Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3220023397562500000000.3	x^16 - 4x^15 - 3x^14 + 9x^13 + 33x^12 + 24x^11 - 82x^10 - 146x^9 - 41x^8 + 190x^7 + 430x^6 + 488x^5 + 392x^4 + 280x^3 + 160x^2 + 64x + 16	\( 2^{8}\cdot 5^{12}\cdot 61^{6} \)	16T852	$[2]$
16.0.76001667856000000000000.7	x^16 + 27x^12 + 274x^8 + 1148x^4 + 1681	\( 2^{16}\cdot 5^{12}\cdot 41^{6} \)	16T852	$[2]$ (GRH)
16.4.243914738067562500000000.3	x^16 - 29x^12 - 154x^8 + 116x^4 + 841	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{6} \)	16T852	Trivial (GRH)
16.4.243914738067562500000000.4	x^16 - 2x^15 - x^14 + 3x^13 + 6x^12 + 6x^11 - 73x^10 - 211x^9 - 43x^8 + 382x^7 + 133x^6 - 393x^5 - 154x^4 + 214x^3 + 26x^2 - 104x + 31	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{6} \)	16T852	Trivial (GRH)
16.0.111314889476126347022565376.1	x^16 + 28x^12 + 226x^8 + 612x^4 + 289	\( 2^{62}\cdot 17^{6} \)	16T852	$[2, 2]$ (GRH)
16.0.111314889476126347022565376.2	x^16 + 36x^12 + 226x^8 + 476x^4 + 289	\( 2^{62}\cdot 17^{6} \)	16T852	$[2, 2]$ (GRH)
16.8.111314889476126347022565376.4	x^16 - 36x^12 + 226x^8 - 476x^4 + 289	\( 2^{62}\cdot 17^{6} \)	16T852	Trivial (GRH)
16.8.111314889476126347022565376.5	x^16 - 92x^12 + 418x^8 - 612x^4 + 289	\( 2^{62}\cdot 17^{6} \)	16T852	Trivial (GRH)
16.0.221385427428590205586181640625.2	x^16 - 4x^15 + 138x^14 - 455x^13 + 8025x^12 - 20077x^11 + 244525x^10 - 526129x^9 + 4146511x^8 - 6434275x^7 + 18725575x^6 + 6108554x^5 - 194441392x^4 + 213506931x^3 - 598932388x^2 - 981739260x + 5151426151	\( 5^{12}\cdot 41^{6}\cdot 661^{4} \)	16T852	$[2, 2]$ (GRH)
16.0.221385427428590205586181640625.3	x^16 - 2x^15 - 33x^14 + 109x^13 + 524x^12 + 741x^11 + 6344x^10 + 2417x^9 + 111358x^8 + 286175x^7 + 545230x^6 + 26325565x^5 + 51478827x^4 - 236712984x^3 + 90662379x^2 + 3769753589x + 5616899611	\( 5^{12}\cdot 41^{6}\cdot 661^{4} \)	16T852	$[2, 2]$ (GRH)
16.0.5534635685714755139654541015625.1	x^16 - 2x^15 - 146x^14 + 103x^13 + 7373x^12 + 9208x^11 - 90799x^10 - 559901x^9 - 3044487x^8 - 3217617x^7 + 18719919x^6 + 280561309x^5 + 1920959023x^4 + 6828187756x^3 + 23208296551x^2 + 48410059339x + 126912289471	\( 5^{14}\cdot 41^{6}\cdot 661^{4} \)	16T852	$[2, 2, 2]$ (GRH)
16.0.5534635685714755139654541015625.2	x^16 - 7x^15 - 29x^14 + 472x^13 - 5229x^12 + 19974x^11 + 9024x^10 - 605119x^9 + 6994857x^8 - 33125809x^7 + 221564424x^6 - 853453216x^5 + 4754727171x^4 - 14727902028x^3 + 53368743541x^2 - 108971734827x + 148680785341	\( 5^{14}\cdot 41^{6}\cdot 661^{4} \)	16T852	$[2, 2, 2]$ (GRH)
16.16.1824424679612065776400000000000000.1	x^16 - 2x^15 - 175x^14 + 390x^13 + 11610x^12 - 27226x^11 - 373958x^10 + 908910x^9 + 6121920x^8 - 15713660x^7 - 47466883x^6 + 136830436x^5 + 129284605x^4 - 511487750x^3 + 82576530x^2 + 487879612x - 248412799	\( 2^{16}\cdot 5^{14}\cdot 61^{6}\cdot 97^{4} \)	16T852	Trivial (GRH)
16.8.467052717980688838758400000000000000.1	x^16 - 6x^15 + 76x^14 - 324x^13 - 10157x^12 + 32504x^11 + 248404x^10 - 91542x^9 - 5379957x^8 - 9218806x^7 + 168371486x^6 + 78373888x^5 - 1989121957x^4 - 3989723662x^3 + 869375994x^2 + 49830668338x + 63700077901	\( 2^{24}\cdot 5^{14}\cdot 61^{6}\cdot 97^{4} \)	16T852	$[2, 2]$ (GRH)
16.8.467052717980688838758400000000000000.2	x^16 - 6x^15 - 84x^14 + 486x^13 - 10012x^12 + 27414x^11 + 141964x^10 - 1018792x^9 + 13800238x^8 - 27974016x^7 + 129179506x^6 + 191867768x^5 - 1406195937x^4 + 6851881008x^3 - 15160486496x^2 + 7365907158x + 3809588801	\( 2^{24}\cdot 5^{14}\cdot 61^{6}\cdot 97^{4} \)	16T852	$[2, 2]$ (GRH)
16.8.467052717980688838758400000000000000.3	x^16 + 224x^14 - 600x^13 + 4207x^12 - 103570x^11 - 894128x^10 + 985700x^9 - 14651525x^8 + 231449980x^7 - 174611312x^6 - 4945685100x^5 + 31494302817x^4 - 20861377640x^3 - 317010550824x^2 + 708955723270x - 378475414519	\( 2^{24}\cdot 5^{14}\cdot 61^{6}\cdot 97^{4} \)	16T852	$[2, 2]$ (GRH)
16.0.6788684232836496753984400000000000000.1	x^16 - 6x^15 + 451x^14 - 2524x^13 + 76128x^12 - 427776x^11 + 6492584x^10 - 34976022x^9 + 321152208x^8 - 1407931996x^7 + 9453260051x^6 - 27067446942x^5 + 145236326283x^4 - 218586158402x^3 + 863745327204x^2 - 523452247142x + 1203481647881	\( 2^{16}\cdot 5^{14}\cdot 61^{8}\cdot 97^{4} \)	16T852	$[2, 2, 2, 2, 1047180]$ (GRH)
16.16.6788684232836496753984400000000000000.1	x^16 - 4x^15 - 469x^14 + 2274x^13 + 78273x^12 - 399734x^11 - 5963666x^10 + 27242342x^9 + 244580013x^8 - 810222424x^7 - 5649150424x^6 + 9143434322x^5 + 65368437133x^4 - 4051510228x^3 - 225185228471x^2 - 81401551558x + 157226892001	\( 2^{16}\cdot 5^{14}\cdot 61^{8}\cdot 97^{4} \)	16T852	$[2]$ (GRH)