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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.3001468113659956604960768.1	x^16 - 17x^12 - 306x^8 - 493x^4 - 17	\( -\,2^{20}\cdot 17^{15} \)	16T1186	$[2]$
16.2.3001468113659956604960768.2	x^16 - 51x^12 - 340x^8 - 357x^4 - 17	\( -\,2^{20}\cdot 17^{15} \)	16T1186	$[2]$
16.6.21836222616789239468130304.3	x^16 - 136x^12 + 396x^8 + 2304x^4 - 1156	\( -\,2^{76}\cdot 17^{2} \)	16T1186	Trivial (GRH)
16.6.21836222616789239468130304.4	x^16 - 8x^12 - 404x^8 + 1568x^4 - 1156	\( -\,2^{76}\cdot 17^{2} \)	16T1186	Trivial (GRH)
16.0.85304566600455667746642216756445184.1	x^16 - 4x^15 + 298x^14 - 572x^13 + 34241x^12 - 39808x^11 + 1970244x^10 - 1978792x^9 + 62512596x^8 - 60883952x^7 + 1132616672x^6 - 906010208x^5 + 11255370396x^4 - 6154880192x^3 + 56568573472x^2 - 15531166208x + 112207690208	\( 2^{44}\cdot 449^{2}\cdot 1889^{5} \)	16T1186	$[2, 2, 4, 772144]$ (GRH)
16.0.85304566600455667746642216756445184.2	x^16 - 4x^15 + 378x^14 - 1308x^13 + 46253x^12 - 135296x^11 + 2675448x^10 - 5940208x^9 + 81603792x^8 - 118159648x^7 + 1413343656x^6 - 1007025840x^5 + 13706396484x^4 - 1069756000x^3 + 72875921600x^2 + 17326720000x + 150100780000	\( 2^{44}\cdot 449^{2}\cdot 1889^{5} \)	16T1186	$[2, 2, 4, 672664]$ (GRH)
16.16.1364873065607290683946275468103122944.1	x^16 - 492x^14 - 96x^13 + 95858x^12 + 32376x^11 - 9438176x^10 - 4234648x^9 + 498003651x^8 + 289793200x^7 - 13786393584x^6 - 11380691704x^5 + 180053223426x^4 + 217601183232x^3 - 762305657052x^2 - 1378932819352x - 573429908638	\( 2^{48}\cdot 449^{2}\cdot 1889^{5} \)	16T1186	Trivial (GRH)
16.16.1364873065607290683946275468103122944.2	x^16 - 464x^14 - 120x^13 + 87302x^12 + 54208x^11 - 8499648x^10 - 9347912x^9 + 448690771x^8 + 774198304x^7 - 11964273276x^6 - 30845655536x^5 + 114829145270x^4 + 473110428024x^3 + 393968857948x^2 - 103460794152x - 126146235134	\( 2^{48}\cdot 449^{2}\cdot 1889^{5} \)	16T1186	Trivial (GRH)
16.8.482442912719743132475274701949659184820649984.1	x^16 - 3380x^14 - 6536x^13 + 384562x^12 + 13075880x^11 + 2771892296x^10 + 7159006480x^9 + 565392805539x^8 - 3265494601808x^7 - 268140864788520x^6 - 1755899218481624x^5 - 70735834258824534x^4 - 133813426495447008x^3 - 371206890725959692x^2 + 11490145946673401496x + 123315291818966506466	\( 2^{48}\cdot 1889^{5}\cdot 8441569^{2} \)	16T1186	$[2, 2]$ (GRH)
16.12.6767652375800250507037432977960083710388731904.1	x^16 - 4896x^14 + 7689860x^12 - 3409772064x^10 - 1266129331670x^8 + 1040831008579456x^6 - 88192020563282736x^4 - 42597270982345604736x^2 + 6580128555447173793296	\( 2^{62}\cdot 1889^{5}\cdot 247007^{2} \)	16T1186	$[2, 2, 2]$ (GRH)
16.12.6767652375800250507037432977960083710388731904.2	x^16 - 1392x^14 - 6229112x^12 + 16501892048x^10 - 13391862498668x^8 + 3209410207612384x^6 + 400452722366707216x^4 - 100599134011721249248x^2 + 1645032138861793448324	\( 2^{62}\cdot 1889^{5}\cdot 247007^{2} \)	16T1186	$[2, 2, 2]$ (GRH)