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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.74365128097098891264.1	x^16 - 7x^14 + 19x^12 - 25x^10 + 25x^8 - 22x^6 + 10x^4 - 4x^2 + 4	\( 2^{30}\cdot 3^{12}\cdot 19^{4} \)	16T1605	Trivial
16.0.74365128097098891264.2	x^16 - 7x^14 + 20x^12 - 28x^10 + 19x^8 - 8x^6 + 8x^4 - 8x^2 + 4	\( 2^{30}\cdot 3^{12}\cdot 19^{4} \)	16T1605	Trivial
16.0.314563212964900000000.1	x^16 - x^15 + 3x^14 - 10x^13 + 5x^12 - 14x^11 + 25x^10 + 5x^9 + 20x^8 - 15x^7 - 31x^6 + 5x^4 + 73x^3 + 39x^2 - 15x + 5	\( 2^{8}\cdot 5^{8}\cdot 17^{6}\cdot 19^{4} \)	16T1605	Trivial
16.0.341391029632900000000.1	x^16 - 4x^15 + 14x^14 - 29x^13 + 69x^12 - 116x^11 + 214x^10 - 265x^9 + 392x^8 - 380x^7 + 518x^6 - 375x^5 + 390x^4 - 143x^3 + 96x^2 + 6x + 1	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial
16.4.341391029632900000000.4	x^16 - 3x^15 + 2x^14 + 7x^12 - 51x^10 + 46x^9 + 144x^8 - 245x^7 - 65x^6 + 348x^5 - 161x^4 - 65x^3 + 47x^2 - 7x + 1	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial
16.4.341391029632900000000.5	x^16 - x^15 - 4x^14 - 2x^13 + 2x^12 + 9x^11 - 17x^10 - 39x^9 - 22x^8 - 61x^7 - 33x^6 + 88x^5 + 150x^4 + 67x^3 - 16x^2 - 20x - 1	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial
16.4.3756480035416900000000.2	x^16 - 4x^15 - x^14 + 23x^13 - 30x^12 - 5x^11 + 22x^10 - 135x^9 + 443x^8 - 195x^7 - 665x^6 + 650x^5 + 5x^4 - 72x^3 - 26x^2 - 11x + 11	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 37^{6} \)	16T1605	Trivial (GRH)
16.4.3756480035416900000000.3	x^16 - 2x^15 + 4x^14 - 5x^13 + 14x^12 + 11x^11 - 78x^10 + 18x^9 + 77x^8 - 284x^7 - 486x^6 - 218x^5 + 19x^4 + 101x^3 + 145x^2 + 93x + 19	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 37^{6} \)	16T1605	Trivial (GRH)
16.4.3756480035416900000000.4	x^16 - x^15 - 6x^14 - 8x^13 + 16x^12 + 49x^11 + 66x^10 + 12x^9 - 331x^8 - 589x^7 + 250x^6 + 743x^5 - 487x^4 - 550x^3 + 365x^2 + 110x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 37^{6} \)	16T1605	Trivial (GRH)
16.0.26316003239526400000000.1	x^16 + 3x^14 - 7x^12 - 13x^10 + 13x^8 - 2x^6 + 10x^4 + 52x^2 + 4	\( 2^{30}\cdot 5^{8}\cdot 89^{4} \)	16T1605	Trivial
16.8.26316003239526400000000.1	x^16 - 3x^14 - 7x^12 + 13x^10 + 13x^8 + 2x^6 + 10x^4 - 52x^2 + 4	\( 2^{30}\cdot 5^{8}\cdot 89^{4} \)	16T1605	Trivial (GRH)
16.0.80528182519014400000000.1	x^16 - 5x^14 + 3x^12 + 21x^10 + 190x^8 - 561x^6 + 765x^4 - 578x^2 + 289	\( 2^{16}\cdot 5^{8}\cdot 17^{6}\cdot 19^{4} \)	16T1605	Trivial (GRH)
16.4.80528182519014400000000.1	x^16 - 4x^15 - 4x^14 + 30x^13 - 13x^12 - 26x^11 - 3x^10 - 106x^9 - 148x^8 + 1148x^7 - 280x^6 - 1748x^5 + 103x^4 + 2142x^3 - 1184x^2 + 142x - 19	\( 2^{16}\cdot 5^{8}\cdot 17^{6}\cdot 19^{4} \)	16T1605	Trivial (GRH)
16.4.87396103586022400000000.1	x^16 - 8x^15 + 38x^14 - 126x^13 + 285x^12 - 436x^11 + 307x^10 + 412x^9 - 1686x^8 + 2908x^7 - 3257x^6 + 2534x^5 - 1358x^4 + 472x^3 - 90x^2 + 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial (GRH)
16.8.87396103586022400000000.1	x^16 - 2x^15 - x^14 + 4x^13 - 41x^12 + 26x^11 - 53x^10 - 112x^9 + 135x^8 - 282x^7 + 10x^6 + 532x^5 - 236x^4 - 56x^3 + 232x^2 - 80x - 16	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial (GRH)
16.8.87396103586022400000000.2	x^16 - 6x^15 + 9x^14 - 16x^13 + 38x^12 + 36x^11 - 82x^10 + 4x^9 - 277x^8 + 56x^7 + 514x^6 + 8x^5 - 24x^4 - 112x^3 - 64x^2 + 80x - 16	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial (GRH)
16.8.87396103586022400000000.3	x^16 - 12x^14 + 48x^12 - 83x^10 + 218x^8 - 962x^6 + 1820x^4 - 1183x^2 + 169	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{4} \)	16T1605	Trivial (GRH)
16.12.421056051832422400000000.1	x^16 - 8x^14 - 12x^12 + 184x^10 - 156x^8 - 912x^6 + 1632x^4 - 704x^2 + 64	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1605	Trivial (GRH)
16.4.421056051832422400000000.1	x^16 + 8x^14 - 12x^12 - 184x^10 - 156x^8 + 912x^6 + 1632x^4 + 704x^2 + 64	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1605	Trivial (GRH)
16.0.454534084285444900000000.1	x^16 - 5x^15 + 22x^14 - 50x^13 + 105x^12 - 105x^11 + 132x^10 + 26x^9 + 236x^8 + 201x^7 + 1735x^6 + 1147x^5 + 5024x^4 + 5994x^3 + 2980x^2 + 3297x + 1699	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1605	$[2]$ (GRH)
16.8.454534084285444900000000.1	x^16 - 4x^15 - 6x^14 + 34x^13 - 70x^12 + 73x^11 + 585x^10 - 1498x^9 + 543x^8 + 7165x^7 - 8137x^6 - 10232x^5 + 16930x^4 + 87x^3 - 9497x^2 + 4554x - 529	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1605	Trivial (GRH)
16.0.454534084285444900000000.2	x^16 - x^15 + 14x^14 - 28x^13 + 140x^12 - 261x^11 + 787x^10 - 1421x^9 + 3700x^8 - 6680x^7 + 12096x^6 - 13965x^5 + 14123x^4 - 7590x^3 + 3770x^2 - 583x + 1159	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1605	$[6]$ (GRH)
16.8.961658889066726400000000.1	x^16 - 8x^14 + 13x^12 + 50x^10 - 222x^8 + 232x^6 + 610x^4 - 1924x^2 + 1369	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{6} \)	16T1605	Trivial (GRH)
16.4.1618287836733993526493184.1	x^16 - 4x^15 + 10x^14 - 16x^13 - 44x^12 - 128x^11 - 526x^10 - 1568x^9 - 2920x^8 - 6408x^7 - 10746x^6 - 13028x^5 - 16632x^4 - 14536x^3 - 6178x^2 + 1128x + 913	\( 2^{34}\cdot 3^{8}\cdot 13^{4}\cdot 709^{2} \)	16T1605	$[2]$ (GRH)
16.4.1618287836733993526493184.2	x^16 - 14x^14 - 12x^13 + 94x^12 + 256x^11 - 596x^10 - 1556x^9 + 1914x^8 + 6484x^7 - 5844x^6 - 14272x^5 + 11552x^4 + 19716x^3 - 10884x^2 - 21776x + 15214	\( 2^{34}\cdot 3^{8}\cdot 13^{4}\cdot 709^{2} \)	16T1605	$[2]$ (GRH)
16.0.2210793102376960000000000.1	x^16 - 5x^14 + 22x^12 - 65x^10 + 336x^8 + 285x^6 + 2655x^4 + 900x^2 + 100	\( 2^{26}\cdot 5^{10}\cdot 241^{4} \)	16T1605	$[3]$ (GRH)
16.12.6736896829318758400000000.3	x^16 - 4x^14 - 67x^12 + 58x^10 + 211x^8 - 356x^6 + 202x^4 - 48x^2 + 4	\( 2^{38}\cdot 5^{8}\cdot 89^{4} \)	16T1605	Trivial (GRH)
16.0.35372689638031360000000000.1	x^16 - 5x^14 + 48x^12 - 165x^10 + 286x^8 - 105x^6 + 995x^4 - 550x^2 + 100	\( 2^{30}\cdot 5^{10}\cdot 241^{4} \)	16T1605	$[3]$ (GRH)
16.8.41884397835209089533503078400000000.1	x^16 + 10x^14 - 12648x^12 - 396284x^10 + 6450775x^8 + 153137826x^6 - 2108753532x^4 + 2269905012x^2 + 24868659204	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 89^{4}\cdot 8761^{2} \)	16T1605	$[2]$ (GRH)
16.8.41884397835209089533503078400000000.2	x^16 - 100x^14 - 3963x^12 + 173140x^10 + 1552105x^8 - 55191090x^6 - 257592006x^4 + 4598473680x^2 + 24868659204	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 89^{4}\cdot 8761^{2} \)	16T1605	$[2]$ (GRH)
16.8.114205898821156016581142118400000000.1	x^16 - 18x^14 - 13001x^12 - 429814x^10 + 7092685x^8 + 161587388x^6 - 1120383490x^4 - 13483094756x^2 + 67809201604	\( 2^{38}\cdot 5^{8}\cdot 89^{4}\cdot 130201^{2} \)	16T1605	Trivial (GRH)
16.8.114205898821156016581142118400000000.2	x^16 - 20x^14 - 7343x^12 + 60096x^10 + 13923457x^8 + 88066646x^6 - 2081661750x^4 - 10571279592x^2 + 67809201604	\( 2^{38}\cdot 5^{8}\cdot 89^{4}\cdot 130201^{2} \)	16T1605	Trivial (GRH)
16.0.10031792466827489906262016000000000000.1	x^16 - 280x^14 + 56040x^12 - 7400800x^10 + 779073750x^8 - 60269405000x^6 + 3199905061000x^4 - 101932286360000x^2 + 1396914918855625	\( 2^{40}\cdot 5^{12}\cdot 41^{4}\cdot 115001^{2} \)	16T1605	$[2, 8]$ (GRH)
16.0.10031792466827489906262016000000000000.2	x^16 - 90x^14 - 2635x^12 + 2149800x^10 - 51985625x^8 - 4722706500x^6 + 533990346625x^4 + 2424077328750x^2 + 1396914918855625	\( 2^{40}\cdot 5^{12}\cdot 41^{4}\cdot 115001^{2} \)	16T1605	$[2, 8]$ (GRH)
16.0.37092500770633898047098480230400000000.1	x^16 - 6x^15 + 624x^14 - 3170x^13 + 159917x^12 - 732770x^11 + 21884676x^10 - 92906620x^9 + 1728619198x^8 - 6755823818x^7 + 78490251388x^6 - 270067793486x^5 + 1877339814623x^4 - 4967931915742x^3 + 18193806946372x^2 - 17935139332092x + 38179500401221	\( 2^{34}\cdot 3^{4}\cdot 5^{8}\cdot 31^{2}\cdot 89^{4}\cdot 33641^{2} \)	16T1605	$[2, 2, 2, 2, 3721904]$ (GRH)
16.0.593480012330142368753575683686400000000.1	x^16 + 966x^14 + 336865x^12 + 54096892x^10 + 4564529155x^8 + 213414926004x^6 + 5474328578946x^4 + 70645633332048x^2 + 352375894935684	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 31^{2}\cdot 89^{4}\cdot 33641^{2} \)	16T1605	$[2, 2, 2, 2, 20522460]$ (GRH)
16.16.60315182355722271054119173521565286400000000.1	x^16 - 3776x^14 + 5554757x^12 - 4064943508x^10 + 1586607526759x^8 - 336361698262014x^6 + 37355497726908528x^4 - 1932548200410874572x^2 + 35811848620410831684	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 71^{2}\cdot 89^{4}\cdot 4682551^{2} \)	16T1605	Trivial (GRH)
16.16.92312550113934353567868968606525030400000000.1	x^16 - 5164x^14 + 9735650x^12 - 8303067008x^10 + 3304853557807x^8 - 655145861893860x^6 + 65194627740035562x^4 - 3079034782068852828x^2 + 54810131401860336324	\( 2^{38}\cdot 3^{4}\cdot 5^{8}\cdot 41^{2}\cdot 89^{4}\cdot 10031689^{2} \)	16T1605	Trivial (GRH)
16.0.1936052704382448567172058182790309478400000000.1	x^16 - 18x^14 - 1618x^12 + 54344x^10 + 13261591x^8 + 578282758x^6 + 12224367358x^4 + 100748182696x^2 + 1211536087204	\( 2^{38}\cdot 5^{8}\cdot 89^{4}\cdot 130201^{4} \)	16T1605	$[2, 129656]$ (GRH)
16.0.1936052704382448567172058182790309478400000000.2	x^16 - 20x^14 + 2637x^12 + 13224x^10 + 1792727x^8 - 27766746x^6 + 5837598720x^4 + 50079521052x^2 + 432808725924	\( 2^{38}\cdot 5^{8}\cdot 89^{4}\cdot 130201^{4} \)	16T1605	$[2, 129656]$ (GRH)