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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.372810566126077697.1	x^16 - 3x^15 + 10x^14 - 16x^13 + 29x^12 - 25x^11 + 33x^10 - 12x^9 + 25x^8 - 12x^7 + 33x^6 - 25x^5 + 29x^4 - 16x^3 + 10x^2 - 3x + 1	\( 59^{3}\cdot 283^{5} \)	16T1760	Trivial
16.6.5567497578575422279.1	x^16 - 6x^15 + 16x^14 - 17x^13 - 30x^12 + 148x^11 - 291x^10 + 338x^9 - 221x^8 + 33x^7 + 108x^6 - 139x^5 + 102x^4 - 59x^3 + 20x^2 - 5x + 1	\( -\,37^{3}\cdot 643^{5} \)	16T1760	Trivial
16.2.13143129108647164799.1	x^16 - 2x^15 - 2x^14 + 19x^13 - 30x^12 - 6x^11 + 111x^10 - 188x^9 + 117x^8 + 139x^7 - 391x^6 + 500x^5 - 409x^4 + 264x^3 - 116x^2 + 39x + 1	\( -\,149^{3}\cdot 331^{5} \)	16T1760	Trivial
16.2.13143129108647164799.2	x^16 - 3x^15 + 11x^14 - 24x^13 + 49x^12 - 89x^11 + 135x^10 - 203x^9 + 251x^8 - 300x^7 + 300x^6 - 288x^5 + 214x^4 - 154x^3 + 61x^2 - 15x + 1	\( -\,149^{3}\cdot 331^{5} \)	16T1760	Trivial
16.4.3579900943023996525397.1	x^16 - 3x^15 + 6x^14 - 16x^13 - 7x^12 - 39x^11 - 29x^10 + 3x^9 - 54x^8 + 77x^7 + 167x^6 - 370x^5 + 483x^4 - 481x^3 + 216x^2 - 35x + 1	\( 37^{3}\cdot 643^{6} \)	16T1760	$[2]$ (GRH)
16.0.4350375734962211548469.1	x^16 - 3x^15 - x^14 + 12x^13 - 3x^12 - 41x^11 + 49x^10 + 28x^9 - 75x^8 + 24x^7 - 12x^6 + 58x^5 + 34x^4 - 162x^3 + 128x^2 - 15x + 1	\( 149^{3}\cdot 331^{6} \)	16T1760	$[2]$ (GRH)
16.2.10823290853689763889152.1	x^16 - 8x^14 + 9x^12 + 109x^10 - 698x^8 + 2249x^6 - 4473x^4 + 5200x^2 - 2777	\( -\,2^{16}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.6.10823290853689763889152.1	x^16 - 9x^14 - 10x^13 + 34x^12 + 60x^11 - 30x^10 - 240x^9 - 22x^8 + 690x^7 + 268x^6 - 986x^5 - 807x^4 - 36x^3 + 370x^2 + 540x + 236	\( -\,2^{16}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.2.10823290853689763889152.2	x^16 - x^14 - 20x^13 - x^12 - 6x^11 + 162x^10 - 72x^9 + 731x^8 - 384x^7 - 3269x^6 - 190x^5 + 4336x^4 + 1108x^3 - 567x^2 - 3514x + 1262	\( -\,2^{16}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.6.10823290853689763889152.2	x^16 - 7x^14 + 20x^12 - 2x^11 - 58x^10 - 58x^9 + 72x^8 + 234x^7 + 58x^6 - 330x^5 - 248x^4 + 184x^3 + 335x^2 + 172x + 31	\( -\,2^{16}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.4.20702617882947030679552.1	x^16 - 14x^14 + 63x^12 - 93x^10 + 93x^8 - 482x^6 + 1090x^4 - 5934x^2 + 14233	\( 2^{16}\cdot 43^{3}\cdot 331^{5} \)	16T1760	Trivial (GRH)
16.6.291790609341075705702599.1	x^16 - 2x^15 - 17x^14 + 36x^13 + 88x^12 - 252x^11 + 162x^10 + 1339x^9 - 3872x^8 - 7533x^7 + 13863x^6 + 25692x^5 - 11472x^4 - 26629x^3 + 5294x^2 + 8456x - 1457	\( -\,149^{5}\cdot 331^{5} \)	16T1760	Trivial (GRH)
16.8.3442109543617248230139232256.1	x^16 + 25x^14 - 193x^12 - 4225x^10 + 5988x^8 + 94522x^6 - 54749x^4 - 471108x^2 + 119411	\( 2^{18}\cdot 43^{3}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.8.3442109543617248230139232256.2	x^16 + 27x^14 - 39x^12 - 3252x^10 + 7091x^8 + 36235x^6 - 56518x^4 - 92020x^2 + 119411	\( 2^{18}\cdot 43^{3}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.16.43618674563639453561184489472.1	x^16 - 7x^15 - 48x^14 + 407x^13 + 654x^12 - 8619x^11 - 687x^10 + 86412x^9 - 43726x^8 - 441604x^7 + 287751x^6 + 1183529x^5 - 599678x^4 - 1642033x^3 + 228613x^2 + 997736x + 297188	\( 2^{12}\cdot 401^{3}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.0.69582098557917678541006176256.1	x^16 + 52x^14 + 1098x^12 + 12063x^10 + 73313x^8 + 241471x^6 + 389897x^4 + 239798x^2 + 48394	\( 2^{23}\cdot 24197^{5} \)	16T1760	$[2, 2, 780]$ (GRH)
16.16.69582098557917678541006176256.1	x^16 - 52x^14 + 1098x^12 - 12063x^10 + 73313x^8 - 241471x^6 + 389897x^4 - 239798x^2 + 48394	\( 2^{23}\cdot 24197^{5} \)	16T1760	Trivial (GRH)
16.0.278328394231670714164024705024.1	x^16 + 70x^14 + 1666x^12 + 18385x^10 + 106319x^8 + 337324x^6 + 589710x^4 + 532260x^2 + 193576	\( 2^{25}\cdot 24197^{5} \)	16T1760	$[2, 2, 1868]$ (GRH)
16.12.1591115136537072994381860110336.1	x^16 - 2x^15 - 53x^14 + 208x^13 - 328x^12 - 4182x^11 + 49440x^10 - 46618x^9 - 650658x^8 + 1448656x^7 + 1449595x^6 - 7645594x^5 + 10657714x^4 + 2280134x^3 - 25260027x^2 + 7724778x + 1642714	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.4.1591115136537072994381860110336.1	x^16 + 61x^14 + 547x^12 - 28280x^10 - 610205x^8 - 1277148x^6 + 55125183x^4 + 436778176x^2 + 883163756	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	$[2]$ (GRH)
16.8.1591115136537072994381860110336.1	x^16 - 4x^15 - 6x^14 + 170x^13 - 1453x^12 - 2480x^11 + 2306x^10 - 8656x^9 + 375038x^8 + 597784x^7 + 3268904x^6 - 7765050x^5 - 40172297x^4 - 60807646x^3 - 67053946x^2 + 5289064x + 49189808	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.12.1591115136537072994381860110336.2	x^16 - 2x^15 - 19x^14 + 76x^13 - 1315x^12 - 704x^11 + 24668x^10 - 16820x^9 + 90295x^8 + 739670x^7 - 3191927x^6 - 8753276x^5 + 11928784x^4 + 32144966x^3 - 1452855x^2 - 22910800x - 6748849	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.4.1591115136537072994381860110336.2	x^16 - 2x^15 + 94x^14 - 188x^13 + 2279x^12 - 9228x^11 + 21074x^10 - 153906x^9 + 194689x^8 - 762930x^7 + 2309973x^6 - 7056x^5 + 10741382x^4 + 2332284x^3 + 17110206x^2 + 18840328x + 4742981	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	$[2]$ (GRH)
16.8.1591115136537072994381860110336.2	x^16 - 2x^15 - 70x^14 - 42x^13 + 347x^12 + 5870x^11 + 28118x^10 - 102844x^9 - 47498x^8 - 113540x^7 - 1244349x^6 + 5656900x^5 - 19099742x^4 + 66098316x^3 - 87981517x^2 + 76194534x - 16911551	\( 2^{16}\cdot 43^{5}\cdot 2777^{5} \)	16T1760	Trivial (GRH)
16.0.152939811242001573361546367598592.1	x^16 - 15x^14 + 337x^12 - 4208x^10 + 37389x^8 - 333687x^6 + 2214990x^4 - 10606853x^2 + 38237707	\( 2^{22}\cdot 43^{3}\cdot 2777^{6} \)	16T1760	$[4, 60]$ (GRH)
16.0.152939811242001573361546367598592.2	x^16 + 21x^14 + 361x^12 + 3656x^10 + 31049x^8 + 166645x^6 + 757674x^4 + 1912167x^2 + 4212667	\( 2^{22}\cdot 43^{3}\cdot 2777^{6} \)	16T1760	$[4, 60]$ (GRH)