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
16.0.3989479416368103396468588544.1	x^16 + 56x^14 + 1232x^12 + 13720x^10 + 81830x^8 + 249704x^6 + 323792x^4 + 96040x^2 + 2401	\( 2^{58}\cdot 7^{12} \)	$Q_{16}$ (as 16T14)	$[2, 14, 14]$ (GRH)
16.16.3989479416368103396468588544.1	x^16 - 56x^14 + 1232x^12 - 13720x^10 + 81830x^8 - 249704x^6 + 323792x^4 - 96040x^2 + 2401	\( 2^{58}\cdot 7^{12} \)	$Q_{16}$ (as 16T14)	Trivial (GRH)
16.0.53178385204239177923287842816.1	x^16 - 4x^15 + 74x^14 - 352x^13 + 2602x^12 - 9704x^11 + 42818x^10 - 121952x^9 + 390370x^8 - 940332x^7 + 2450022x^6 - 5077560x^5 + 9984474x^4 - 14175360x^3 + 16341750x^2 - 8146152x + 1385757	\( 2^{32}\cdot 3^{12}\cdot 13^{12} \)	$Q_{16}$ (as 16T14)	$[2, 2, 4, 4, 4, 8]$ (GRH)
16.16.53178385204239177923287842816.1	x^16 - 4x^15 - 82x^14 + 428x^13 + 1666x^12 - 11264x^11 - 11158x^10 + 122968x^9 + 6103x^8 - 634260x^7 + 185526x^6 + 1445736x^5 - 609876x^4 - 880416x^3 + 770220x^2 - 217296x + 21069	\( 2^{32}\cdot 3^{12}\cdot 13^{12} \)	$Q_{16}$ (as 16T14)	$[2]$ (GRH)
16.0.275103767122062920083301025390625.39	x^16 - x^15 + 98x^14 - 90x^13 + 4761x^12 - 4435x^11 + 130737x^10 - 30422x^9 + 2024471x^8 + 1410010x^7 + 20731015x^6 + 33449130x^5 + 101899505x^4 + 367664500x^3 + 495143825x^2 + 212747625x + 730770125	\( 5^{12}\cdot 101^{12} \)	$Q_{16}$ (as 16T14)	$[2, 2, 2, 6, 6, 12, 12]$ (GRH)
16.0.11445391768549949624817238631584321.55	x^16 - x^15 + 133x^14 - 103x^13 + 6081x^12 - 5825x^11 + 129015x^10 - 395763x^9 + 2239826x^8 - 15443166x^7 + 42987317x^6 - 243806269x^5 + 1187076972x^4 - 3260668645x^3 + 8997200644x^2 - 18857570867x + 15497228633	\( 13^{12}\cdot 53^{12} \)	$Q_{16}$ (as 16T14)	$[2, 2, 2, 4, 4, 28, 28]$ (GRH)
16.0.61841248347955294332328765542314401.45	x^16 - 3x^15 + 168x^14 - 118x^13 + 8143x^12 + 19673x^11 + 268861x^10 + 996458x^9 + 6562747x^8 + 28125680x^7 + 116312303x^6 + 424196239x^5 + 1236318043x^4 + 3216880296x^3 + 7235716110x^2 + 10185930767x + 17602483739	\( 13^{12}\cdot 61^{12} \)	$Q_{16}$ (as 16T14)	$[2, 2, 2, 2, 2, 68, 68]$ (GRH)
16.0.477639401035264016929733847900390625.18	x^16 - 3x^15 + 64x^14 - 267x^13 - 254x^12 - 4890x^11 - 7005x^10 + 138170x^9 + 706440x^8 + 2483375x^7 + 6028400x^6 + 11861450x^5 + 42649275x^4 + 4094000x^3 + 371963750x^2 - 453825000x + 1051559375	\( 5^{12}\cdot 89^{14} \)	$Q_{16}$ (as 16T14)	$[4, 8, 8, 8, 8]$ (GRH)
16.16.82717106576700383216526055870773061489.2	x^16 - 3x^15 - 288x^14 + 351x^13 + 32164x^12 + 6818x^11 - 1712220x^10 - 2050498x^9 + 43855038x^8 + 73975139x^7 - 504661128x^6 - 805577043x^5 + 2530948457x^4 + 2475352300x^3 - 4676812808x^2 - 174707192x + 1104680656	\( 17^{14}\cdot 53^{12} \)	$Q_{16}$ (as 16T14)	$[4]$ (GRH)
16.16.100677405300724224532172039540740068462931681.2	x^16 - 5x^15 - 787x^14 + 5051x^13 + 224913x^12 - 1883696x^11 - 26837605x^10 + 308362799x^9 + 840421984x^8 - 20027658582x^7 + 49055322017x^6 + 242254120296x^5 - 1022348955259x^4 - 574159811286x^3 + 5148673520590x^2 - 479019525519x - 6904626882871	\( 41^{14}\cdot 61^{12} \)	$Q_{16}$ (as 16T14)	$[4]$ (GRH)
16.16.788235353584876852533663970039941030620064481.1	x^16 - 5x^15 - 1567x^14 + 5036x^13 + 913132x^12 - 2632325x^11 - 251203331x^10 + 944435243x^9 + 33537176305x^8 - 194082565895x^7 - 1854337101495x^6 + 17178191896767x^5 + 713563290839x^4 - 408109365395354x^3 + 1450005309994863x^2 - 1532647000809550x - 134701390338101	\( 37^{12}\cdot 149^{12} \)	$Q_{16}$ (as 16T14)	$[4]$ (GRH)
16.0.1476442430876140116899060702773874183614562881.43	x^16 - 3x^15 + 1245x^14 - 929x^13 + 344716x^12 + 477002x^11 + 9678642x^10 + 527271324x^9 + 2476254439x^8 - 16644451521x^7 + 234290252130x^6 + 2895427880223x^5 + 1622671062847x^4 + 13345645225409x^3 + 709619381151297x^2 + 3629213187441572x + 5423234506172099	\( 37^{12}\cdot 157^{12} \)	$Q_{16}$ (as 16T14)	$[2, 2, 2, 2, 2, 3196, 3196]$ (GRH)