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 27 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.494965078673757801201.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 109x^12 - 108x^11 - 22x^10 + 385x^9 - 411x^8 - 710x^7 + 1946x^6 - 1731x^5 - 1705x^4 + 4698x^3 - 1838x^2 - 566x + 4483	\( 3^{8}\cdot 16573^{4} \)	16T1869	Trivial
16.0.494965078673757801201.2	x^16 - 5x^15 + 20x^14 - 75x^13 + 156x^12 - 325x^11 + 548x^10 - 279x^9 + 554x^8 + 51x^7 - 1277x^6 - 2053x^5 - 1505x^4 + 1586x^3 + 4632x^2 + 3971x + 2749	\( 3^{8}\cdot 16573^{4} \)	16T1869	Trivial
16.0.1476542153672250390625.1	x^16 - 3x^15 + 5x^14 - 29x^13 + 90x^12 - 159x^11 + 382x^10 - 821x^9 + 901x^8 - 1151x^7 + 2315x^6 - 2337x^5 + 1761x^4 - 2270x^3 + 2929x^2 - 2150x + 625	\( 5^{8}\cdot 7841^{4} \)	16T1869	Trivial
16.0.4749880336539844140625.1	x^16 - x^15 + 3x^14 - 16x^13 + 51x^12 - 123x^11 + 265x^10 - 562x^9 + 1131x^8 - 1606x^7 + 1567x^6 - 2429x^5 + 3069x^4 + 3438x^3 - 7695x^2 - 279x + 3491	\( 5^{8}\cdot 10501^{4} \)	16T1869	Trivial
16.0.196417177218537844140625.1	x^16 - 3x^15 + 9x^14 - 20x^13 + 57x^12 - 154x^11 + 890x^10 - 2775x^9 + 5444x^8 - 7210x^7 + 9714x^6 - 10126x^5 + 14764x^4 - 14510x^3 + 14457x^2 - 20828x + 39019	\( 5^{8}\cdot 31^{4}\cdot 859^{4} \)	16T1869	$[2]$
16.4.226047687124631531640625.1	x^16 - 3x^15 + 13x^14 - 17x^13 - 41x^12 + 265x^11 - 1141x^10 + 2371x^9 - 4122x^8 + 3160x^7 + 3681x^6 - 18463x^5 + 38654x^4 - 52041x^3 + 47410x^2 - 26237x + 8521	\( 5^{8}\cdot 27581^{4} \)	16T1869	Trivial (GRH)
16.4.226047687124631531640625.2	x^16 - 3x^15 + 8x^14 - 37x^13 + 37x^12 + 43x^11 - 193x^10 + 890x^9 - 945x^8 - 389x^7 + 268x^6 - 1721x^5 - 1079x^4 + 372x^3 + 21369x^2 - 25449x + 16969	\( 5^{8}\cdot 27581^{4} \)	16T1869	Trivial (GRH)
16.4.2372805251213789306640625.1	x^16 - 6x^15 + 26x^14 - 52x^13 + 80x^12 + 68x^11 - 314x^10 + 1115x^9 - 1113x^8 + 993x^7 + 349x^6 + 279x^5 - 4943x^4 + 11070x^3 - 19806x^2 + 14673x - 2389	\( 5^{12}\cdot 9929^{4} \)	16T1869	Trivial (GRH)
16.8.2372805251213789306640625.1	x^16 - 10x^14 - 30x^13 - 38x^12 + 250x^11 + 495x^10 - 205x^9 - 1906x^8 - 4170x^7 + 1860x^6 + 16415x^5 + 21733x^4 + 3975x^3 - 40155x^2 - 42635x - 2609	\( 5^{12}\cdot 9929^{4} \)	16T1869	Trivial (GRH)
16.0.2372805251213789306640625.2	x^16 - x^15 + 19x^14 - 17x^13 + 159x^12 - 64x^11 + 886x^10 + 317x^9 + 3641x^8 + 2710x^7 + 9575x^6 + 6550x^5 + 14055x^4 + 7275x^3 + 10625x^2 + 2550x + 3100	\( 5^{12}\cdot 9929^{4} \)	16T1869	$[2]$
16.4.2372805251213789306640625.2	x^16 - 3x^15 + 11x^14 - 37x^13 + 74x^12 - 57x^11 - 168x^10 + 1319x^9 - 4769x^8 + 8355x^7 - 9298x^6 + 4549x^5 + 19594x^4 - 65145x^3 + 103105x^2 - 90016x + 32756	\( 5^{12}\cdot 9929^{4} \)	16T1869	Trivial (GRH)
16.0.6047916661441537600000000.1	x^16 - 4x^15 + 2x^14 + 64x^13 + 6x^12 - 570x^11 + 888x^10 + 5130x^9 + 1390x^8 - 13266x^7 - 9170x^6 + 118200x^5 + 448796x^4 + 68274x^3 - 2070881x^2 - 867030x + 4273025	\( 2^{12}\cdot 5^{8}\cdot 7841^{4} \)	16T1869	Trivial (GRH)
16.0.6047916661441537600000000.2	x^16 - 3x^15 - 22x^14 + 95x^13 + 307x^12 - 1596x^11 - 2156x^10 + 15748x^9 + 8573x^8 - 98637x^7 - 3020x^6 + 324405x^5 + 39628x^4 - 327971x^3 - 291719x^2 - 2518894x + 5375956	\( 2^{12}\cdot 5^{8}\cdot 7841^{4} \)	16T1869	Trivial (GRH)
16.4.80598448663702095469140625.1	x^16 - x^15 + 18x^14 + 31x^13 - 57x^12 + 677x^11 - 2446x^10 + 5995x^9 - 23176x^8 + 48188x^7 - 121259x^6 + 220610x^5 - 300350x^4 + 404439x^3 - 184740x^2 + 186782x + 146959	\( 5^{8}\cdot 119851^{4} \)	16T1869	$[2]$ (GRH)
16.4.80598448663702095469140625.2	x^16 - x^15 + 12x^14 - 22x^13 - 175x^12 - 578x^11 - 3517x^10 - 9030x^9 - 27574x^8 - 63964x^7 - 136379x^6 - 239398x^5 - 381259x^4 - 573105x^3 - 408453x^2 - 763918x - 89701	\( 5^{8}\cdot 119851^{4} \)	16T1869	$[2]$ (GRH)
16.8.122760735761586152587890625.1	x^16 - 4x^15 - 10x^14 + 148x^13 - 420x^12 - 761x^11 + 5351x^10 - 7759x^9 - 12884x^8 + 46881x^7 - 49477x^6 + 177589x^5 + 2194168x^4 - 9206881x^3 + 4572271x^2 + 8322007x - 263899	\( 5^{12}\cdot 31^{4}\cdot 859^{4} \)	16T1869	Trivial (GRH)
16.0.9719010308971681000000000000.1	x^16 - 2x^15 + 52x^14 - 107x^13 + 1290x^12 - 2290x^11 + 18491x^10 - 26109x^9 + 169521x^8 - 176611x^7 + 1019176x^6 - 698966x^5 + 3965073x^4 - 1463547x^3 + 9216181x^2 - 997033x + 10180861	\( 2^{12}\cdot 5^{12}\cdot 9929^{4} \)	16T1869	$[2, 2]$ (GRH)
16.8.9719010308971681000000000000.1	x^16 - 5x^15 - 34x^14 + 246x^13 - 116x^12 - 3193x^11 + 11638x^10 + 489x^9 - 96243x^8 + 197723x^7 - 100986x^6 - 193583x^5 + 2062068x^4 - 3089100x^3 - 5371768x^2 + 5532183x + 4156921	\( 2^{12}\cdot 5^{12}\cdot 9929^{4} \)	16T1869	Trivial (GRH)
16.0.12872396126194096153600000000.1	x^16 + 70x^14 + 1783x^12 + 22049x^10 + 229588x^8 + 3837981x^6 + 48944102x^4 + 303996664x^2 + 709103641	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{4} \)	16T1869	$[2, 2]$ (GRH)
16.8.12872396126194096153600000000.1	x^16 - 25x^14 - 508x^12 + 9740x^10 + 144774x^8 - 1237785x^6 - 17521882x^4 + 47000185x^2 + 709103641	\( 2^{16}\cdot 5^{8}\cdot 31^{4}\cdot 859^{4} \)	16T1869	Trivial (GRH)
16.8.50374030414813809668212890625.1	x^16 - 3x^15 - 68x^14 + 377x^13 - 208x^12 - 5997x^11 + 35742x^10 + 10218x^9 - 477001x^8 + 417900x^7 + 2297256x^6 - 3629051x^5 - 2500217x^4 + 4705425x^3 - 24665835x^2 + 37541221x + 130562021	\( 5^{12}\cdot 119851^{4} \)	16T1869	Trivial (GRH)
16.8.490237983424834767085031640625.1	x^16 - 5x^15 - 40x^14 + 307x^13 - 966x^12 - 1659x^11 + 40346x^10 - 135524x^9 - 23894x^8 + 1946502x^7 - 5668399x^6 + 3245050x^5 + 23736488x^4 - 77068202x^3 + 112248421x^2 - 90190604x + 32715509	\( 5^{8}\cdot 439^{4}\cdot 2411^{4} \)	16T1869	Trivial (GRH)
16.8.490237983424834767085031640625.2	x^16 - 7x^15 - 10x^14 - 49x^13 - 486x^12 + 4169x^11 + 24032x^10 + 82573x^9 + 113753x^8 - 328690x^7 - 2162497x^6 - 5295348x^5 - 3651274x^4 + 13271587x^3 + 41038390x^2 + 48594476x + 21906751	\( 5^{8}\cdot 439^{4}\cdot 2411^{4} \)	16T1869	Trivial (GRH)
16.0.190734124825347477084727321600000000.1	x^16 + 536x^14 + 111100x^12 + 11304513x^10 + 596833141x^8 + 16129436971x^6 + 215761836571x^4 + 1286266114845x^2 + 2729569883881	\( 2^{16}\cdot 5^{8}\cdot 1652141^{4} \)	16T1869	$[2, 2, 2328432]$ (GRH)
16.16.190734124825347477084727321600000000.1	x^16 - 462x^14 + 89327x^12 - 9310893x^10 + 559562474x^8 - 19075067464x^6 + 331665376040x^4 - 2176436381363x^2 + 2729569883881	\( 2^{16}\cdot 5^{8}\cdot 1652141^{4} \)	16T1869	Trivial (GRH)
16.0.190734124825347477084727321600000000.2	x^16 + 496x^14 + 99711x^12 + 10503607x^10 + 620292337x^8 + 20131740705x^6 + 319403408552x^4 + 1786640146669x^2 + 2729569883881	\( 2^{16}\cdot 5^{8}\cdot 1652141^{4} \)	16T1869	$[2, 2, 3714216]$ (GRH)
16.16.190734124825347477084727321600000000.2	x^16 - 496x^14 + 99711x^12 - 10503607x^10 + 620292337x^8 - 20131740705x^6 + 319403408552x^4 - 1786640146669x^2 + 2729569883881	\( 2^{16}\cdot 5^{8}\cdot 1652141^{4} \)	16T1869	Trivial (GRH)