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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.121260259409849938345984.1	x^20 - 5x^18 + 17x^16 - 30x^14 + 21x^12 + 21x^10 - 57x^8 + 50x^6 - 21x^4 + 3x^2 - 1	\( -\,2^{28}\cdot 277^{6} \)	20T365	Trivial
20.2.121260259409849938345984.2	x^20 + 5x^18 + 17x^16 + 30x^14 + 21x^12 - 21x^10 - 57x^8 - 50x^6 - 21x^4 - 3x^2 - 1	\( -\,2^{28}\cdot 277^{6} \)	20T365	Trivial
20.4.568572957038667426725888.1	x^20 + 5x^18 + 11x^16 + 4x^14 - 23x^12 - 37x^10 + 28x^6 - 24x^4 - 16x^2 + 32	\( 2^{15}\cdot 1609^{6} \)	20T365	Trivial (GRH)
20.4.568572957038667426725888.2	x^20 - x^18 - 3x^16 + 7x^14 - 37x^10 - 46x^8 + 16x^6 + 88x^4 + 80x^2 + 32	\( 2^{15}\cdot 1609^{6} \)	20T365	Trivial (GRH)
20.2.173467927083915868031188992.1	x^20 + 3x^18 + 5x^16 + 6x^14 - 23x^12 - 51x^10 - 74x^8 - 168x^6 - 232x^4 - 144x^2 - 32	\( -\,2^{15}\cdot 3^{16}\cdot 223^{6} \)	20T365	Trivial (GRH)
20.6.173467927083915868031188992.1	x^20 - 9x^18 + 29x^16 - 42x^14 + 37x^12 - 51x^10 + 46x^8 + 24x^6 - 40x^4 + 48x^2 - 32	\( -\,2^{15}\cdot 3^{16}\cdot 223^{6} \)	20T365	Trivial (GRH)
20.0.358403934413091314563284992.1	x^20 - x^18 - 11x^16 + 12x^14 + 39x^12 - 41x^10 - 58x^8 + 47x^6 + 62x^4 - 64x^2 + 17	\( 2^{20}\cdot 17^{7}\cdot 97^{6} \)	20T365	Trivial (GRH)
20.0.358403934413091314563284992.2	x^20 - 8x^18 + 21x^16 + 6x^14 - 109x^12 + 210x^10 - 161x^8 - 12x^6 + 110x^4 - 74x^2 + 17	\( 2^{20}\cdot 17^{7}\cdot 97^{6} \)	20T365	Trivial (GRH)
20.2.1455584035932861642867736576.1	x^20 + 5x^18 + 20x^16 + 56x^14 + 129x^12 + 242x^10 + 325x^8 + 287x^6 + 139x^4 + 25x^2 - 1	\( -\,2^{18}\cdot 19^{8}\cdot 83^{6} \)	20T365	Trivial (GRH)
20.6.1455584035932861642867736576.1	x^20 - 3x^18 + 6x^16 - 9x^14 + 17x^12 - 30x^10 + 4x^8 + 6x^6 + 14x^4 + 3x^2 - 1	\( -\,2^{18}\cdot 19^{8}\cdot 83^{6} \)	20T365	Trivial (GRH)
20.8.11644672287462893142941892608.1	x^20 - 10x^18 + 21x^16 + 8x^14 - 18x^12 - 88x^10 + 151x^8 - 149x^6 + 80x^4 + 60x^2 + 8	\( 2^{21}\cdot 19^{8}\cdot 83^{6} \)	20T365	Trivial (GRH)
20.8.11644672287462893142941892608.2	x^20 - 8x^18 + 17x^16 + 8x^14 - 59x^12 + 11x^10 + 101x^8 - 20x^6 - 92x^4 + 8x^2 + 32	\( 2^{21}\cdot 19^{8}\cdot 83^{6} \)	20T365	Trivial (GRH)
20.12.12304157611974151730282412109.1	x^20 - 3x^19 - 6x^18 + 32x^17 - 23x^16 - 78x^15 + 214x^14 - 180x^13 - 256x^12 + 823x^11 - 764x^10 - 160x^9 + 1367x^8 - 1673x^7 + 495x^6 + 859x^5 - 1096x^4 + 589x^3 - 162x^2 + 21x - 1	\( 61^{7}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.8.12304157611974151730282412109.1	x^20 - 3x^19 + 5x^18 - 2x^17 - 27x^16 + 53x^15 - 74x^14 - 11x^13 + 200x^12 - 177x^11 + 238x^10 - 121x^9 - 157x^8 + 798x^7 - 497x^6 - 193x^5 + 239x^4 - 275x^3 - 15x^2 + 24x + 11	\( 61^{7}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.0.38683347739713238570955145216.1	x^20 - 4x^19 + 18x^18 - 43x^17 + 112x^16 - 179x^15 + 296x^14 - 285x^13 + 209x^12 - 79x^11 - 207x^10 - 250x^9 - 307x^8 - 318x^7 + 230x^6 + 610x^5 + 22x^4 + 533x^3 + 2172x^2 + 2327x + 841	\( 2^{15}\cdot 3^{16}\cdot 223^{7} \)	20T365	$[2]$ (GRH)
20.0.46578689149851572571767570432.1	x^20 + 8x^18 + 17x^16 - 8x^14 - 59x^12 - 11x^10 + 101x^8 + 20x^6 - 92x^4 - 8x^2 + 32	\( 2^{23}\cdot 19^{8}\cdot 83^{6} \)	20T365	$[2]$ (GRH)
20.12.80077878228749807162657665693.1	x^20 - 10x^19 + 37x^18 - 39x^17 - 175x^16 + 871x^15 - 1906x^14 + 2191x^13 - 459x^12 - 2512x^11 + 4147x^10 - 3819x^9 + 2525x^8 - 108x^7 - 2164x^6 + 2004x^5 - 501x^4 - 164x^3 + 87x^2 - 4x - 1	\( 61^{6}\cdot 397^{7} \)	20T365	Trivial (GRH)
20.8.80077878228749807162657665693.1	x^20 - 9x^19 + 20x^18 + 41x^17 - 189x^16 - 49x^15 + 843x^14 - 384x^13 - 2007x^12 + 2558x^11 - 481x^10 - 869x^9 + 2547x^8 - 2485x^7 - 1487x^6 + 1063x^5 + 1736x^4 + 171x^3 - 636x^2 - 422x - 59	\( 61^{6}\cdot 397^{7} \)	20T365	Trivial (GRH)
20.10.206548481879697235603429344256.1	x^20 - 5x^18 - 41x^16 + 80x^14 + 693x^12 + 809x^10 - 588x^8 - 919x^6 + 193x^4 + 29x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.10.206548481879697235603429344256.2	x^20 + 5x^18 - 41x^16 - 80x^14 + 693x^12 - 809x^10 - 588x^8 + 919x^6 + 193x^4 - 29x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.14.12599457394661531371809189999616.1	x^20 - 9x^19 + 25x^18 + 12x^17 - 190x^16 + 364x^15 - 471x^14 + 735x^13 + 1134x^12 - 7506x^11 + 7866x^10 + 10262x^9 - 24618x^8 + 3795x^7 + 24064x^6 - 15181x^5 - 7254x^4 + 8491x^3 - 749x^2 - 993x + 221	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.6.12599457394661531371809189999616.1	x^20 + 2x^18 + 15x^16 - 129x^15 - 310x^14 + 1078x^13 - 868x^12 - 2445x^11 + 4350x^10 + 8799x^9 + 2111x^8 - 7238x^7 - 7224x^6 - 4740x^5 - 245x^4 + 1095x^3 + 924x^2 + 262x + 13	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.14.64121688708081656137869829341184.1	x^20 - 9x^18 - 35x^16 + 414x^14 - 555x^12 - 1279x^10 + 2315x^8 - 90x^6 - 365x^4 + 43x^2 - 1	\( -\,2^{28}\cdot 7877^{6} \)	20T365	Trivial (GRH)
20.6.64121688708081656137869829341184.1	x^20 + 9x^18 - 35x^16 - 414x^14 - 555x^12 + 1279x^10 + 2315x^8 + 90x^6 - 365x^4 - 43x^2 - 1	\( -\,2^{28}\cdot 7877^{6} \)	20T365	Trivial (GRH)
20.20.11229672440193284982132039906757357.1	x^20 - 8x^19 - 20x^18 + 255x^17 - 4x^16 - 2775x^15 + 1522x^14 + 13900x^13 - 8492x^12 - 34079x^11 + 18900x^10 + 40805x^9 - 21107x^8 - 24051x^7 + 11902x^6 + 6747x^5 - 3168x^4 - 767x^3 + 317x^2 + 16x - 1	\( 61^{7}\cdot 97^{3}\cdot 397^{6} \)	20T365	Trivial (GRH)
20.0.72098801162275858741260523848334336.1	x^20 - 5x^19 + 21x^18 - 27x^17 + 111x^16 - 259x^15 + 253x^14 - 95x^13 + 1552x^12 + 672x^11 + 3307x^10 + 7274x^9 + 32883x^8 + 76288x^7 + 224448x^6 + 456093x^5 + 786619x^4 + 872615x^3 + 686603x^2 + 258966x + 49111	\( 2^{10}\cdot 31^{3}\cdot 36497^{6} \)	20T365	$[2, 644]$ (GRH)
20.20.72098801162275858741260523848334336.1	x^20 - 3x^19 - 47x^18 + 82x^17 + 851x^16 - 624x^15 - 7290x^14 + 482x^13 + 30546x^12 + 9479x^11 - 61882x^10 - 31321x^9 + 57458x^8 + 35306x^7 - 23958x^6 - 17096x^5 + 3713x^4 + 3410x^3 - 23x^2 - 195x - 9	\( 2^{10}\cdot 31^{3}\cdot 36497^{6} \)	20T365	Trivial (GRH)
20.0.3298534069058336679408162982643892224.1	x^20 + 45x^18 + 808x^16 + 7681x^14 + 42680x^12 + 143136x^10 + 286911x^8 + 326809x^6 + 189453x^4 + 42713x^2 + 1331	\( 2^{20}\cdot 11^{3}\cdot 36497^{6} \)	20T365	$[2, 3676]$ (GRH)