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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.12010577056389693116416.1	x^20 - x^18 + 3x^16 - 11x^14 + 6x^12 + 6x^10 + 5x^8 - 13x^6 + 7x^4 - 5x^2 + 1	\( 2^{12}\cdot 41381^{4} \)	20T568	Trivial (GRH)
20.4.15363369498681819529216.1	x^20 + 3x^18 + x^16 - 3x^14 - 2x^12 + x^10 + 6x^8 - 9x^6 - 7x^4 + 1	\( 2^{24}\cdot 5501^{4} \)	20T568	Trivial (GRH)
20.12.119834225764331755130589184.1	x^20 - 20x^18 + 163x^16 - 717x^14 + 1904x^12 - 3263x^10 + 3779x^8 - 2996x^6 + 1540x^4 - 441x^2 + 49	\( 2^{12}\cdot 7^{6}\cdot 137^{4}\cdot 163^{4} \)	20T568	Trivial (GRH)
20.12.455293169564857148863676416.2	x^20 - 10x^18 + 39x^16 - 72x^14 + 82x^12 - 156x^10 + 337x^8 - 372x^6 + 179x^4 - 30x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T568	Trivial (GRH)
20.4.635400276596182371643949056.1	x^20 + 4x^18 + 10x^16 + 30x^14 - 26x^12 - 74x^10 - 31x^8 - 160x^6 + 18x^2 + 1	\( 2^{40}\cdot 4903^{4} \)	20T568	Trivial (GRH)
20.4.635400276596182371643949056.2	x^20 + 10x^18 + 30x^16 - 177x^12 - 402x^10 - 388x^8 - 162x^6 - 10x^4 + 10x^2 + 1	\( 2^{40}\cdot 4903^{4} \)	20T568	Trivial (GRH)
20.12.12180532532810607890279383957504.1	x^20 + 4x^18 - 51x^16 - 58x^14 + 562x^12 - 628x^10 - 166x^8 + 434x^6 - 27x^4 - 76x^2 + 4	\( 2^{38}\cdot 83^{4}\cdot 983^{4} \)	20T568	Trivial (GRH)
20.20.12180532532810607890279383957504.1	x^20 - 24x^18 + 231x^16 - 1156x^14 + 3282x^12 - 5426x^10 + 5186x^8 - 2774x^6 + 769x^4 - 94x^2 + 4	\( 2^{38}\cdot 83^{4}\cdot 983^{4} \)	20T568	Trivial (GRH)
20.4.12180532532810607890279383957504.1	x^20 + 16x^18 + 86x^16 + 162x^14 - 54x^12 - 506x^10 - 521x^8 - 126x^6 + 65x^4 + 34x^2 + 4	\( 2^{38}\cdot 83^{4}\cdot 983^{4} \)	20T568	$[5]$ (GRH)
20.12.12180532532810607890279383957504.2	x^20 - 2x^18 - 53x^16 + 148x^14 + 445x^12 - 1678x^10 + 905x^8 + 830x^6 - 279x^4 - 52x^2 + 4	\( 2^{38}\cdot 83^{4}\cdot 983^{4} \)	20T568	Trivial (GRH)
20.4.12180532532810607890279383957504.2	x^20 + 20x^18 + 120x^16 + 248x^14 + 48x^12 - 404x^10 - 435x^8 - 104x^6 + 53x^4 + 30x^2 + 4	\( 2^{38}\cdot 83^{4}\cdot 983^{4} \)	20T568	Trivial (GRH)
20.20.11373139009496303026630652133746934582083584.1	x^20 - 402x^18 + 60719x^16 - 4459274x^14 + 177613248x^12 - 4031618042x^10 + 53145939552x^8 - 409200511192x^6 + 1794975547533x^4 - 4105303940014x^2 + 3734857726084	\( 2^{38}\cdot 83^{4}\cdot 983^{8} \)	20T568	Trivial (GRH)