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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.16.3051757812500000000000000000000.2	x^20 - 10x^18 - 5x^16 + 225x^14 - 700x^12 + 885x^10 - 425x^8 - 75x^6 + 150x^4 - 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.4.3051757812500000000000000000000.2	x^20 + 15x^18 + 70x^16 + 75x^14 - 250x^12 - 615x^10 - 125x^8 + 725x^6 + 675x^4 + 175x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.3	x^20 - 5x^18 - 5x^16 + 50x^14 - 25x^12 - 120x^10 + 100x^8 + 75x^6 - 75x^4 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.16.3051757812500000000000000000000.3	x^20 - 15x^18 + 70x^16 - 75x^14 - 250x^12 + 615x^10 - 125x^8 - 725x^6 + 675x^4 - 175x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.4.3051757812500000000000000000000.3	x^20 + 10x^18 - 5x^16 - 225x^14 - 700x^12 - 885x^10 - 425x^8 + 75x^6 + 150x^4 + 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.3	x^20 - 5x^18 - 30x^16 + 100x^14 + 250x^12 - 245x^10 - 875x^8 - 650x^6 - 125x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.4	x^20 - 5x^18 - 30x^16 + 75x^14 + 200x^12 - 245x^10 - 400x^8 + 250x^6 + 175x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.16.3051757812500000000000000000000.4	x^20 - 10x^18 + 20x^16 + 75x^14 - 325x^12 + 385x^10 - 50x^8 - 225x^6 + 175x^4 - 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.4.3051757812500000000000000000000.4	x^20 + 15x^18 + 70x^16 + 100x^14 - 100x^12 - 365x^10 - 225x^8 + 100x^6 + 150x^4 + 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.4	x^20 - 10x^18 - 5x^16 + 200x^14 - 100x^12 - 490x^10 - 175x^8 + 200x^6 + 175x^4 + 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.5	x^20 + 10x^18 - 5x^16 - 200x^14 - 100x^12 + 490x^10 - 175x^8 - 200x^6 + 175x^4 - 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.16.3051757812500000000000000000000.5	x^20 - 15x^18 + 70x^16 - 100x^14 - 100x^12 + 365x^10 - 225x^8 - 100x^6 + 150x^4 - 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.4.3051757812500000000000000000000.5	x^20 + 10x^18 + 20x^16 - 75x^14 - 325x^12 - 385x^10 - 50x^8 + 225x^6 + 175x^4 + 50x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.5	x^20 + 5x^18 - 30x^16 - 100x^14 + 75x^12 + 370x^10 + 125x^8 - 225x^6 - 100x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.6	x^20 + 5x^18 - 55x^16 + 75x^14 + 225x^12 - 630x^10 + 375x^8 + 175x^6 - 200x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.6	x^20 + 5x^18 - 30x^16 - 125x^14 + 325x^12 + 870x^10 - 1000x^8 - 1850x^6 - 600x^4 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.7	x^20 - 55x^16 + 175x^14 + 50x^12 - 650x^10 + 350x^8 + 525x^6 - 425x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.7	x^20 + 5x^18 - 5x^16 - 50x^14 - 25x^12 + 120x^10 + 100x^8 - 75x^6 - 75x^4 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.8	x^20 - 10x^18 + 20x^16 + 75x^14 - 275x^12 + 60x^10 + 450x^8 - 200x^6 - 175x^4 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.8	x^20 - 55x^16 - 175x^14 + 50x^12 + 650x^10 + 350x^8 - 525x^6 - 425x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.9	x^20 + 5x^18 - 30x^16 - 125x^14 + 250x^12 + 495x^10 - 650x^8 - 250x^6 + 325x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.9	x^20 - 25x^16 + 200x^12 + 50x^10 - 625x^8 - 375x^6 + 625x^4 + 625x^2 + 125	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.10	x^20 - 5x^18 - 30x^16 + 100x^14 + 75x^12 - 370x^10 + 125x^8 + 225x^6 - 100x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.10	x^20 - 30x^16 - 25x^14 + 275x^12 + 400x^10 - 625x^8 - 1250x^6 - 325x^4 + 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.11	x^20 - 10x^18 + 20x^16 + 75x^14 - 275x^12 + 10x^10 + 700x^8 - 575x^6 - 150x^4 + 200x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.11	x^20 - 5x^18 - 55x^16 - 75x^14 + 225x^12 + 630x^10 + 375x^8 - 175x^6 - 200x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.12	x^20 - 10x^18 + 20x^16 + 75x^14 - 250x^12 - 115x^10 + 700x^8 + 25x^6 - 475x^4 - 125x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.12	x^20 + 10x^18 + 20x^16 - 50x^14 - 175x^12 - 10x^10 + 325x^8 + 200x^6 - 50x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.13	x^20 + 5x^18 - 30x^16 - 100x^14 + 250x^12 + 245x^10 - 875x^8 + 650x^6 - 125x^4 - 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.13	x^20 + 5x^18 - 30x^16 - 75x^14 + 200x^12 + 245x^10 - 400x^8 - 250x^6 + 175x^4 + 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.14	x^20 - 30x^16 + 25x^14 + 275x^12 - 400x^10 - 625x^8 + 1250x^6 - 325x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.14	x^20 + 10x^18 + 20x^16 - 50x^14 - 125x^12 + 115x^10 + 200x^8 - 150x^6 - 50x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.15	x^20 + 5x^18 - 30x^16 - 100x^14 + 125x^12 + 245x^10 - 275x^8 - 125x^6 + 225x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.15	x^20 - 5x^18 - 30x^16 + 100x^14 + 125x^12 - 245x^10 - 275x^8 + 125x^6 + 225x^4 + 75x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.3051757812500000000000000000000.16	x^20 - 10x^18 + 20x^16 + 50x^14 - 175x^12 + 10x^10 + 325x^8 - 200x^6 - 50x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.8.3051757812500000000000000000000.16	x^20 + 10x^18 + 20x^16 - 75x^14 - 275x^12 - 60x^10 + 450x^8 + 200x^6 - 175x^4 + 5	\( 2^{20}\cdot 5^{35} \)	20T344	Trivial (GRH)
20.12.1470391355634309152000000000000000.1	x^20 - 5x^18 - 110x^16 + 800x^14 + 975x^12 - 18000x^10 + 31875x^8 + 38125x^6 - 123750x^4 + 59375x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	20T344	Trivial (GRH)
20.8.1470391355634309152000000000000000.1	x^20 + 5x^18 - 110x^16 - 800x^14 + 975x^12 + 18000x^10 + 31875x^8 - 38125x^6 - 123750x^4 - 59375x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	20T344	Trivial (GRH)
20.12.1470391355634309152000000000000000.2	x^20 - 15x^18 - 110x^16 + 2625x^14 - 10950x^12 + 1250x^10 + 53000x^8 - 41875x^6 - 55000x^4 + 31250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	20T344	Trivial (GRH)
20.8.1470391355634309152000000000000000.2	x^20 + 15x^18 - 110x^16 - 2625x^14 - 10950x^12 - 1250x^10 + 53000x^8 + 41875x^6 - 55000x^4 - 31250x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	20T344	Trivial (GRH)
20.0.3155164409182739257812500000000000000000000.2	x^20 + 310x^18 + 39870x^16 + 2798650x^14 + 118780475x^12 + 3179289615x^10 + 54008113350x^8 + 566304002475x^6 + 3383696380375x^4 + 9384437729375x^2 + 5169421368005	\( 2^{20}\cdot 5^{35}\cdot 251^{2}\cdot 4051^{2} \)	20T344	$[2, 2, 2, 2, 2488294]$ (GRH)
20.0.3155164409182739257812500000000000000000000.3	x^20 + 220x^18 + 21170x^16 + 1171050x^14 + 41145925x^12 + 956975255x^10 + 14871874050x^8 + 151833201625x^6 + 968854356725x^4 + 3458572341425x^2 + 5169421368005	\( 2^{20}\cdot 5^{35}\cdot 251^{2}\cdot 4051^{2} \)	20T344	$[2, 2, 2, 2, 2584302]$ (GRH)
20.20.247056608274284803549371247668512000000000000000.2	x^20 - 1025x^18 + 444245x^16 - 106256150x^14 + 15353076700x^12 - 1378772819750x^10 + 76277301787625x^8 - 2487800964728750x^6 + 43566322711008125x^4 - 334901325114803125x^2 + 525065587402128125	\( 2^{20}\cdot 5^{15}\cdot 11^{16}\cdot 331^{2}\cdot 39161^{2} \)	20T344	Trivial (GRH)
20.20.247056608274284803549371247668512000000000000000.3	x^20 - 1120x^18 + 521290x^16 - 130885375x^14 + 19269155025x^12 - 1694385726125x^10 + 86930584311625x^8 - 2450150378240625x^6 + 34983624030843125x^4 - 229894048766759375x^2 + 525065587402128125	\( 2^{20}\cdot 5^{15}\cdot 11^{16}\cdot 331^{2}\cdot 39161^{2} \)	20T344	Trivial (GRH)