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
16.0.490184257318560000.1	x^16 - 7x^15 + 26x^14 - 59x^13 + 80x^12 - 38x^11 - 87x^10 + 216x^9 - 200x^8 + 9x^7 + 246x^6 - 314x^5 + 239x^4 - 80x^3 + 20x^2 - 4x + 1	\( 2^{8}\cdot 3^{12}\cdot 5^{4}\cdot 7^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial
16.0.1736306936100000000.1	x^16 - 3x^14 + 15x^12 - 29x^10 + 48x^8 - 29x^6 + 15x^4 - 3x^2 + 1	\( 2^{8}\cdot 3^{4}\cdot 5^{8}\cdot 11^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial
16.0.23373022359076208640000.1	x^16 - 4x^15 + 8x^14 - 22x^12 + 88x^11 - 68x^10 - 24x^9 + 352x^8 - 216x^7 + 76x^6 + 488x^5 - 148x^4 + 168x^3 + 224x^2 - 344x + 94	\( 2^{46}\cdot 3^{12}\cdot 5^{4} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2]$
16.8.23373022359076208640000.1	x^16 - 4x^15 - 4x^14 + 24x^13 + 14x^12 - 56x^11 - 56x^10 + 144x^9 - 152x^8 - 336x^7 + 844x^6 + 776x^5 - 688x^4 - 1056x^3 - 472x^2 - 80x - 2	\( 2^{46}\cdot 3^{12}\cdot 5^{4} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.0.30579925039548072984576.2	x^16 - 5x^12 + 39x^8 + 13x^4 + 16	\( 2^{28}\cdot 3^{12}\cdot 11^{8} \)	$C_2^4:C_2^2$ (as 16T119)	$[4]$
16.8.30579925039548072984576.4	x^16 - 10x^14 - 38x^12 + 8x^10 + 79x^8 + 8x^6 - 38x^4 - 10x^2 + 1	\( 2^{28}\cdot 3^{12}\cdot 11^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.8.120109163751936100000000.1	x^16 - 5x^15 + 2x^14 + 27x^13 - 54x^12 - 88x^11 + 153x^10 + 452x^9 + 390x^8 - 471x^7 - 2690x^6 - 2982x^5 + 5581x^4 + 10232x^3 - 2816x^2 - 11092x - 4519	\( 2^{8}\cdot 5^{8}\cdot 7^{4}\cdot 29^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.8.525737701618167519903744.1	x^16 - 8x^14 + 40x^12 - 144x^10 + 340x^8 - 480x^6 + 344x^4 - 96x^2 + 4	\( 2^{50}\cdot 3^{4}\cdot 7^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.0.525737701618167519903744.2	x^16 + 8x^14 + 40x^12 + 144x^10 + 340x^8 + 480x^6 + 344x^4 + 96x^2 + 4	\( 2^{50}\cdot 3^{4}\cdot 7^{8} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2]$ (GRH)
16.0.1552829235277976100000000.1	x^16 - x^14 + 8x^12 - 33x^10 + 549x^8 + 297x^6 + 648x^4 + 729x^2 + 6561	\( 2^{8}\cdot 3^{4}\cdot 5^{8}\cdot 61^{8} \)	$C_2^4:C_2^2$ (as 16T119)	$[2]$ (GRH)
16.0.56118626684141976944640000.1	x^16 - 8x^15 + 36x^14 - 104x^13 + 228x^12 - 288x^11 + 180x^10 + 848x^9 - 1002x^8 + 888x^7 + 12924x^6 - 35352x^5 + 95420x^4 - 146992x^3 + 193260x^2 - 175344x + 117889	\( 2^{46}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2, 28]$ (GRH)
16.16.56118626684141976944640000.1	x^16 - 4x^15 - 36x^14 + 200x^13 + 150x^12 - 2496x^11 + 3132x^10 + 8632x^9 - 23208x^8 + 2976x^7 + 42012x^6 - 39672x^5 - 10540x^4 + 29920x^3 - 9072x^2 - 3768x + 1774	\( 2^{46}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.0.56118626684141976944640000.2	x^16 - 4x^15 + 24x^14 - 112x^13 + 474x^12 - 1560x^11 + 4176x^10 - 9968x^9 + 19152x^8 - 28104x^7 + 32076x^6 - 33696x^5 + 73280x^4 - 188216x^3 + 269568x^2 - 186288x + 49726	\( 2^{46}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2, 14]$ (GRH)
16.0.56118626684141976944640000.3	x^16 - 8x^15 + 60x^14 - 272x^13 + 1044x^12 - 2952x^11 + 6792x^10 - 11872x^9 + 16512x^8 - 19200x^7 + 17520x^6 - 5904x^5 - 4264x^4 + 4928x^3 - 528x^2 - 384x + 376	\( 2^{46}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2, 2]$ (GRH)
16.16.82146515877838674984960000.1	x^16 - 32x^14 - 16x^13 + 372x^12 + 392x^11 - 1844x^10 - 3064x^9 + 2892x^8 + 8448x^7 + 2392x^6 - 5480x^5 - 3784x^4 + 456x^3 + 948x^2 + 216x + 9	\( 2^{48}\cdot 3^{4}\cdot 5^{4}\cdot 7^{8} \)	$C_2^4:C_2^2$ (as 16T119)	Trivial (GRH)
16.0.3012946948663968153600000000.1	x^16 + 34x^14 + 401x^12 + 2074x^10 + 5089x^8 + 6086x^6 + 3368x^4 + 680x^2 + 16	\( 2^{20}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12} \)	$C_2^4:C_2^2$ (as 16T119)	$[2, 2, 48]$ (GRH)