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 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.502656297790633035773771776.1	x^20 - 8x^16 + 32x^12 - 64x^8 + 84x^4 + 16	\( 2^{56}\cdot 17^{8} \)	20T685	Trivial (GRH)
20.0.502656297790633035773771776.2	x^20 + 8x^16 + 24x^12 + 32x^8 + 20x^4 + 16	\( 2^{56}\cdot 17^{8} \)	20T685	Trivial (GRH)
20.0.13159743603708897876219265024.1	x^20 + 10x^18 + 37x^16 + 56x^14 + 12x^12 - 40x^10 + 32x^6 + 4x^4 + 8x^2 + 4	\( 2^{50}\cdot 43^{8} \)	20T685	Trivial (GRH)
20.0.33358391371048988384259823632384.1	x^20 + 10x^18 + 41x^16 + 88x^14 + 105x^12 + 70x^10 + 26x^8 - 7x^4 + 2x^2 + 1	\( 2^{40}\cdot 3^{18}\cdot 23^{8} \)	20T685	$[2]$ (GRH)
20.4.97419780315043664183472890576896.1	x^20 + 4x^16 - 9x^12 - 48x^8 - 32x^4 + 16	\( 2^{28}\cdot 881^{8} \)	20T685	Trivial (GRH)
20.4.389679121260174656733891562307584.1	x^20 + 4x^16 - 13x^12 - 61x^8 - 40x^4 + 1	\( 2^{30}\cdot 881^{8} \)	20T685	Trivial (GRH)
20.8.6234865940162794507742264996921344.1	x^20 - 89x^16 + 2219x^12 - 13583x^8 - 680x^4 + 104976	\( 2^{34}\cdot 881^{8} \)	20T685	Trivial (GRH)
20.8.6234865940162794507742264996921344.2	x^20 + 12x^16 - 320x^12 + 1744x^8 - 2880x^4 + 256	\( 2^{34}\cdot 881^{8} \)	20T685	Trivial (GRH)
20.4.335020786449938452658321179902214144.1	x^20 - 10x^18 + 41x^16 - 200x^14 + 3154x^12 - 25652x^10 + 87746x^8 - 98856x^6 - 12487x^4 - 19770x^2 + 7921	\( 2^{50}\cdot 29^{14} \)	20T685	$[2]$ (GRH)
20.4.335020786449938452658321179902214144.2	x^20 - 17x^18 + 68x^16 - 196x^14 + 48x^12 - 576x^8 - 896x^6 + 5332x^4 - 12436x^2 + 64	\( 2^{50}\cdot 29^{14} \)	20T685	$[2]$ (GRH)
20.0.1136304317594669299036027795688914944.1	x^20 + 60x^16 + 1264x^12 + 11264x^8 + 39936x^4 + 36864	\( 2^{32}\cdot 3^{6}\cdot 881^{8} \)	20T685	$[2]$ (GRH)
20.0.1136304317594669299036027795688914944.2	x^20 - 6x^18 - 16x^16 - 362x^14 + 581x^12 + 14130x^10 + 40115x^8 + 22002x^6 + 302910x^4 + 65196x^2 + 19881	\( 2^{32}\cdot 3^{6}\cdot 881^{8} \)	20T685	$[2]$ (GRH)
20.8.104998320447888184347713805079613092096.1	x^20 - 5x^19 - 20x^18 + 121x^17 - 496x^16 + 575x^15 + 4920x^14 + 1993x^13 + 8582x^12 + 70505x^11 + 16138x^10 - 913337x^9 - 1607591x^8 - 452270x^7 + 5400288x^6 + 14324844x^5 + 10554156x^4 - 14248548x^3 - 34304492x^2 - 23378904x - 5242576	\( 2^{8}\cdot 11^{10}\cdot 29^{6}\cdot 113^{8} \)	20T685	Trivial (GRH)
20.8.104998320447888184347713805079613092096.2	x^20 - 2x^19 - 29x^18 - 37x^17 + 223x^16 + 2033x^15 + 183x^14 - 11230x^13 + 18547x^12 - 86592x^11 - 332923x^10 + 372539x^9 - 591011x^8 - 1209547x^7 + 5897933x^6 + 690636x^5 + 994948x^4 + 16017428x^3 - 4643676x^2 - 34530300x - 31131268	\( 2^{8}\cdot 11^{10}\cdot 29^{6}\cdot 113^{8} \)	20T685	Trivial (GRH)
20.12.8164704108216363029154042909041980029184.1	x^20 - 8x^19 + 6x^18 + 248x^17 - 965x^16 - 2342x^15 + 5142x^14 + 15514x^13 + 69492x^12 + 8758x^11 - 572575x^10 - 388182x^9 + 1437004x^8 + 385692x^7 - 2938609x^6 + 1134628x^5 + 5654272x^4 - 1544872x^3 - 5110428x^2 + 468272x + 1494004	\( 2^{8}\cdot 11^{8}\cdot 29^{6}\cdot 97^{2}\cdot 113^{8} \)	20T685	$[2, 2]$ (GRH)
20.16.987929197094179926527639191994079583531264.1	x^20 - 7x^19 - 100x^18 + 589x^17 + 3668x^16 - 14811x^15 - 54634x^14 + 70129x^13 + 58825x^12 + 1529886x^11 + 6128738x^10 - 7613976x^9 - 25178445x^8 - 133065235x^7 - 464904726x^6 + 803384665x^5 + 3619285090x^4 + 396586263x^3 - 6317835878x^2 - 5216416927x - 1117748779	\( 2^{8}\cdot 11^{10}\cdot 29^{6}\cdot 97^{2}\cdot 113^{8} \)	20T685	Trivial (GRH)
20.4.162227550009689191338250866824451128329832704.1	x^20 - x^19 + 124x^18 - 173x^17 + 4721x^16 - 10397x^15 + 58765x^14 - 215931x^13 - 889345x^12 + 364678x^11 - 45537012x^10 + 71053240x^9 - 748475745x^8 + 1311602064x^7 - 4298401557x^6 + 10516055144x^5 - 3531065208x^4 - 16676950480x^3 + 26431197108x^2 - 22891892208x + 11449628084	\( 2^{8}\cdot 11^{12}\cdot 29^{6}\cdot 113^{10} \)	20T685	$[2, 2, 8]$ (GRH)
20.12.761936733720316773653074450825066341622349824.1	x^20 - 7x^19 - 92x^18 + 435x^17 + 1741x^16 + 18900x^15 - 67527x^14 - 979307x^13 + 5008645x^12 - 31077848x^11 + 76184585x^10 + 919008309x^9 - 5672893696x^8 + 10488672339x^7 + 5107389961x^6 - 68290842738x^5 + 151048249292x^4 - 72847922392x^3 - 253823856008x^2 + 421030711344x - 189844967504	\( 2^{20}\cdot 11^{8}\cdot 29^{6}\cdot 113^{8}\cdot 463^{2} \)	20T685	$[2, 2]$ (GRH)
20.0.893602148088241764671254530709325445044692320256.1	x^20 + 410x^18 + 67655x^16 + 5818824x^14 + 283412583x^12 + 7971501014x^10 + 126881028663x^8 + 1063562823422x^6 + 3887283749351x^4 + 3093889227992x^2 + 694607231761	\( 2^{28}\cdot 11^{8}\cdot 29^{6}\cdot 113^{8}\cdot 991^{2} \)	20T685	$[2, 2, 2, 2, 2, 21662660]$ (GRH)