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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.27532918184214528.1	x^16 - 4x^15 + 10x^14 - 12x^13 + 6x^12 + 8x^11 - 6x^10 - 24x^9 + 70x^8 - 88x^7 + 58x^6 - 8x^5 - 18x^4 + 12x^3 + 2x^2 - 4x + 1	\( 2^{28}\cdot 3^{12}\cdot 193 \)	16T1461	Trivial
16.0.48653926400000000.1	x^16 + 2x^14 - 4x^13 - 16x^11 - 16x^10 - 28x^9 + 7x^8 + 56x^7 + 112x^6 + 132x^5 + 108x^4 + 68x^3 + 30x^2 + 8x + 1	\( 2^{32}\cdot 5^{8}\cdot 29 \)	16T1461	Trivial
16.8.21299554301855078125.1	x^16 - 3x^15 - 5x^14 + 21x^13 + 12x^12 - 73x^11 - 31x^10 + 147x^9 + 96x^8 - 135x^7 - 151x^6 + 12x^5 + 84x^4 + 40x^3 - 6x^2 - 9x - 1	\( 5^{8}\cdot 29^{8}\cdot 109 \)	16T1461	Trivial
16.6.27161816953741796875.1	x^16 - 2x^15 - x^14 - 2x^13 + 11x^12 + 24x^11 - 63x^10 - 16x^9 + 29x^8 + 137x^7 - 79x^6 - 107x^5 + 28x^4 + 32x^3 + 21x^2 - 11x - 1	\( -\,5^{8}\cdot 29^{8}\cdot 139 \)	16T1461	Trivial
16.4.29115904504370703125.1	x^16 - 2x^15 - 5x^14 + 12x^13 + 12x^12 - 38x^11 - 9x^10 + 51x^9 - 8x^8 + 26x^7 - 120x^6 + 106x^5 - 48x^4 + 24x^3 - 30x^2 + 13x - 1	\( 5^{8}\cdot 29^{8}\cdot 149 \)	16T1461	Trivial
16.10.34978167156257421875.1	x^16 - 3x^15 - 3x^14 + 9x^13 + 18x^12 - 29x^11 - 79x^10 + 103x^9 + 59x^8 - 145x^7 + 96x^6 + 10x^5 - 87x^4 + 59x^3 - 6x^2 - 5x + 1	\( -\,5^{8}\cdot 29^{8}\cdot 179 \)	16T1461	Trivial
16.10.50024641296100000000.1	x^16 - 8x^14 + 12x^12 + 40x^10 - 116x^8 + 48x^6 + 47x^4 + 2x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.6.50024641296100000000.1	x^16 + 2x^14 - 12x^12 - 26x^10 + 17x^8 + 36x^6 - 5x^4 - 11x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.8.183879638514180078125.1	x^16 - 6x^15 + 15x^14 - 26x^13 + 36x^12 - 37x^11 + 21x^10 + 25x^9 - 71x^8 + 67x^7 - 30x^6 - 31x^5 + 59x^4 - 4x^3 - 20x^2 - x + 1	\( 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial
16.2.2451207423508900000000.1	x^16 + 2x^14 - 11x^13 + 23x^12 - 29x^11 + 23x^10 - 64x^9 + 57x^8 + 56x^7 - 62x^6 + 247x^5 - 394x^4 + 560x^3 - 385x^2 + 150x - 25	\( -\,2^{8}\cdot 5^{8}\cdot 7^{2}\cdot 29^{8} \)	16T1461	Trivial
16.10.12806308171801600000000.1	x^16 - 6x^14 + 40x^10 - 31x^8 - 58x^6 + 43x^4 + 11x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.14.12806308171801600000000.1	x^16 - 7x^14 + 5x^12 + 70x^10 - 221x^8 + 264x^6 - 138x^4 + 28x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.2.12806308171801600000000.1	x^16 + 7x^14 + 5x^12 - 70x^10 - 221x^8 - 264x^6 - 138x^4 - 28x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	$[2]$
16.6.12806308171801600000000.1	x^16 + 6x^14 - 40x^10 - 31x^8 + 58x^6 + 43x^4 - 11x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.10.12806308171801600000000.2	x^16 + 7x^14 + 4x^12 - 36x^10 - 7x^8 + 70x^6 - 52x^4 + 13x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.6.12806308171801600000000.2	x^16 - 7x^14 + 4x^12 + 36x^10 - 7x^8 - 70x^6 - 52x^4 - 13x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.10.12806308171801600000000.3	x^16 - 4x^14 - 9x^12 + 63x^10 - 92x^8 + 25x^6 + 27x^4 - 9x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.6.12806308171801600000000.3	x^16 + 4x^14 - 9x^12 - 63x^10 - 92x^8 - 25x^6 + 27x^4 + 9x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial
16.12.18197440315231689453125.1	x^16 - 3x^15 - 12x^14 + 50x^13 - 15x^12 - 162x^11 + 354x^10 - 390x^9 + 79x^8 + 600x^7 - 1119x^6 + 911x^5 - 235x^4 - 150x^3 + 112x^2 - 21x + 1	\( 5^{12}\cdot 29^{8}\cdot 149 \)	16T1461	Trivial (GRH)
16.0.22530408855590584451072.1	x^16 - 10x^14 + 59x^12 - 236x^10 + 555x^8 - 666x^6 + 545x^4 - 744x^2 + 752	\( 2^{36}\cdot 17^{8}\cdot 47 \)	16T1461	Trivial
16.8.24486475688175761328125.1	x^16 - 2x^15 - 11x^14 + 11x^13 + 35x^12 + 3x^11 + 4x^10 + 13x^9 + 88x^8 + 171x^7 - 188x^6 - 720x^5 - 869x^4 - 620x^3 - 205x^2 + 25x + 25	\( 5^{8}\cdot 29^{10}\cdot 149 \)	16T1461	Trivial (GRH)
16.10.33886027624210926171875.1	x^16 - 8x^15 + 25x^14 - 35x^13 - 4x^12 + 115x^11 - 215x^10 + 140x^9 + 123x^8 - 353x^7 + 301x^6 - 26x^5 - 144x^4 + 109x^3 - 18x^2 - 11x + 1	\( -\,5^{8}\cdot 7^{2}\cdot 29^{8}\cdot 3539 \)	16T1461	Trivial (GRH)
16.8.35461549523190423748608.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 18x^12 + 108x^11 - 152x^10 + 56x^9 + 117x^8 - 188x^7 + 100x^6 + 24x^5 - 60x^4 + 28x^3 - 4x + 1	\( 2^{44}\cdot 3^{12}\cdot 3793 \)	16T1461	Trivial
16.8.114924774071362548828125.1	x^16 - 16x^14 - 10x^13 + 42x^12 + 35x^11 + 152x^10 + 415x^9 + 15x^8 - 995x^7 + 398x^6 + 610x^5 - 1628x^4 + 2390x^3 - 924x^2 - 55x + 1	\( 5^{12}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.6.158869467362435769921875.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 171x^12 - 207x^11 + 97x^10 + 197x^9 - 511x^8 + 587x^7 - 294x^6 - 152x^5 + 395x^4 - 334x^3 + 124x^2 - 8x - 16	\( -\,5^{8}\cdot 29^{8}\cdot 139\cdot 5849 \)	16T1461	Trivial
16.0.183119493251821345964032.1	x^16 - 2x^15 + 7x^14 - 22x^13 + 55x^12 - 144x^11 + 324x^10 - 636x^9 + 1165x^8 - 1838x^7 + 3011x^6 - 4890x^5 + 5981x^4 - 4848x^3 + 2470x^2 - 724x + 94	\( 2^{37}\cdot 17^{8}\cdot 191 \)	16T1461	Trivial
16.14.204900930748825600000000.1	x^16 - 16x^14 + 97x^12 - 268x^10 + 277x^8 + 152x^6 - 500x^4 + 272x^2 - 16	\( -\,2^{20}\cdot 5^{8}\cdot 29^{8} \)	16T1461	Trivial (GRH)
16.4.268417979723357389651968.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 255x^12 - 438x^11 + 553x^10 - 466x^9 + 141x^8 + 274x^7 - 527x^6 + 498x^5 - 279x^4 + 76x^3 + 12x^2 - 16x + 4	\( 2^{16}\cdot 3^{12}\cdot 11^{8}\cdot 157\cdot 229 \)	16T1461	Trivial
16.12.387093214663037617578125.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 123x^12 + 101x^11 + 187x^10 - 407x^9 + 147x^8 + 391x^7 - 488x^6 - 4x^5 + 299x^4 - 142x^3 - 56x^2 + 64x + 16	\( 5^{8}\cdot 29^{8}\cdot 1980941 \)	16T1461	Trivial (GRH)
16.8.499533918682529008713728.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 56x^12 + 28x^11 - 182x^10 + 272x^9 - 175x^8 - 52x^7 + 190x^6 - 136x^5 + 20x^4 + 28x^3 - 14x^2 + 1	\( 2^{32}\cdot 17^{8}\cdot 16673 \)	16T1461	Trivial (GRH)
16.12.646402195901533980078125.1	x^16 - 7x^15 + 10x^14 + 29x^13 - 160x^12 + 429x^11 - 216x^10 - 1669x^9 + 3252x^8 - 1256x^7 - 3040x^6 + 7439x^5 - 5983x^4 - 2643x^3 + 4895x^2 - 609x - 521	\( 5^{8}\cdot 29^{8}\cdot 149^{3} \)	16T1461	Trivial (GRH)
16.8.646402195901533980078125.1	x^16 - 7x^15 + 22x^14 - 290x^12 + 1440x^11 - 4330x^10 + 9051x^9 - 13375x^8 + 12445x^7 - 3620x^6 - 7269x^5 + 12540x^4 - 10622x^3 + 5190x^2 - 1298x + 121	\( 5^{8}\cdot 29^{8}\cdot 149^{3} \)	16T1461	Trivial (GRH)
16.0.1610243178680162900000000.1	x^16 + 16x^14 - 10x^13 + 121x^12 - 143x^11 + 557x^10 - 950x^9 + 2081x^8 - 4116x^7 + 8288x^6 - 13460x^5 + 26320x^4 - 38016x^3 + 47640x^2 - 35536x + 13136	\( 2^{8}\cdot 5^{8}\cdot 29^{8}\cdot 32189 \)	16T1461	$[48]$
16.0.12050735989665305600000000.1	x^16 + 33x^14 + 422x^12 + 2723x^10 + 9543x^8 + 18119x^6 + 17608x^4 + 7531x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	$[2, 76]$ (GRH)
16.12.12050735989665305600000000.1	x^16 - 14x^14 + 29x^12 + 272x^10 - 1047x^8 + 96x^6 + 3251x^4 - 3408x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.16.12050735989665305600000000.1	x^16 - 33x^14 + 422x^12 - 2723x^10 + 9543x^8 - 18119x^6 + 17608x^4 - 7531x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.4.12050735989665305600000000.1	x^16 + 8x^14 - 43x^12 - 433x^10 - 32x^8 + 5427x^6 + 12257x^4 + 7973x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.8.12050735989665305600000000.1	x^16 + 5x^14 - 112x^12 - 211x^10 + 2179x^8 + 1021x^6 - 7974x^4 - 5889x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.12.12050735989665305600000000.2	x^16 - 19x^14 + 103x^12 + 41x^10 - 2042x^8 + 6009x^6 - 4267x^4 - 3151x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.4.12050735989665305600000000.2	x^16 + 19x^14 + 103x^12 - 41x^10 - 2042x^8 - 6009x^6 - 4267x^4 + 3151x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	$[2]$ (GRH)
16.8.12050735989665305600000000.2	x^16 - 5x^14 - 112x^12 + 211x^10 + 2179x^8 - 1021x^6 - 7974x^4 + 5889x^2 + 941	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 941 \)	16T1461	Trivial (GRH)
16.16.14202195762527974400000000.1	x^16 - 31x^14 + 389x^12 - 2575x^10 + 9704x^8 - 20697x^6 + 22925x^4 - 10425x^2 + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{8}\cdot 1109 \)	16T1461	Trivial (GRH)
16.12.14227370888234854365790208.1	x^16 - 24x^14 + 188x^12 - 568x^10 + 312x^8 + 1344x^6 - 1624x^4 - 400x^2 + 548	\( 2^{54}\cdot 7^{8}\cdot 137 \)	16T1461	Trivial (GRH)
16.4.267033524201279981591516413952.1	x^16 - 8x^15 + 20x^14 - 120x^13 + 440x^12 - 544x^11 + 864x^10 + 320x^9 - 11682x^8 + 15928x^7 + 43160x^6 + 27728x^5 + 147356x^4 + 45600x^3 + 260704x^2 + 1500912x + 1244322	\( 2^{54}\cdot 7^{8}\cdot 137^{3} \)	16T1461	$[2]$ (GRH)
16.4.267033524201279981591516413952.2	x^16 - 8x^15 + 36x^14 - 112x^13 + 240x^12 - 296x^11 - 2568x^10 + 1168x^9 - 12978x^8 + 83464x^7 - 282080x^6 + 816464x^5 - 1205276x^4 + 1586144x^3 - 1192448x^2 + 739504x - 192398	\( 2^{54}\cdot 7^{8}\cdot 137^{3} \)	16T1461	$[2, 2]$ (GRH)
16.8.138864899053729330143760914317312.1	x^16 + 18x^14 - 192x^13 - 700x^12 - 3300x^11 - 1766x^10 + 74908x^9 + 271449x^8 + 1112084x^7 + 982078x^6 - 4576660x^5 - 16548400x^4 - 54882132x^3 - 49423048x^2 + 73520356x + 63951713	\( 2^{32}\cdot 17^{8}\cdot 16673^{3} \)	16T1461	$[2, 2]$ (GRH)