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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.15802861880872333999079424.1	x^20 - 4x^19 + 10x^18 - 16x^17 + 15x^16 + 20x^15 - 62x^14 - 36x^13 + 456x^12 - 1288x^11 + 1928x^10 - 862x^9 - 1680x^8 + 1604x^7 + 4435x^6 - 12624x^5 + 15361x^4 - 11076x^3 + 4962x^2 - 1296x + 153	\( 2^{20}\cdot 3^{10}\cdot 761^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$
20.4.45215251470640684072265625.1	x^20 - 3x^17 - 23x^16 + 46x^15 - 62x^14 + 306x^13 - 395x^12 + 394x^11 - 779x^10 + 893x^9 - 548x^8 + 25x^7 - 264x^6 + 420x^5 - 391x^4 + 51x^3 + 118x^2 - 17x - 11	\( 3^{10}\cdot 5^{10}\cdot 601^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	Trivial (GRH)
20.4.62402607650205857900390625.1	x^20 - 8x^19 + 24x^18 - 36x^17 + 23x^16 + 86x^15 - 278x^14 + 87x^13 + 286x^12 + 72x^11 + 43x^10 - 395x^9 - 349x^8 - 200x^7 + 363x^6 + 534x^5 + 625x^4 + 377x^3 + 171x^2 + 32x + 1	\( 3^{10}\cdot 5^{10}\cdot 641^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	Trivial (GRH)
20.0.185646500000000000000000000.1	x^20 - 2x^19 + x^18 - 14x^17 + 39x^16 - 10x^15 + 52x^14 - 240x^13 + 180x^12 + 8x^11 + 487x^10 - 840x^9 + 62x^8 + 162x^7 + 864x^6 - 792x^5 - 514x^4 + 748x^3 - 12x^2 - 220x + 65	\( 2^{20}\cdot 5^{21}\cdot 13^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	Trivial
20.2.10929603344110461118702419968.1	x^20 - 8x^19 + 34x^18 - 88x^17 + 134x^16 - 16x^15 - 474x^14 + 1376x^13 - 2062x^12 + 1604x^11 + 412x^10 - 2160x^9 + 1615x^8 + 1392x^7 - 3080x^6 + 2060x^5 + 596x^4 - 1504x^3 + 56x^2 + 600x - 199	\( -\,2^{40}\cdot 1583^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	Trivial
20.2.232246326086930752913583984375.1	x^20 - 4x^19 + 20x^18 - 80x^17 + 308x^16 - 1028x^15 + 2823x^14 - 6346x^13 + 11274x^12 - 14162x^11 + 6132x^10 + 27074x^9 - 96544x^8 + 197534x^7 - 299095x^6 + 354922x^5 - 333566x^4 + 243846x^3 - 133473x^2 + 49824x - 10161	\( -\,3^{10}\cdot 5^{10}\cdot 3319^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	Trivial (GRH)
20.0.822190157101803765760000000000.1	x^20 - 4x^18 - 12x^16 + 344x^14 - 1760x^12 + 2528x^10 + 19328x^8 - 15232x^6 - 185856x^4 + 1062400x^2 + 615424	\( 2^{30}\cdot 5^{10}\cdot 601^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[20]$ (GRH)
20.0.1134723530638764277760000000000.1	x^20 + 12x^18 + 12x^16 - 720x^14 - 4464x^12 + 1696x^10 + 100224x^8 + 417024x^6 + 903168x^4 + 1142784x^2 + 656384	\( 2^{30}\cdot 5^{10}\cdot 641^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[16]$ (GRH)
20.10.1215000000000000000000000000000000.1	x^20 - 10x^19 + 25x^18 + 60x^17 - 500x^16 + 1348x^15 - 2250x^14 + 3380x^13 - 2795x^12 - 8710x^11 + 31089x^10 - 37080x^9 + 7320x^8 + 32500x^7 - 45840x^6 + 31812x^5 - 13315x^4 + 3470x^3 - 565x^2 + 60x - 4	\( -\,2^{30}\cdot 3^{5}\cdot 5^{31} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$ (GRH)
20.10.1215000000000000000000000000000000.2	x^20 - 40x^18 - 30x^17 + 580x^16 + 888x^15 - 3375x^14 - 8190x^13 + 3820x^12 + 24330x^11 + 15884x^10 - 13500x^9 - 24005x^8 - 22560x^7 - 14565x^6 - 2388x^5 + 250x^4 + 930x^3 + 860x^2 - 60x + 1	\( -\,2^{30}\cdot 3^{5}\cdot 5^{31} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$ (GRH)
20.0.1316926149061478577602560000000000.1	x^20 - 10x^19 + 59x^18 - 216x^17 + 521x^16 - 808x^15 + 894x^14 - 1546x^13 + 4905x^12 - 8670x^11 + 5177x^10 + 7432x^9 - 18513x^8 - 19136x^7 + 21318x^6 - 30316x^5 + 268819x^4 + 16550x^3 + 337065x^2 + 37050x + 94025	\( 2^{28}\cdot 5^{10}\cdot 3469^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[198]$ (GRH)
20.0.20213777905110009806334605947265625.1	x^20 - 4x^19 + 34x^18 - 96x^17 + 337x^16 - 610x^15 + 1271x^14 - 1037x^13 + 2070x^12 + 2371x^11 + 5375x^10 + 6616x^9 + 42851x^8 - 19136x^7 + 183155x^6 - 111821x^5 + 401105x^4 - 200424x^3 + 487862x^2 - 125820x + 297859	\( 3^{10}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2, 1116]$ (GRH)
20.20.7428460430560760661253303852421087232.1	x^20 - 60x^18 + 1410x^16 - 17660x^14 + 132675x^12 - 630384x^10 + 1928971x^8 - 3766752x^6 + 4502727x^4 - 2981448x^2 + 832113	\( 2^{40}\cdot 3^{10}\cdot 10273^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$ (GRH)
20.20.367565560090157680064211189760000000000.1	x^20 - 96x^18 + 3392x^16 - 62272x^14 + 678944x^12 - 4668608x^10 + 20662784x^8 - 58205312x^6 + 99352320x^4 - 91360768x^2 + 33055744	\( 2^{30}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$ (GRH)