Global number field search results

Further refine search

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
20.4.48902390003204345703125.1	x^20 - 2x^15 - 10x^10 + 11x^5 - 1	\( 5^{22}\cdot 29^{5} \)	$D_5^2:C_4$ (as 20T94)	Trivial
20.4.2392888293548614501953125.1	x^20 - 8x^18 - 4x^17 + 24x^16 + 10x^15 - 26x^14 + x^13 - x^12 + 112x^10 - 2x^9 - 330x^8 - 213x^7 + 168x^6 + 215x^5 + 81x^4 + 28x^3 + 14x^2 + 1	\( 5^{15}\cdot 601^{5} \)	$D_5^2:C_4$ (as 20T94)	Trivial
20.2.149990431964397430419921875.1	x^20 - 3x^15 + 3x^10 - 3x^5 + 1	\( -\,5^{30}\cdot 11^{5} \)	$D_5^2:C_4$ (as 20T94)	Trivial (GRH)
20.2.976562500000000000000000000.1	x^20 - 2x^15 - 2x^10 - 2x^5 + 1	\( -\,2^{20}\cdot 5^{30} \)	$D_5^2:C_4$ (as 20T94)	Trivial (GRH)
20.0.6918932897792000000000000000.1	x^20 - 4x^19 + 4x^18 - 12x^17 + 51x^16 - 48x^15 + 252x^14 - 1060x^13 + 2100x^12 - 2584x^11 + 3116x^10 + 612x^9 - 10644x^8 + 13508x^7 + 2512x^6 - 15200x^5 + 7107x^4 + 5688x^3 - 4584x^2 - 580x + 841	\( 2^{28}\cdot 5^{15}\cdot 61^{5} \)	$D_5^2:C_4$ (as 20T94)	$[2, 4]$ (GRH)
20.0.51277872500000000000000000000.1	x^20 + 10x^16 - 20x^14 + 65x^12 - 86x^10 + 260x^8 - 230x^6 + 340x^4 + 220x^2 + 29	\( 2^{20}\cdot 5^{22}\cdot 29^{5} \)	$D_5^2:C_4$ (as 20T94)	$[2]$
20.10.250000000000000000000000000000.1	x^20 - 20x^18 + 170x^16 - 2x^15 - 800x^14 + 30x^13 + 2275x^12 - 180x^11 - 4002x^10 + 550x^9 + 4270x^8 - 900x^7 - 2570x^6 + 758x^5 + 725x^4 - 290x^3 - 50x^2 + 40x - 4	\( -\,2^{28}\cdot 5^{30} \)	$D_5^2:C_4$ (as 20T94)	Trivial (GRH)
20.10.2196009914390742778778076171875.1	x^20 - 15x^18 + 90x^16 - 8x^15 - 375x^14 + 35x^13 + 1075x^12 - 245x^11 - 1880x^10 + 750x^9 + 2195x^8 - 1150x^7 - 1705x^6 + 994x^5 + 475x^4 - 250x^3 + 5x - 1	\( -\,5^{30}\cdot 11^{9} \)	$D_5^2:C_4$ (as 20T94)	Trivial (GRH)
20.0.1004734915970976698000000000000000.1	x^20 - 2x^19 + 27x^18 - 50x^17 + 249x^16 - 570x^15 + 1254x^14 - 3934x^13 + 6887x^12 - 13648x^11 + 30841x^10 - 44850x^9 + 78071x^8 - 119082x^7 + 145974x^6 - 178652x^5 + 172159x^4 - 56358x^3 + 212471x^2 + 51356x + 99301	\( 2^{16}\cdot 5^{15}\cdot 3469^{5} \)	$D_5^2:C_4$ (as 20T94)	$[2, 4, 36]$ (GRH)
20.0.1069756574259831337445098876953125.1	x^20 + 22x^18 - 8x^17 + 207x^16 - 159x^15 + 1229x^14 - 1352x^13 + 5527x^12 - 6687x^11 + 19563x^10 - 26099x^9 + 61052x^8 - 84787x^7 + 142519x^6 - 138535x^5 + 133978x^4 - 34522x^3 - 24228x^2 + 24879x + 22171	\( 5^{15}\cdot 19^{5}\cdot 1699^{5} \)	$D_5^2:C_4$ (as 20T94)	$[6, 60]$ (GRH)
20.20.4115394215817120555008000000000000000.1	x^20 - 4x^19 - 70x^18 + 258x^17 + 1914x^16 - 6574x^15 - 25582x^14 + 84064x^13 + 169380x^12 - 566144x^11 - 486202x^10 + 1945052x^9 + 353024x^8 - 3209444x^7 + 582960x^6 + 2274052x^5 - 798688x^4 - 469792x^3 + 133648x^2 + 16872x - 124	\( 2^{28}\cdot 5^{15}\cdot 3469^{5} \)	$D_5^2:C_4$ (as 20T94)	$[2]$ (GRH)
20.20.28964050250000000000000000000000000000.1	x^20 - 40x^18 + 680x^16 - 2x^15 - 6400x^14 + 60x^13 + 36400x^12 - 720x^11 - 128126x^10 + 4400x^9 + 274520x^8 - 14400x^7 - 337640x^6 + 24252x^5 + 210400x^4 - 18520x^3 - 50400x^2 + 5040x - 124	\( 2^{28}\cdot 5^{30}\cdot 41^{5} \)	$D_5^2:C_4$ (as 20T94)	Trivial (GRH)