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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.347455511790057216.1	x^14 - 5x^13 + 12x^12 - 22x^11 + 40x^10 - 71x^9 + 138x^8 - 274x^7 + 472x^6 - 647x^5 + 709x^4 - 591x^3 + 345x^2 - 122x + 19	\( -\,2^{8}\cdot 3^{7}\cdot 7^{10}\cdot 13^{3} \)	14T45	Trivial
14.0.2877279093133463805696.1	x^14 - 5x^13 + 3x^12 + 29x^11 - 51x^10 - 136x^9 + 391x^8 + 16x^7 - 655x^6 + 99x^5 + 1902x^4 - 892x^3 - 393x^2 + 716x + 2092	\( -\,2^{8}\cdot 3^{7}\cdot 7^{12}\cdot 13^{5} \)	14T45	Trivial (GRH)
14.2.325573429585516975729147904.1	x^14 - 6x^13 + 29x^12 - 120x^11 + 239x^10 - 442x^9 + 277x^8 + 2984x^7 - 5118x^6 + 4052x^5 - 3310x^4 - 484x^3 + 11915x^2 - 3294x + 9153	\( 2^{27}\cdot 7^{10}\cdot 97^{5} \)	14T45	Trivial (GRH)
14.14.59392624219577526338317393617920000000.1	x^14 - 409x^12 - 1110x^11 + 61042x^10 + 320088x^9 - 3552936x^8 - 29533232x^7 + 29134016x^6 + 846683944x^5 + 2357606616x^4 - 604500464x^3 - 10859275264x^2 - 12992824640x - 2589545456	\( 2^{16}\cdot 5^{7}\cdot 7^{8}\cdot 19^{5}\cdot 93319^{3} \)	14T45	Trivial (GRH)
14.14.438334755667873937053743125776163667968.1	x^14 - 6x^13 - 457x^12 + 2720x^11 + 64336x^10 - 240364x^9 - 4549640x^8 + 4488436x^7 + 160506141x^6 + 181130646x^5 - 2435588247x^4 - 6624859400x^3 + 8042614275x^2 + 46379325210x + 44040163721	\( 2^{27}\cdot 7^{12}\cdot 223^{3}\cdot 463^{5} \)	14T45	Trivial (GRH)
14.8.194600400675149389603579413527667469123584.1	x^14 - 525x^12 - 518x^11 + 109942x^10 + 211890x^9 - 11363289x^8 - 32202766x^7 + 562633386x^6 + 2124722810x^5 - 8943505081x^4 - 47478809070x^3 - 109890439183x^2 - 304854167870x - 299096421324	\( -\,2^{16}\cdot 3^{8}\cdot 7^{10}\cdot 13^{7}\cdot 294467^{3} \)	14T45	Trivial (GRH)
14.8.1136553186048642579467300999397100786548736.1	x^14 - 2x^13 - 29x^12 + 2684x^11 - 50815x^10 - 101186x^9 + 2905773x^8 - 96986796x^7 + 393809153x^6 + 2822730482x^5 - 59621810879x^4 + 536849629536x^3 + 366359666251x^2 - 19410042679742x + 49980715777967	\( -\,2^{27}\cdot 7^{12}\cdot 409^{5}\cdot 3767^{3} \)	14T45	Trivial (GRH)
14.2.1926377462756066120847727193419105645413531648.1	x^14 - 2x^13 - 1657x^12 + 10232x^11 + 916925x^10 - 8273862x^9 - 203574775x^8 + 2500711652x^7 + 11370375683x^6 - 238430330210x^5 + 435254400205x^4 + 11976481209516x^3 - 121702249507305x^2 + 237150347682498x - 613625842441849	\( 2^{27}\cdot 3^{6}\cdot 7^{11}\cdot 263^{3}\cdot 3529^{5} \)	14T45	Trivial (GRH)