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
20.0.7222093946953199903123949223936.1	x^20 - 4x^19 + 8x^18 - 12x^17 + 16x^16 - 36x^15 + 52x^14 + 16x^13 - 64x^12 - 56x^11 + 200x^10 + 192x^9 + 136x^8 + 208x^7 + 64x^6 - 96x^5 + 64x^4 + 192x^3 + 64x^2 + 32	\( 2^{30}\cdot 7^{10}\cdot 47^{8} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.0.32056524103267394907090712890625.1	x^20 - 2x^19 + 2x^18 + 2x^17 - 6x^16 + 4x^15 + 39x^14 - 126x^13 + 137x^12 + 47x^11 - 321x^10 + 359x^9 + 246x^8 - 1174x^7 + 2192x^6 - 1341x^5 - 8x^4 + 2400x^3 - 576x^2 + 1024	\( 5^{10}\cdot 13^{10}\cdot 47^{8} \)	$D_5\times A_4$ (as 20T37)	$[2]$ (GRH)
20.4.315252767308030713643991421826778089.1	x^20 - 2x^19 + 2x^18 + 4x^17 - 10x^16 + 104x^15 + 675x^14 + 770x^13 + 1759x^12 - 195x^11 - 4565x^10 + 3085x^9 + 10111x^8 + 16588x^7 + 38727x^6 + 13729x^5 - 45405x^4 - 23166x^3 - 94770x^2 + 59049	\( 47^{8}\cdot 163^{10} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.4.1002983435921998221381095607508396689.1	x^20 - 3x^17 - 63x^15 + 1011x^14 - 1728x^13 + 5107x^12 - 4020x^11 - 11221x^10 + 11955x^9 - 5805x^8 + 840x^7 + 1068x^6 - 1584x^5 - 803x^4 - 180x^3 - 23x^2 + 1	\( 3^{10}\cdot 47^{8}\cdot 61^{10} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.0.202784731012754939641986471226953957376.1	x^20 - 6x^19 - 2x^18 + 64x^17 - 14x^16 - 436x^15 + 478x^14 + 806x^13 - 353x^12 - 3450x^11 + 4838x^10 - 4132x^9 + 8903x^8 - 13704x^7 + 21364x^6 - 16984x^5 + 18589x^4 - 20038x^3 + 35838x^2 - 13398x + 17123	\( 2^{30}\cdot 7^{10}\cdot 401^{8} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.0.1791006002586548906938780335646468734976.1	x^20 - 6x^19 - 10x^18 + 104x^17 + 34x^16 - 876x^15 + 466x^14 + 2726x^13 - 57x^12 - 8874x^11 + 5254x^10 + 820x^9 + 9099x^8 - 7864x^7 + 23172x^6 - 27568x^5 + 44861x^4 - 60510x^3 + 126562x^2 - 54390x + 58471	\( 2^{30}\cdot 7^{14}\cdot 199^{8} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.20.8851788427171493976819614872351019223900649.1	x^20 - x^19 - 58x^18 + 41x^17 + 1325x^16 - 653x^15 - 15442x^14 + 5251x^13 + 99299x^12 - 23893x^11 - 357547x^10 + 66887x^9 + 703666x^8 - 120039x^7 - 712988x^6 + 132265x^5 + 330432x^4 - 70240x^3 - 51122x^2 + 11872x - 643	\( 163^{10}\cdot 401^{8} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)
20.20.28162154599151343753050158965307922722863249.1	x^20 - 4x^19 - 49x^18 + 183x^17 + 916x^16 - 3140x^15 - 8616x^14 + 26624x^13 + 44550x^12 - 121756x^11 - 129120x^10 + 305362x^9 + 203500x^8 - 406080x^7 - 160387x^6 + 260630x^5 + 54133x^4 - 67485x^3 - 9972x^2 + 5958x + 873	\( 3^{10}\cdot 61^{10}\cdot 401^{8} \)	$D_5\times A_4$ (as 20T37)	Trivial (GRH)