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
16.0.942874023903914622976.1	x^16 - 8x^15 + 16x^14 + 22x^13 - 90x^12 - 36x^11 + 320x^10 - 14x^9 - 778x^8 - 104x^7 + 1312x^6 + 774x^5 - 700x^4 - 744x^3 + 200x^2 + 318x + 73	\( 2^{28}\cdot 37^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.0.2565726409000000000000.1	x^16 - 2x^15 - 2x^14 + 19x^13 - 45x^12 + 48x^11 + 102x^10 - 434x^9 + 540x^8 + 46x^7 - 444x^6 + 604x^5 + 104x^4 - 312x^3 + 364x^2 - 24x + 36	\( 2^{12}\cdot 5^{12}\cdot 37^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2]$ (GRH)
16.0.2821046020387461136384.1	x^16 - 4x^14 - 8x^13 + 6x^12 + 28x^11 + 56x^10 + 20x^9 + 10x^8 - 56x^7 - 36x^6 - 40x^5 + 90x^4 - 24x^3 + 80x^2 - 96x + 54	\( 2^{40}\cdot 37^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.0.2821046020387461136384.2	x^16 + 4x^14 - 2x^12 - 20x^11 + 32x^10 + 20x^9 + 46x^8 - 184x^7 - 268x^6 - 184x^5 + 398x^4 + 376x^3 + 304x^2 + 144x + 46	\( 2^{40}\cdot 37^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.4.5381489931190917922816.1	x^16 - 8x^15 + 22x^14 - 128x^12 + 196x^11 + 220x^10 - 704x^9 - 49x^8 + 1176x^7 - 370x^6 - 728x^5 + 30x^4 + 268x^3 + 120x^2 + 24x + 2	\( 2^{36}\cdot 23^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.4.10464242526589378625536.5	x^16 - 40x^12 + 88x^10 + 310x^8 - 1696x^6 + 3064x^4 - 2552x^2 + 841	\( 2^{44}\cdot 29^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.0.2324101713520230400000000.1	x^16 - 2x^15 - 2x^14 + 24x^13 - 50x^12 - 38x^11 + 250x^10 - 308x^9 - 110x^8 + 1014x^7 - 1178x^6 - 188x^5 + 1484x^4 - 1626x^3 + 862x^2 - 220x + 137	\( 2^{28}\cdot 5^{8}\cdot 53^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[4]$ (GRH)
16.0.3524840520547043444260864.1	x^16 - 8x^15 + 36x^14 - 92x^13 + 164x^12 - 244x^11 + 342x^10 + 32x^9 - 1033x^8 + 2924x^7 - 2214x^6 - 844x^5 + 4286x^4 - 3832x^3 + 2390x^2 - 604x + 109	\( 2^{32}\cdot 7^{6}\cdot 17^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2]$ (GRH)
16.8.2163460585448341410282471424.1	x^16 + 4x^14 - 296x^12 - 492x^10 + 13534x^8 + 11740x^6 - 151240x^4 + 68684x^2 + 49729	\( 2^{44}\cdot 223^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2]$ (GRH)
16.8.2163460585448341410282471424.2	x^16 - 32x^14 + 240x^12 + 584x^10 - 6434x^8 - 10272x^6 + 35712x^4 + 87416x^2 + 49729	\( 2^{44}\cdot 223^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.0.4567293201244188864763920384.1	x^16 - 6x^14 - 48x^12 - 90x^10 + 2070x^8 + 22518x^6 + 30240x^4 - 95094x^2 + 68121	\( 2^{34}\cdot 3^{12}\cdot 29^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[4, 12]$ (GRH)
16.0.4567293201244188864763920384.2	x^16 - 12x^14 + 93x^12 - 540x^10 + 2448x^8 - 9720x^6 + 30132x^4 - 69984x^2 + 104976	\( 2^{34}\cdot 3^{12}\cdot 29^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[4, 12]$ (GRH)
16.0.7921586895449647259644140625.1	x^16 - 8x^15 + 82x^14 - 400x^13 + 2138x^12 - 6903x^11 + 23397x^10 - 54193x^9 + 122896x^8 - 215474x^7 + 376822x^6 - 532544x^5 + 741836x^4 - 830694x^3 + 842431x^2 - 553149x + 226071	\( 5^{8}\cdot 19^{8}\cdot 103^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2, 2, 404]$ (GRH)
16.16.7921586895449647259644140625.1	x^16 - x^15 - 59x^14 + 93x^13 + 1231x^12 - 2708x^11 - 10417x^10 + 31709x^9 + 24297x^8 - 148144x^7 + 81692x^6 + 184877x^5 - 244557x^4 + 69777x^3 + 19997x^2 - 9338x + 821	\( 5^{8}\cdot 19^{8}\cdot 103^{6} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)
16.0.707449591835873807436932448256.1	x^16 + 64x^14 + 1502x^12 + 16268x^10 + 83671x^8 + 189924x^6 + 165718x^4 + 48020x^2 + 2401	\( 2^{44}\cdot 7^{8}\cdot 17^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	$[2, 2, 390]$ (GRH)
16.16.707449591835873807436932448256.1	x^16 - 64x^14 + 1502x^12 - 16268x^10 + 83671x^8 - 189924x^6 + 165718x^4 - 48020x^2 + 2401	\( 2^{44}\cdot 7^{8}\cdot 17^{8} \)	$Q_8:C_2^2.D_6$ (as 16T754)	Trivial (GRH)