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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.164475020247040000000000.1	x^20 - 6x^19 + 15x^18 - 18x^17 + x^16 + 46x^15 - 138x^14 + 300x^13 - 521x^12 + 716x^11 - 763x^10 + 598x^9 - 273x^8 - 58x^7 + 250x^6 - 272x^5 + 199x^4 - 110x^3 + 43x^2 - 10x + 1	\( 2^{28}\cdot 5^{10}\cdot 89^{4} \)	20T1013	Trivial (GRH)
20.0.1547745882534914172125184.2	x^20 + 2x^18 + 4x^12 - 8x^10 - 14x^8 + 8x^6 + 15x^4 - 8x^2 + 1	\( 2^{28}\cdot 3^{10}\cdot 13^{4}\cdot 43^{4} \)	20T1013	Trivial (GRH)
20.0.1547745882534914172125184.3	x^20 + 2x^18 - 7x^16 - 20x^14 - x^12 + 41x^10 + 81x^8 + 65x^6 + 25x^4 + 5x^2 + 1	\( 2^{28}\cdot 3^{10}\cdot 13^{4}\cdot 43^{4} \)	20T1013	Trivial (GRH)
20.4.23619542166035402500000000.1	x^20 + 5x^18 + x^16 - 25x^14 - 19x^12 + 47x^10 + 16x^8 - 39x^6 + 16x^4 + 12x^2 + 1	\( 2^{8}\cdot 5^{10}\cdot 9859^{4} \)	20T1013	Trivial (GRH)
20.4.42105605183242240000000000.1	x^20 + 15x^16 - 4x^14 + 53x^12 - 42x^10 + 64x^8 - 96x^6 + 40x^4 - 48x^2 + 16	\( 2^{36}\cdot 5^{10}\cdot 89^{4} \)	20T1013	Trivial (GRH)
20.4.54798168594108112464510976.1	x^20 + 2x^18 - 12x^17 - 11x^16 - 12x^15 + 12x^14 + 44x^13 + 10x^12 - 20x^11 - 44x^10 - 20x^9 + 10x^8 + 44x^7 + 12x^6 - 12x^5 - 11x^4 - 12x^3 + 2x^2 + 1	\( 2^{40}\cdot 2657^{4} \)	20T1013	Trivial (GRH)
20.8.219192674376432449858043904.1	x^20 - 2x^16 + 42x^14 + 25x^12 - 88x^10 - 31x^8 + 62x^6 + 10x^4 - 16x^2 + 1	\( 2^{42}\cdot 2657^{4} \)	20T1013	Trivial (GRH)
20.8.219192674376432449858043904.2	x^20 + 2x^18 - 19x^16 - 12x^14 + 134x^12 - 120x^10 - 182x^8 + 140x^6 + x^4 - 10x^2 + 1	\( 2^{42}\cdot 2657^{4} \)	20T1013	Trivial (GRH)
20.4.5985123684000933883603515625.1	x^20 - 2x^19 - 4x^18 + 7x^17 + 13x^16 - 2x^15 - 99x^14 - 79x^13 + 165x^12 + 385x^11 + 455x^10 - 255x^9 - 680x^8 - 172x^7 - 45x^6 + x^5 + 232x^4 + 155x^3 + 15x^2 - 3x + 1	\( 5^{10}\cdot 71^{6}\cdot 263^{4} \)	20T1013	Trivial (GRH)
20.8.5985123684000933883603515625.1	x^20 - 2x^19 - 6x^18 + 21x^17 + x^16 - 70x^15 + 74x^14 + 108x^13 - 268x^12 + 70x^11 + 401x^10 - 627x^9 + 198x^8 + 557x^7 - 817x^6 + 415x^5 + 8x^4 - 87x^3 + 22x^2 + 3x - 1	\( 5^{10}\cdot 71^{6}\cdot 263^{4} \)	20T1013	Trivial (GRH)
20.4.11939665233708135040000000000.1	x^20 - 3x^19 + x^18 + 2x^17 - 4x^16 + 4x^15 + 24x^14 - 40x^13 + 32x^12 - 80x^10 + 128x^8 - 320x^7 + 384x^6 + 128x^5 - 256x^4 + 256x^3 + 256x^2 - 1536x + 1024	\( 2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.8.191034643739330160640000000000.1	x^20 + 6x^18 - 35x^16 - 196x^14 - 38x^12 + 576x^10 + 258x^8 - 236x^6 - 91x^4 + 10x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.8.191034643739330160640000000000.2	x^20 + 17x^18 + 61x^16 - 116x^14 - 484x^12 + 140x^10 + 1032x^8 + 144x^6 - 528x^4 - 32x^2 + 16	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.12.1244962716142623139840000000000.1	x^20 - 9x^18 + 21x^16 - 46x^14 + 216x^12 - 637x^10 + 983x^8 - 809x^6 + 332x^4 - 54x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1013	Trivial (GRH)
20.8.1244962716142623139840000000000.1	x^20 + x^18 - 7x^16 + 23x^14 + 74x^12 - 104x^10 - 728x^8 - 248x^6 + 555x^4 - 47x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1013	Trivial (GRH)
20.12.1244962716142623139840000000000.2	x^20 - 5x^18 + 17x^16 - 137x^14 + 530x^12 - 954x^10 + 905x^8 - 476x^6 + 136x^4 - 19x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 263^{4} \)	20T1013	Trivial (GRH)
20.12.3056554299829282570240000000000.1	x^20 - 11x^18 + 7x^16 + 230x^14 - 347x^12 - 1553x^10 + 1541x^8 + 2710x^6 + 555x^4 - 139x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.16.3056554299829282570240000000000.1	x^20 - 18x^18 + 93x^16 + 44x^14 - 1686x^12 + 4800x^10 - 4846x^8 + 1428x^6 - 59x^4 - 14x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.4.3056554299829282570240000000000.1	x^20 + 18x^18 + 119x^16 + 324x^14 + 93x^12 - 1418x^10 - 3171x^8 - 2844x^6 - 1113x^4 - 154x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.12.3056554299829282570240000000000.2	x^20 - 18x^18 + 71x^16 + 352x^14 - 2619x^12 + 2522x^10 + 4249x^8 + 304x^6 - 353x^4 - 14x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.16.3056554299829282570240000000000.2	x^20 - 26x^18 + 225x^16 - 700x^14 + 300x^12 + 1996x^10 - 2660x^8 + 576x^6 + 368x^4 - 160x^2 + 16	\( 2^{24}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.4.5297130689384517848057641959424.1	x^20 + 12x^18 + 20x^16 - 96x^14 - 6x^12 + 160x^10 - 114x^8 - 8x^6 + 49x^4 - 20x^2 + 4	\( 2^{54}\cdot 41^{4}\cdot 101^{4} \)	20T1013	Trivial (GRH)
20.12.160660135384776665098240000000000.1	x^20 - 9x^19 + 36x^18 - 104x^17 + 187x^16 + 218x^15 - 2262x^14 + 6106x^13 - 9188x^12 + 5426x^11 + 14778x^10 - 46356x^9 + 41756x^8 + 27444x^7 - 65968x^6 + 4388x^5 + 34376x^4 - 536x^3 - 7788x^2 - 2112x - 164	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{6}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.12.160660135384776665098240000000000.2	x^20 - 3x^19 - 19x^18 + 51x^17 + 135x^16 - 248x^15 - 668x^14 + 432x^13 + 2098x^12 + 926x^11 - 3514x^10 - 6670x^9 + 750x^8 + 15800x^7 + 9300x^6 - 20000x^5 - 17875x^4 + 13125x^3 + 13125x^2 - 3125x - 3125	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{6}\cdot 31^{4} \)	20T1013	Trivial (GRH)
20.12.25496315463173953254560344368631250944.1	x^20 - 46x^18 + 699x^16 - 2364x^14 - 28999x^12 + 52254x^10 + 3670193x^8 - 33525396x^6 + 122407130x^4 - 199176704x^2 + 113592964	\( 2^{54}\cdot 73^{4}\cdot 2657^{4} \)	20T1013	Trivial (GRH)
20.20.728595962694391038340952582792874557440000000000.1	x^20 - 438x^18 + 80864x^16 - 8271656x^14 + 517755720x^12 - 20646179760x^10 + 528715968864x^8 - 8538377065024x^6 + 82763463901760x^4 - 433542795843328x^2 + 931139348459776	\( 2^{40}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4}\cdot 1381^{4} \)	20T1013	Trivial (GRH)