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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.61359411351395634249728.4	x^16 + 8x^14 + 7x^12 - 80x^10 - 257x^8 - 292x^6 - 108x^4 - 8x^2 + 2	\( 2^{43}\cdot 17^{8} \)	16T994	Trivial (GRH)
16.4.61359411351395634249728.5	x^16 - 3x^12 - 14x^10 - 29x^8 + 72x^6 - 4x^4 - 32x^2 + 8	\( 2^{43}\cdot 17^{8} \)	16T994	Trivial (GRH)
16.0.35692930361212119068612493312.1	x^16 - 16x^14 + 120x^12 - 960x^10 + 6864x^8 - 23232x^6 + 34848x^4 - 10368x^2 + 5832	\( 2^{79}\cdot 3^{10} \)	16T994	Trivial (GRH)
16.0.35692930361212119068612493312.2	x^16 - 16x^14 + 88x^12 - 384x^10 + 3408x^8 + 576x^6 + 11424x^4 - 17280x^2 + 5832	\( 2^{79}\cdot 3^{10} \)	16T994	Trivial (GRH)
16.16.80552894728007447787305078125.1	x^16 - 3x^15 - 76x^14 + 243x^13 + 1864x^12 - 5771x^11 - 21340x^10 + 62058x^9 + 129025x^8 - 341579x^7 - 431147x^6 + 984154x^5 + 783788x^4 - 1387281x^3 - 711570x^2 + 735684x + 263509	\( 5^{8}\cdot 101^{6}\cdot 181^{5} \)	16T994	Trivial (GRH)
16.16.80552894728007447787305078125.2	x^16 - 65x^14 - 48x^13 + 1573x^12 + 1869x^11 - 18308x^10 - 26990x^9 + 108699x^8 + 178312x^7 - 325315x^6 - 546496x^5 + 487504x^4 + 733199x^3 - 380087x^2 - 331256x + 164089	\( 5^{8}\cdot 101^{6}\cdot 181^{5} \)	16T994	Trivial (GRH)
16.0.50345559205004654867065673828125.1	x^16 - 7x^15 + 169x^14 - 721x^13 + 10352x^12 - 32647x^11 + 314218x^10 - 802681x^9 + 5362186x^8 - 11468099x^7 + 53717753x^6 - 95434883x^5 + 311549332x^4 - 428392404x^3 + 959344879x^2 - 794857148x + 1187058641	\( 5^{12}\cdot 101^{6}\cdot 181^{5} \)	16T994	$[2, 2, 2, 2, 10974]$ (GRH)
16.0.50345559205004654867065673828125.2	x^16 - 5x^15 + 124x^14 - 604x^13 + 6872x^12 - 30262x^11 + 214133x^10 - 801805x^9 + 4005147x^8 - 12138424x^7 + 45602362x^6 - 105886889x^5 + 306325756x^4 - 497742168x^3 + 1090515202x^2 - 981056326x + 1503349111	\( 5^{12}\cdot 101^{6}\cdot 181^{5} \)	16T994	$[2, 2, 2, 2, 10838]$ (GRH)
16.4.649643018047387088671190961146262716416.1	x^16 + 140x^14 + 6730x^12 + 151178x^10 + 1620865x^8 + 7832890x^6 + 11264552x^4 - 13328640x^2 + 2369536	\( 2^{25}\cdot 13^{7}\cdot 17^{8}\cdot 89^{7} \)	16T994	$[2, 8]$ (GRH)
16.4.649643018047387088671190961146262716416.2	x^16 - 2x^15 - 71x^14 - 34x^13 + 723x^12 - 8832x^11 - 94666x^10 - 468360x^9 - 1918375x^8 - 7734654x^7 - 41515411x^6 - 295108878x^5 - 1500851413x^4 - 4355717896x^3 - 7041595136x^2 - 6108741920x - 2267436592	\( 2^{25}\cdot 13^{7}\cdot 17^{8}\cdot 89^{7} \)	16T994	$[2, 2, 4]$ (GRH)
16.6.55013835857676939099088270698740000784693073140191887871554093056.1	x^16 + 6392x^14 + 9542174x^12 - 690444484x^10 - 4139016974887x^8 + 721181608173092x^6 - 36554998011899960x^4 + 422775017521333932x^2 - 180141748647795219	\( -\,2^{48}\cdot 3^{11}\cdot 7^{8}\cdot 294337^{7} \)	16T994	$[2, 2, 2]$ (GRH)
16.6.55013835857676939099088270698740000784693073140191887871554093056.2	x^16 - 5228x^14 + 1344530x^12 + 2572006372x^10 - 93193540402x^8 - 288635660521604x^6 - 27550249139175866x^4 - 142053998213105748x^2 - 180141748647795219	\( -\,2^{48}\cdot 3^{11}\cdot 7^{8}\cdot 294337^{7} \)	16T994	$[2, 2, 4]$ (GRH)