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 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.49226653653406684545024.2	x^20 + x^18 + x^16 + 3x^14 + 7x^12 + 9x^10 + 2x^8 + 3x^6 + 4x^4 - x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2} \)	20T1030	Trivial (GRH)
20.0.49226653653406684545024.3	x^20 - x^18 - 5x^16 + 2x^14 + 12x^12 + 2x^10 - 13x^8 - 8x^6 + 5x^4 + 5x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2} \)	20T1030	Trivial (GRH)
20.4.802821734410240000000000.1	x^20 - 7x^18 + 21x^16 - 36x^14 + 42x^12 - 43x^10 + 41x^8 - 28x^6 + 15x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T1030	Trivial (GRH)
20.4.802821734410240000000000.2	x^20 - 7x^18 + 24x^16 - 53x^14 + 81x^12 - 87x^10 + 67x^8 - 38x^6 + 15x^4 - 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T1030	Trivial (GRH)
20.4.12164157316311040000000000.1	x^20 - 8x^18 + 27x^16 - 52x^14 + 63x^12 - 49x^10 + 20x^8 + x^6 - 6x^4 + 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.8.12164157316311040000000000.1	x^20 - 4x^18 + 2x^16 + 7x^14 + x^12 - 27x^10 + 29x^8 - 4x^6 - 4x^4 - x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.4.12164157316311040000000000.2	x^20 - x^18 - 4x^16 + 3x^14 - 4x^12 + 25x^10 - 30x^8 + 6x^6 + 5x^4 - 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.8.12164157316311040000000000.2	x^20 + x^14 - 17x^12 + 3x^10 + 34x^8 - 41x^6 + 25x^4 - 8x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1030	Trivial (GRH)
20.8.20749170740660742431640625.1	x^20 - 3x^19 - 2x^18 + 11x^17 - 16x^16 + 15x^15 + 9x^14 - 32x^13 + 63x^12 - 75x^11 + 83x^10 - 75x^9 + 63x^8 - 32x^7 + 9x^6 + 15x^5 - 16x^4 + 11x^3 - 2x^2 - 3x + 1	\( 5^{12}\cdot 419^{2}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.8.113652932754887702500000000.1	x^20 + 5x^18 - 2x^16 - 36x^14 - 19x^12 + 79x^10 + 24x^8 - 38x^6 - 9x^4 + 5x^2 + 1	\( 2^{8}\cdot 5^{10}\cdot 491^{2}\cdot 434249^{2} \)	20T1030	Trivial (GRH)
20.8.215613371594352640000000000.1	x^20 - 7x^18 + 17x^16 - 12x^14 - 15x^12 + 34x^10 - 43x^8 + 31x^6 + 4x^4 - 10x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 4588681^{2} \)	20T1030	Trivial (GRH)
20.8.215613371594352640000000000.2	x^20 - 10x^18 + 41x^16 - 82x^14 + 62x^12 + 51x^10 - 135x^8 + 93x^6 - 21x^4 - 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 4588681^{2} \)	20T1030	Trivial (GRH)
20.4.276787479753533440000000000.1	x^20 + 3x^18 + x^16 + 2x^14 + 6x^12 - 5x^10 - 2x^8 + 3x^6 - 6x^4 - 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T1030	Trivial (GRH)
20.4.1254027648371107840000000000.1	x^20 + x^18 - 3x^16 + 2x^14 - 10x^10 + 5x^8 + 7x^6 - 3x^4 + 1	\( 2^{20}\cdot 5^{10}\cdot 11066329^{2} \)	20T1030	Trivial (GRH)
20.4.7753892385981245440000000000.1	x^20 + 8x^18 + 26x^16 + 40x^14 + 13x^12 - 50x^10 - 68x^8 - 20x^6 + 11x^4 + 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1030	Trivial (GRH)
20.8.7753892385981245440000000000.1	x^20 + 7x^18 + 8x^16 - 13x^14 - 46x^12 - 29x^10 + 51x^8 + 58x^6 + x^4 - 8x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1030	Trivial (GRH)
20.8.7753892385981245440000000000.2	x^20 - x^18 - 7x^16 + 6x^14 + 6x^12 - 4x^10 + 9x^8 - 9x^4 - x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1030	Trivial (GRH)
20.4.8239247507322480640000000000.1	x^20 + 11x^18 + 52x^16 + 143x^14 + 258x^12 + 303x^10 + 190x^8 + 18x^6 - 31x^4 - 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1030	Trivial (GRH)
20.4.37682138330093578240000000000.1	x^20 + 5x^18 - 11x^16 - 41x^14 + 76x^12 + 61x^10 - 182x^8 + 90x^6 - 13x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T1030	Trivial (GRH)
20.8.37682138330093578240000000000.1	x^20 - 5x^18 + 6x^16 + 6x^14 - 15x^12 + 12x^8 + 4x^6 - 5x^4 - 4x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T1030	Trivial (GRH)
20.4.37682138330093578240000000000.2	x^20 + 5x^18 + 6x^16 - 6x^14 - 15x^12 - 6x^10 - 3x^8 - 2x^6 + 13x^4 + 11x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T1030	Trivial (GRH)
20.12.52236018166732810240000000000.1	x^20 - 13x^18 + 73x^16 - 235x^14 + 484x^12 - 669x^10 + 629x^8 - 397x^6 + 157x^4 - 30x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 19^{2}\cdot 349^{2}\cdot 10771^{2} \)	20T1030	Trivial (GRH)
20.12.115518346967817840640000000000.1	x^20 - 12x^18 + 63x^16 - 192x^14 + 377x^12 - 498x^10 + 448x^8 - 267x^6 + 94x^4 - 16x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{6}\cdot 199^{2}\cdot 401^{2} \)	20T1030	Trivial (GRH)
20.8.398768247298782423040000000000.1	x^20 + 2x^18 - 15x^16 - 24x^14 + 25x^12 + 126x^10 + 87x^8 - 65x^6 - 43x^4 + 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 1630891^{2} \)	20T1030	Trivial (GRH)
20.12.870283298342363146240000000000.1	x^20 - 2x^18 - 12x^16 + 14x^14 + 37x^12 - 33x^10 - 32x^8 + 29x^6 + 5x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.4.870283298342363146240000000000.1	x^20 + 14x^18 + 78x^16 + 218x^14 + 310x^12 + 179x^10 - 34x^8 - 71x^6 - 11x^4 + 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.12.870283298342363146240000000000.2	x^20 - 6x^18 + 6x^16 + 26x^14 - 54x^12 - 13x^10 + 88x^8 - 31x^6 - 33x^4 + 14x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.8.982692381976802928640000000000.1	x^20 + x^18 - 20x^16 - 35x^14 + 67x^12 + 195x^10 + 131x^8 + x^6 - 21x^4 - 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{2}\cdot 28162171^{2} \)	20T1030	Trivial (GRH)
20.4.1275284484745083136000000000000.1	x^20 + 12x^18 + 53x^16 + 89x^14 - 48x^12 - 402x^10 - 588x^8 - 359x^6 - 79x^4 - x^2 + 1	\( 2^{20}\cdot 5^{12}\cdot 1039^{2}\cdot 67931^{2} \)	20T1030	Trivial (GRH)
20.12.1342861649047383255040000000000.1	x^20 + 2x^18 - 22x^16 - 12x^14 + 157x^12 - 82x^10 - 239x^8 + 172x^6 + 51x^4 - 30x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 5471^{2}\cdot 66191^{2} \)	20T1030	Trivial (GRH)
20.12.1533846811270295971840000000000.1	x^20 - 7x^18 - x^16 + 59x^14 - 7x^12 - 104x^10 - 40x^8 + 7x^6 + 31x^4 - 11x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 29^{2}\cdot 13345751^{2} \)	20T1030	Trivial (GRH)
20.8.1875079856162081587840000000000.1	x^20 - x^18 - 9x^16 + 10x^14 + 19x^12 - 19x^10 - 14x^8 + 16x^6 + 3x^4 - 6x^2 + 1	\( 2^{16}\cdot 5^{10}\cdot 1711669441^{2} \)	20T1030	Trivial (GRH)
20.20.14387599164522371678218240000000000.1	x^20 - 57x^18 + 1264x^16 - 14363x^14 + 92035x^12 - 342567x^10 + 734019x^8 - 870342x^6 + 533489x^4 - 147741x^2 + 14641	\( 2^{20}\cdot 5^{10}\cdot 11^{6}\cdot 28162171^{2} \)	20T1030	Trivial (GRH)
20.12.17379204847431458802903040000000000.1	x^20 - 25x^18 + 182x^16 - 287x^14 - 460x^12 - 3649x^10 + 10370x^8 + 42199x^6 - 100719x^4 - 41154x^2 + 130321	\( 2^{20}\cdot 5^{10}\cdot 19^{4}\cdot 149^{2}\cdot 765899^{2} \)	20T1030	Trivial (GRH)
20.16.114079310946033402667018240000000000.1	x^20 - 70x^18 + 2104x^16 - 36334x^14 + 405861x^12 - 3056070x^10 + 15118553x^8 - 45402178x^6 + 73638590x^4 - 53794497x^2 + 13845841	\( 2^{20}\cdot 5^{10}\cdot 61^{4}\cdot 3169^{2}\cdot 8951^{2} \)	20T1030	Trivial (GRH)
20.16.401784688398260722928486785556640625.1	x^20 - 4x^19 - 53x^18 + 163x^17 + 926x^16 - 2177x^15 - 6101x^14 + 6905x^13 + 14743x^12 + 69919x^11 - 77732x^10 - 498941x^9 + 641383x^8 + 476564x^7 - 996698x^6 + 1541404x^5 - 2636562x^4 + 574525x^3 + 2216019x^2 - 1608972x + 302989	\( 5^{10}\cdot 419^{2}\cdot 695771^{4} \)	20T1030	Trivial (GRH)
20.12.2776853807987152620436695040000000000.1	x^20 - 13x^18 - 378x^16 + 3608x^14 + 27898x^12 - 146505x^10 - 235376x^8 + 1383668x^6 - 36982x^4 - 3652813x^2 + 2825761	\( 2^{20}\cdot 5^{10}\cdot 11^{2}\cdot 41^{4}\cdot 28162171^{2} \)	20T1030	Trivial (GRH)
20.16.6460201183313501581242920151040000000000.1	x^20 - 176x^18 + 13263x^16 - 566509x^14 + 15329496x^12 - 277754804x^10 + 3450341169x^8 - 29250980295x^6 + 162553060056x^4 - 534105315061x^2 + 784076601361	\( 2^{20}\cdot 5^{10}\cdot 941^{4}\cdot 3169^{2}\cdot 8951^{2} \)	20T1030	Trivial (GRH)
20.20.198414240316397285634688570992640000000000.1	x^20 - 179x^18 + 13413x^16 - 557393x^14 + 14304640x^12 - 237925889x^10 + 2606127441x^8 - 18610574474x^6 + 83093153544x^4 - 209841439956x^2 + 227988105361	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 691^{4}\cdot 695771^{2} \)	20T1030	Trivial (GRH)
20.12.370270629040986660253142367975040000000000.1	x^20 - 316x^18 + 42619x^16 - 3247364x^14 + 155690232x^12 - 4929882768x^10 + 104758408713x^8 - 1478902722150x^6 + 13305245801616x^4 - 69041174949655x^2 + 157218521219761	\( 2^{16}\cdot 5^{10}\cdot 3541^{4}\cdot 60662149^{2} \)	20T1030	Trivial (GRH)
20.12.782003552575825933249006620682240000000000.1	x^20 - 275x^18 + 23171x^16 - 248166x^14 - 50014572x^12 + 1810191294x^10 + 5037137676x^8 - 843346065511x^6 + 5645857496273x^4 + 34720939507619x^2 + 100853031438721	\( 2^{20}\cdot 5^{10}\cdot 3169^{4}\cdot 27517559^{2} \)	20T1030	Trivial (GRH)
20.12.4005869174343660274328698855843840000000000.1	x^20 - 304x^18 + 38949x^16 - 2808026x^14 + 127489037x^12 - 3839138862x^10 + 78102567868x^8 - 1064005067775x^6 + 9311802693856x^4 - 47343128591330x^2 + 106306843291441	\( 2^{20}\cdot 5^{10}\cdot 13^{8}\cdot 19^{4}\cdot 60662149^{2} \)	20T1030	Trivial (GRH)