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
20.12.3051757812500000000000000000000.1	x^20 - 30x^16 + 50x^14 + 100x^12 - 275x^10 + 125x^8 + 100x^6 - 75x^4 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.16.3051757812500000000000000000000.1	x^20 - 5x^18 - 55x^16 + 500x^14 - 1425x^12 + 1630x^10 - 500x^8 - 400x^6 + 325x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.4.3051757812500000000000000000000.1	x^20 + 5x^18 - 55x^16 - 500x^14 - 1425x^12 - 1630x^10 - 500x^8 + 400x^6 + 325x^4 + 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.8.3051757812500000000000000000000.1	x^20 - 30x^16 - 50x^14 + 100x^12 + 275x^10 + 125x^8 - 100x^6 - 75x^4 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.12.3051757812500000000000000000000.2	x^20 + 5x^18 - 30x^16 - 100x^14 + 375x^12 + 370x^10 - 1625x^8 + 1025x^6 - 150x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.8.3051757812500000000000000000000.2	x^20 - 5x^18 - 30x^16 + 100x^14 + 375x^12 - 370x^10 - 1625x^8 - 1025x^6 - 150x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.16.1470391355634309152000000000000000.1	x^20 - 10x^18 - 55x^16 + 900x^14 - 2550x^12 - 4000x^10 + 32500x^8 - 63125x^6 + 55000x^4 - 21875x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.4.1470391355634309152000000000000000.1	x^20 + 10x^18 - 55x^16 - 900x^14 - 2550x^12 + 4000x^10 + 32500x^8 + 63125x^6 + 55000x^4 + 21875x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	$C_4\times C_2^4:C_5$ (as 20T75)	Trivial (GRH)
20.0.3155164409182739257812500000000000000000000.1	x^20 + 320x^18 + 42620x^16 + 3089950x^14 + 133406025x^12 + 3518361755x^10 + 55944354250x^8 + 513229518325x^6 + 2534690146825x^4 + 5948819670525x^2 + 5169421368005	\( 2^{20}\cdot 5^{35}\cdot 251^{2}\cdot 4051^{2} \)	$C_4\times C_2^4:C_5$ (as 20T75)	$[2, 2, 2, 12, 399660]$ (GRH)
20.0.3575414809573364257812500000000000000000000.1	x^20 + 370x^18 + 55620x^16 + 4488850x^14 + 214685475x^12 + 6306436255x^10 + 113790309300x^8 + 1220914673775x^6 + 7148125674525x^4 + 18168127845025x^2 + 5857959624005	\( 2^{20}\cdot 5^{35}\cdot 601^{2}\cdot 1801^{2} \)	$C_4\times C_2^4:C_5$ (as 20T75)	$[2, 2, 2, 160, 32320]$ (GRH)
20.20.247056608274284803549371247668512000000000000000.1	x^20 - 925x^18 + 345290x^16 - 69250575x^14 + 8294073900x^12 - 620327617375x^10 + 29331554339500x^8 - 864153686645000x^6 + 15118770876116875x^4 - 140883697770453125x^2 + 525065587402128125	\( 2^{20}\cdot 5^{15}\cdot 11^{16}\cdot 331^{2}\cdot 39161^{2} \)	$C_4\times C_2^4:C_5$ (as 20T75)	$[2]$ (GRH)
20.20.17505265916412191723617107336923861792000000000000000.1	x^20 - 2585x^18 + 2796035x^16 - 1660412600x^14 + 598407347450x^12 - 136595530105375x^10 + 19966245005965500x^8 - 1840082858463815625x^6 + 101865903320796257500x^4 - 3042306203259125790625x^2 + 37203670831694647878125	\( 2^{20}\cdot 5^{15}\cdot 11^{18}\cdot 661^{2}\cdot 474541^{2} \)	$C_4\times C_2^4:C_5$ (as 20T75)	$[2]$ (GRH)