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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.125585627375390625.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 14x^12 - 17x^11 + 16x^10 - 8x^9 - 10x^8 + 31x^7 - 50x^6 + 61x^5 - 59x^4 + 43x^3 - 22x^2 + 7x - 1	\( 3^{4}\cdot 5^{8}\cdot 251^{4} \)	16T1049	Trivial
16.0.203831936618070016.1	x^16 - 2x^14 + 2x^12 - 4x^10 + 3x^8 + 2x^4 - 2x^2 + 1	\( 2^{32}\cdot 83^{4} \)	16T1049	Trivial
16.0.203831936618070016.2	x^16 - 2x^14 + 3x^12 - 6x^10 + 12x^8 - 14x^6 + 10x^4 - 4x^2 + 1	\( 2^{32}\cdot 83^{4} \)	16T1049	Trivial
16.0.32970588989188734976.2	x^16 - 4x^14 + 8x^12 - 20x^10 + 48x^8 + 48x^6 + 20x^4 + 8x^2 + 4	\( 2^{44}\cdot 37^{4} \)	16T1049	Trivial (GRH)
16.0.46874452048800770304.1	x^16 + 19x^12 + 46x^8 + 36x^4 + 9	\( 2^{8}\cdot 3^{10}\cdot 1327^{4} \)	16T1049	Trivial
16.0.53719833934797928704.1	x^16 - 6x^14 + 8x^12 + 24x^10 - 11x^8 - 60x^6 + 87x^4 - 45x^2 + 9	\( 2^{8}\cdot 3^{10}\cdot 1373^{4} \)	16T1049	Trivial
16.4.90740103577600000000.1	x^16 - 4x^15 + 4x^14 - 6x^13 + 14x^12 - 2x^11 - 10x^10 - 4x^9 + 43x^8 - 82x^7 + 50x^6 - 44x^5 + 54x^4 + 2x^3 - 14x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 61^{4} \)	16T1049	Trivial
16.0.527529423827019759616.1	x^16 + 2x^12 + 4	\( 2^{48}\cdot 37^{4} \)	16T1049	Trivial (GRH)
16.0.137259324635521594140625.1	x^16 - 2x^15 + 10x^14 - 26x^13 + 49x^12 - 6x^11 + 419x^10 - 273x^9 + 573x^8 - 890x^7 + 56x^6 - 185x^5 + 2091x^4 - 14907x^3 + 7491x^2 + 9894x + 2876	\( 5^{8}\cdot 97^{4}\cdot 251^{4} \)	16T1049	Trivial (GRH)
16.0.337643925412249600000000.1	x^16 + 10x^14 - 2x^13 + 51x^12 - 28x^11 + 198x^10 - 136x^9 + 865x^8 - 226x^7 + 2462x^6 - 16x^5 + 4950x^4 - 3172x^3 + 5528x^2 - 2120x + 916	\( 2^{24}\cdot 5^{8}\cdot 61^{6} \)	16T1049	$[2]$ (GRH)
16.8.337643925412249600000000.1	x^16 - 16x^14 - 10x^13 + 102x^12 + 154x^11 - 354x^10 - 1068x^9 + 257x^8 + 3714x^7 + 3366x^6 - 2964x^5 - 6428x^4 - 2918x^3 + 334x^2 + 302x - 41	\( 2^{24}\cdot 5^{8}\cdot 61^{6} \)	16T1049	Trivial (GRH)
16.8.550026747803854214004736.1	x^16 - 6x^14 - x^12 + 6x^10 + 8x^8 + 10x^6 + 67x^4 - 34x^2 + 1	\( 2^{40}\cdot 29^{8} \)	16T1049	Trivial (GRH)
16.8.1455732972800792995037184.1	x^16 - 8x^15 + 24x^14 + 2x^13 - 247x^12 + 762x^11 - 704x^10 - 1376x^9 + 4443x^8 - 3812x^7 - 1640x^6 + 4860x^5 - 1909x^4 - 1198x^3 + 804x^2 + 10x - 11	\( 2^{24}\cdot 3^{14}\cdot 367^{4} \)	16T1049	Trivial (GRH)
16.8.1455732972800792995037184.2	x^16 - 6x^15 + 2x^14 + 66x^13 - 200x^12 + 78x^11 + 806x^10 - 1890x^9 + 1246x^8 + 1854x^7 - 4402x^6 + 3846x^5 - 2120x^4 + 666x^3 - 118x^2 - 6x + 1	\( 2^{24}\cdot 3^{14}\cdot 367^{4} \)	16T1049	Trivial (GRH)
16.8.1455732972800792995037184.3	x^16 - 2x^15 - 16x^14 + 48x^13 + 17x^12 - 178x^11 + 148x^10 + 456x^9 - 488x^8 - 678x^7 + 466x^6 + 190x^5 - 406x^4 - 24x^3 + 74x^2 - 16x + 1	\( 2^{24}\cdot 3^{14}\cdot 367^{4} \)	16T1049	$[2]$ (GRH)
16.8.3071964089470207282642944.2	x^16 - 8x^15 + 24x^14 + 2x^13 - 239x^12 + 714x^11 - 560x^10 - 1740x^9 + 5203x^8 - 4548x^7 - 2368x^6 + 7400x^5 - 3849x^4 - 1398x^3 + 1492x^2 - 42x - 71	\( 2^{24}\cdot 3^{10}\cdot 1327^{4} \)	16T1049	Trivial (GRH)
16.0.40430096994638233600000000.1	x^16 + 24x^14 + 210x^12 + 844x^10 + 1711x^8 + 1732x^6 + 750x^4 + 68x^2 + 1	\( 2^{36}\cdot 5^{8}\cdot 197^{4} \)	16T1049	$[2, 14]$ (GRH)
16.16.40430096994638233600000000.2	x^16 - 24x^14 + 210x^12 - 844x^10 + 1711x^8 - 1732x^6 + 750x^4 - 68x^2 + 1	\( 2^{36}\cdot 5^{8}\cdot 197^{4} \)	16T1049	Trivial (GRH)
16.0.25268810621648896000000000000.1	x^16 - 4x^15 + 30x^14 - 12x^13 + 104x^12 + 252x^11 + 1450x^10 + 300x^9 + 1196x^8 + 38020x^7 + 120690x^6 + 169284x^5 + 155096x^4 + 111532x^3 + 40462x^2 - 7692x + 17271	\( 2^{36}\cdot 5^{12}\cdot 197^{4} \)	16T1049	$[2, 2, 116]$ (GRH)
16.16.25268810621648896000000000000.1	x^16 - 4x^15 - 50x^14 + 292x^13 + 296x^12 - 4656x^11 + 5914x^10 + 21260x^9 - 59021x^8 + 6120x^7 + 129786x^6 - 139552x^5 - 21664x^4 + 125736x^3 - 86440x^2 + 24532x - 2549	\( 2^{36}\cdot 5^{12}\cdot 197^{4} \)	16T1049	Trivial (GRH)
16.8.120847583024191777328789520384.1	x^16 + 9x^14 - 82x^12 - 651x^10 + 551x^8 + 6489x^6 - 1610x^4 - 11259x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{8}\cdot 1327^{4} \)	16T1049	Trivial (GRH)
16.8.120847583024191777328789520384.2	x^16 - 9x^14 - 82x^12 + 651x^10 + 551x^8 - 6489x^6 - 1610x^4 + 11259x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{8}\cdot 1327^{4} \)	16T1049	$[2]$ (GRH)
16.0.51078407858373713535118085896290697216.1	x^16 + 152x^14 + 9504x^12 + 315376x^10 + 6001288x^8 + 66741728x^6 + 431686272x^4 + 1556049088x^2 + 2607940624	\( 2^{36}\cdot 151^{8}\cdot 229^{4} \)	16T1049	$[6]$ (GRH)
16.0.140468608726897677774715983455580718320263888896.1	x^16 + 2066x^14 + 1805514x^12 + 874215952x^10 + 252657800140x^8 + 43587599577536x^6 + 4535677481540424x^4 + 266656622707871824x^2 + 7171989230975632144	\( 2^{36}\cdot 151^{8}\cdot 229^{8} \)	16T1049	$[2, 6]$ (GRH)