdot 5^{12} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial (GRH)
16.8.325640214614016000000000000.1	x^16 - 2x^15 - 4x^14 - 2x^13 - 159x^12 + 114x^11 - 1146x^10 + 238x^9 + 6656x^8 - 4018x^7 + 47180x^6 - 22628x^5 - 199258x^4 + 218166x^3 + 113850x^2 - 262368x + 88801	\( 2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 59^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.0.6197644519014400000000000000.1	x^16 - 30x^14 - 75x^12 + 10020x^10 - 25140x^8 - 934650x^6 + 2738850x^4 + 17874600x^2 + 23088025	\( 2^{40}\cdot 5^{14}\cdot 31^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.0.6197644519014400000000000000.2	x^16 - 30x^14 - 255x^12 + 13860x^10 - 36765x^8 - 1776300x^6 + 11171625x^4 + 31280550x^2 + 23088025	\( 2^{40}\cdot 5^{14}\cdot 31^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.0.303413777032806400000000000000.1	x^16 - 8x^15 + 116x^14 - 552x^13 + 4636x^12 - 17024x^11 + 97564x^10 - 298656x^9 + 1206042x^8 - 3186136x^7 + 8682804x^6 - 17888024x^5 + 34056956x^4 - 49012432x^3 + 62192636x^2 - 51389008x + 32169161	\( 2^{44}\cdot 5^{14}\cdot 41^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2, 2, 2, 2, 942]$ (GRH)
16.16.303413777032806400000000000000.1	x^16 - 8x^15 - 84x^14 + 608x^13 + 2556x^12 - 17344x^11 - 33076x^10 + 238504x^9 + 158082x^8 - 1675736x^7 + 137564x^6 + 5810256x^5 - 3144804x^4 - 8237872x^3 + 6583356x^2 + 1846232x - 1112399	\( 2^{44}\cdot 5^{14}\cdot 41^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial (GRH)
16.8.303413777032806400000000000000.1	x^16 - 4x^15 - 36x^14 + 196x^13 - 644x^12 + 2448x^11 + 13656x^10 - 181492x^9 + 603497x^8 + 407312x^7 - 7407844x^6 + 21863772x^5 - 38194794x^4 + 40597764x^3 - 15956176x^2 - 14234616x + 11325721	\( 2^{44}\cdot 5^{14}\cdot 41^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.8.303413777032806400000000000000.2	x^16 - 4x^15 + 24x^14 - 244x^13 - 714x^12 - 2012x^11 - 15764x^10 + 41228x^9 + 98082x^8 + 12812x^7 + 579816x^6 + 2228892x^5 - 1022814x^4 - 15272956x^3 + 2510564x^2 + 9102284x + 2091041	\( 2^{44}\cdot 5^{14}\cdot 41^{4} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2]$ (GRH)
16.8.15413672017951201296000000000000.1	x^16 - 20x^14 - 113x^12 + 2010x^10 + 9364x^8 - 19600x^6 - 80172x^4 - 4890x^2 + 72361	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{8} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2, 2]$ (GRH)
16.0.111400390403760848896000000000000.1	x^16 + 112x^14 + 5056x^12 + 118256x^10 + 1522024x^8 + 10475168x^6 + 34284184x^4 + 42173824x^2 + 1860496	\( 2^{44}\cdot 5^{12}\cdot 11^{10} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	$[2, 2, 2148]$ (GRH)
16.16.111400390403760848896000000000000.1	x^16 - 112x^14 + 5076x^12 - 120256x^10 + 1595004x^8 - 11687808x^6 + 43186704x^4 - 63547264x^2 + 12082576	\( 2^{44}\cdot 5^{12}\cdot 11^{10} \)	$(C_2\times D_4).C_2^3$ (as 16T315)	Trivial (GRH)