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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.106467006734893163592286208.3	x^16 - 156x^12 + 832x^10 - 678x^8 - 1728x^6 + 780x^4 + 768x^2 + 113	\( 2^{66}\cdot 113^{3} \)	16T859	Trivial (GRH)
16.8.106467006734893163592286208.4	x^16 - 156x^12 - 832x^10 - 678x^8 + 1728x^6 + 780x^4 - 768x^2 + 113	\( 2^{66}\cdot 113^{3} \)	16T859	Trivial (GRH)
16.0.207330778063908903462109184.3	x^16 + 24x^12 - 16x^10 + 88x^8 + 8x^4 + 32x^2 + 14	\( 2^{79}\cdot 7^{3} \)	16T859	Trivial (GRH)
16.0.207330778063908903462109184.4	x^16 + 24x^12 + 16x^10 + 88x^8 + 8x^4 - 32x^2 + 14	\( 2^{79}\cdot 7^{3} \)	16T859	Trivial (GRH)
16.10.6310668336252090206289657856.1	x^16 - 16x^14 - 332x^12 + 8992x^10 - 73262x^8 + 280160x^6 - 602276x^4 + 707472x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	Trivial (GRH)
16.2.6310668336252090206289657856.1	x^16 + 16x^14 - 332x^12 - 8992x^10 - 73262x^8 - 280160x^6 - 602276x^4 - 707472x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	$[2, 2]$ (GRH)
16.6.6310668336252090206289657856.1	x^16 - 324x^12 + 1360x^10 + 17970x^8 - 164560x^6 + 773364x^4 - 1100512x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	Trivial (GRH)
16.10.6310668336252090206289657856.2	x^16 - 16x^14 - 300x^12 + 3744x^10 + 28578x^8 - 181152x^6 + 40460x^4 + 393040x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	Trivial (GRH)
16.2.6310668336252090206289657856.2	x^16 + 16x^14 - 300x^12 - 3744x^10 + 28578x^8 + 181152x^6 + 40460x^4 - 393040x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	$[2, 2]$ (GRH)
16.6.6310668336252090206289657856.2	x^16 - 324x^12 - 1360x^10 + 17970x^8 + 164560x^6 + 773364x^4 + 1100512x^2 - 83521	\( -\,2^{76}\cdot 17^{4} \)	16T859	Trivial (GRH)
16.0.124072986059627688411885857786694729728.1	x^16 + 784x^14 + 233444x^12 + 35068304x^10 + 2901858458x^8 + 133415695888x^6 + 3219023669900x^4 + 35156129966736x^2 + 131686311606833	\( 2^{66}\cdot 113^{3}\cdot 1039^{4} \)	16T859	$[2, 2, 2, 2, 6505842]$ (GRH)
16.16.124072986059627688411885857786694729728.1	x^16 - 992x^14 - 208x^13 + 356704x^12 + 87600x^11 - 57863576x^10 - 9972320x^9 + 4455644214x^8 + 1188103936x^7 - 167097841240x^6 - 67051400272x^5 + 2855439882632x^4 + 1097830640448x^3 - 16905504082608x^2 + 4093471289648x + 17362718655679	\( 2^{66}\cdot 113^{3}\cdot 1039^{4} \)	16T859	Trivial (GRH)
16.16.124072986059627688411885857786694729728.2	x^16 - 784x^14 + 233444x^12 - 35068304x^10 + 2901858458x^8 - 133415695888x^6 + 3219023669900x^4 - 35156129966736x^2 + 131686311606833	\( 2^{66}\cdot 113^{3}\cdot 1039^{4} \)	16T859	Trivial (GRH)