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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.33090677680473274083073.1	x^20 - x^19 - 5x^18 + 12x^16 + 8x^15 - 2x^14 - 21x^13 - 17x^12 + 13x^11 + x^10 + 20x^9 - 23x^8 + 34x^7 - 17x^6 - 10x^5 + 20x^4 - 20x^3 + 11x^2 - 4x + 1	\( 97^{3}\cdot 13799^{4} \)	20T791	Trivial
20.4.197550394506345032237009.1	x^20 - 2x^18 - 5x^17 + x^16 + 12x^15 - 4x^14 - 27x^13 + 19x^11 + 6x^10 + 18x^9 + 20x^8 - 7x^7 - 29x^6 - 27x^5 - 4x^4 + 12x^3 + 11x^2 + 5x + 1	\( 1609^{4}\cdot 3089^{3} \)	20T791	Trivial (GRH)
20.8.1734361690558178085830656.1	x^20 - 4x^19 - 2x^18 + 30x^17 - 29x^16 - 88x^15 + 222x^14 - 70x^13 - 398x^12 + 668x^11 - 300x^10 - 382x^9 + 684x^8 - 460x^7 + 166x^6 - 78x^5 + 29x^4 + 44x^3 - 30x^2 - 8x + 1	\( 2^{20}\cdot 31^{4}\cdot 53^{4}\cdot 61^{3} \)	20T791	Trivial (GRH)
20.0.2160851692712640782593529.1	x^20 - 2x^19 + 7x^18 - 10x^17 + 5x^16 + 6x^15 - 16x^14 + 61x^13 - 62x^12 + 49x^11 - 47x^10 + 134x^9 + 23x^8 - 443x^7 + 632x^6 - 310x^5 + 390x^4 - 53x^3 + 67x^2 - 2x + 1	\( 7^{6}\cdot 41^{5}\cdot 631^{4} \)	20T791	Trivial (GRH)
20.0.2160851692712640782593529.2	x^20 - 4x^19 + 18x^18 - 48x^17 + 123x^16 - 238x^15 + 429x^14 - 662x^13 + 971x^12 - 1292x^11 + 1604x^10 - 1758x^9 + 1890x^8 - 1704x^7 + 1704x^6 - 1134x^5 + 1020x^4 - 468x^3 + 436x^2 - 54x + 103	\( 7^{6}\cdot 41^{5}\cdot 631^{4} \)	20T791	Trivial (GRH)
20.8.13928692418928729728745472.1	x^20 - 5x^19 + 9x^18 - 5x^17 - 23x^16 + 102x^15 - 254x^14 + 440x^13 - 517x^12 + 307x^11 + 313x^10 - 1221x^9 + 1967x^8 - 2052x^7 + 1492x^6 - 824x^5 + 399x^4 - 179x^3 + 63x^2 - 13x + 1	\( 2^{24}\cdot 13^{3}\cdot 4409^{4} \)	20T791	Trivial (GRH)
20.4.31488450440572657262410929.1	x^20 - x^19 - 6x^18 + 3x^17 + 13x^16 - 6x^15 + 5x^14 + 62x^13 - 94x^12 - 251x^11 + 177x^10 + 284x^9 + 36x^8 + 324x^7 - 280x^6 - 987x^5 - 169x^4 + 640x^3 + 466x^2 + 124x + 11	\( 3^{6}\cdot 17^{4}\cdot 97^{4}\cdot 1801^{3} \)	20T791	Trivial (GRH)
20.4.222859078702859675659927552.1	x^20 + x^18 - 42x^16 - 121x^14 - 60x^12 + 127x^10 + 240x^8 + 259x^6 + 178x^4 + 65x^2 + 13	\( 2^{28}\cdot 13^{3}\cdot 4409^{4} \)	20T791	Trivial (GRH)
20.0.1000279093533991156053497085952.1	x^20 + 2x^18 - 13x^16 + 12x^14 + 237x^12 + 438x^10 + 512x^8 + 806x^6 + 689x^4 + 182x^2 + 13	\( 2^{40}\cdot 13^{7}\cdot 347^{4} \)	20T791	Trivial (GRH)
20.12.1000279093533991156053497085952.1	x^20 - 2x^18 - 13x^16 - 12x^14 + 237x^12 - 438x^10 + 512x^8 - 806x^6 + 689x^4 - 182x^2 + 13	\( 2^{40}\cdot 13^{7}\cdot 347^{4} \)	20T791	Trivial (GRH)
20.0.5366967411805924279952897736704.1	x^20 + 23x^18 + 234x^16 + 1390x^14 + 5344x^12 + 13889x^10 + 24687x^8 + 29606x^6 + 22919x^4 + 10345x^2 + 2069	\( 2^{20}\cdot 2069^{3}\cdot 4903^{4} \)	20T791	$[5]$ (GRH)
20.12.5366967411805924279952897736704.1	x^20 - 23x^18 + 234x^16 - 1390x^14 + 5344x^12 - 13889x^10 + 24687x^8 - 29606x^6 + 22919x^4 - 10345x^2 + 2069	\( 2^{20}\cdot 2069^{3}\cdot 4903^{4} \)	20T791	Trivial (GRH)
20.20.12165018069685667093786785275365009.1	x^20 - x^19 - 48x^18 + 35x^17 + 774x^16 - 403x^15 - 5434x^14 + 1971x^13 + 17945x^12 - 4390x^11 - 27500x^10 + 4390x^9 + 17945x^8 - 1971x^7 - 5434x^6 + 403x^5 + 774x^4 - 35x^3 - 48x^2 + x + 1	\( 13^{2}\cdot 34361^{3}\cdot 36497^{4} \)	20T791	Trivial (GRH)
20.20.13759442815773208688023459670194289.1	x^20 - 8x^19 - 15x^18 + 303x^17 - 555x^16 - 3208x^15 + 13518x^14 - 598x^13 - 87741x^12 + 161427x^11 + 72963x^10 - 616042x^9 + 772164x^8 + 5776x^7 - 1098720x^6 + 1470208x^5 - 1028544x^4 + 436608x^3 - 112896x^2 + 16384x - 1024	\( 13^{2}\cdot 35801^{3}\cdot 36497^{4} \)	20T791	Trivial (GRH)
20.16.46448101386381742412977375753011200.1	x^20 - 8x^18 - 83x^16 + 866x^14 - 10x^12 - 19938x^10 + 67851x^8 - 80860x^6 + 36857x^4 - 6800x^2 + 425	\( 2^{40}\cdot 5^{2}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T791	Trivial (GRH)
20.4.46448101386381742412977375753011200.1	x^20 + 8x^18 - 83x^16 - 866x^14 - 10x^12 + 19938x^10 + 67851x^8 + 80860x^6 + 36857x^4 + 6800x^2 + 425	\( 2^{40}\cdot 5^{2}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T791	$[2, 2]$ (GRH)
20.0.92823398950633472182737117276798976.1	x^20 + 31x^18 + 398x^16 + 2833x^14 + 12506x^12 + 36026x^10 + 68956x^8 + 86978x^6 + 69452x^4 + 31805x^2 + 6361	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 6361^{3} \)	20T791	$[38, 76]$ (GRH)
20.12.92823398950633472182737117276798976.1	x^20 - 3x^18 - 56x^16 + 177x^14 + 947x^12 - 3121x^10 - 5245x^8 + 18745x^6 + 2076x^4 - 19083x^2 + 6361	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 6361^{3} \)	20T791	Trivial (GRH)
20.8.92823398950633472182737117276798976.1	x^20 + 3x^18 - 56x^16 - 177x^14 + 947x^12 + 3121x^10 - 5245x^8 - 18745x^6 + 2076x^4 + 19083x^2 + 6361	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 6361^{3} \)	20T791	Trivial (GRH)
20.0.93878033821762240604784858628096000.1	x^20 + 30x^18 + 383x^16 + 2742x^14 + 12217x^12 + 35517x^10 + 68497x^8 + 86874x^6 + 69606x^4 + 31925x^2 + 6385	\( 2^{20}\cdot 5^{3}\cdot 61^{4}\cdot 397^{4}\cdot 1277^{3} \)	20T791	$[2, 10, 170]$ (GRH)
20.12.93878033821762240604784858628096000.1	x^20 - 2x^18 - 66x^16 + 174x^14 + 1245x^12 - 3969x^10 - 6195x^8 + 26542x^6 - 10254x^4 - 12770x^2 + 6385	\( 2^{20}\cdot 5^{3}\cdot 61^{4}\cdot 397^{4}\cdot 1277^{3} \)	20T791	Trivial (GRH)
20.8.93878033821762240604784858628096000.1	x^20 + 2x^18 - 66x^16 - 174x^14 + 1245x^12 + 3969x^10 - 6195x^8 - 26542x^6 - 10254x^4 + 12770x^2 + 6385	\( 2^{20}\cdot 5^{3}\cdot 61^{4}\cdot 397^{4}\cdot 1277^{3} \)	20T791	$[2]$ (GRH)
20.16.2318086769644146560696307751895171072.1	x^20 + 8x^18 - 218x^16 + 28x^14 + 16025x^12 - 112839x^10 + 349689x^8 - 548948x^6 + 423866x^4 - 148744x^2 + 18593	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 18593^{3} \)	20T791	Trivial (GRH)
20.4.2318086769644146560696307751895171072.1	x^20 - 8x^18 - 218x^16 - 28x^14 + 16025x^12 + 112839x^10 + 349689x^8 + 548948x^6 + 423866x^4 + 148744x^2 + 18593	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 18593^{3} \)	20T791	$[2, 4]$ (GRH)