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 23 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.13934496372519102386176.1	x^20 + 4x^18 + 9x^16 + 10x^14 - x^12 - 11x^10 - 9x^8 - x^6 + 8x^4 + 6x^2 + 1	\( 2^{12}\cdot 67^{4}\cdot 641^{4} \)	20T1100	Trivial (GRH)
20.4.238121705371228558065664.1	x^20 - 8x^18 + 28x^16 - 58x^14 + 80x^12 - 78x^10 + 53x^8 - 20x^6 - 2x^4 + 4x^2 + 1	\( 2^{30}\cdot 17^{4}\cdot 227^{4} \)	20T1100	Trivial (GRH)
20.0.238121705371228558065664.2	x^20 + 8x^18 + 28x^16 + 58x^14 + 80x^12 + 78x^10 + 53x^8 + 20x^6 - 2x^4 - 4x^2 + 1	\( 2^{30}\cdot 17^{4}\cdot 227^{4} \)	20T1100	Trivial (GRH)
20.4.891807767841222552715264.1	x^20 - x^19 - 10x^18 - 2x^17 + 50x^16 + 55x^15 - 108x^14 - 242x^13 + 21x^12 + 435x^11 + 295x^10 - 283x^9 - 434x^8 - 28x^7 + 216x^6 + 74x^5 - 94x^4 - 112x^3 - 52x^2 - 13x - 1	\( 2^{18}\cdot 67^{4}\cdot 641^{4} \)	20T1100	Trivial (GRH)
20.4.43406142794035599452422144.1	x^20 - 6x^18 + 8x^16 + x^14 + 9x^12 + 21x^10 - 70x^8 - 62x^6 + 14x^4 + 10x^2 + 1	\( 2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.8.43406142794035599452422144.1	x^20 - 11x^18 + 45x^16 - 75x^14 + 4x^12 + 142x^10 - 145x^8 + 8x^6 + 41x^4 - 10x^2 + 1	\( 2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.4.43406142794035599452422144.2	x^20 + 2x^18 + 4x^16 + 29x^14 + 53x^12 + 4x^10 - 53x^8 - 38x^6 - 6x^4 + 4x^2 + 1	\( 2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.8.43406142794035599452422144.2	x^20 - 5x^18 + 53x^14 + 19x^12 - 41x^10 - 8x^8 - 26x^6 + 37x^4 - 12x^2 + 1	\( 2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.0.2777993138818278364955017216.1	x^20 - 2x^18 - 5x^16 + 24x^14 + 35x^12 - 32x^10 - 54x^8 + x^6 + 23x^4 + 9x^2 + 1	\( 2^{20}\cdot 307^{4}\cdot 739^{4} \)	20T1100	$[2]$ (GRH)
20.12.2777993138818278364955017216.1	x^20 - 8x^18 + 19x^16 - 7x^14 - 7x^12 - 74x^10 + 205x^8 - 218x^6 + 110x^4 - 23x^2 + 1	\( 2^{20}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.0.2777993138818278364955017216.2	x^20 + 4x^18 - 3x^16 - 23x^14 - 6x^12 + 81x^10 + 187x^8 + 207x^6 + 111x^4 + 23x^2 + 1	\( 2^{20}\cdot 307^{4}\cdot 739^{4} \)	20T1100	$[3]$ (GRH)
20.12.2777993138818278364955017216.2	x^20 - 4x^18 - 3x^16 + 23x^14 - 6x^12 - 81x^10 + 187x^8 - 207x^6 + 111x^4 - 23x^2 + 1	\( 2^{20}\cdot 307^{4}\cdot 739^{4} \)	20T1100	Trivial (GRH)
20.8.706496593452575742775878906250000.1	x^20 - 9x^18 - 147x^16 + 75x^14 + 2737x^12 - 680x^10 - 12587x^8 + 6734x^6 + 1300x^4 + 66x^2 + 1	\( 2^{4}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.12.1103900927269649598087310791015625.1	x^20 - 6x^19 - 8x^18 + 140x^17 - 340x^16 - 131x^15 + 2077x^14 - 3836x^13 + 713x^12 + 8711x^11 - 14925x^10 + 5941x^9 + 12519x^8 - 19464x^7 + 6722x^6 + 8392x^5 - 8292x^4 + 520x^3 + 1631x^2 - 393x + 23	\( 5^{18}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.12.5342880487985104054742584228515625.1	x^20 - 8x^19 - 3x^18 + 242x^17 - 1006x^16 + 1092x^15 + 4062x^14 - 17936x^13 + 32283x^12 - 27724x^11 - 7128x^10 + 62966x^9 - 116535x^8 + 137513x^7 - 105769x^6 + 45579x^5 - 5795x^4 - 2775x^3 + 1085x^2 - 130x + 5	\( 5^{16}\cdot 11^{6}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.8.17662414836314393569396972656250000.1	x^20 - 3x^19 - 7x^18 - 36x^17 + 295x^16 - 291x^15 - 143x^14 + 558x^13 - 7445x^12 + 15971x^11 - 17544x^10 + 9076x^9 + 21514x^8 - 37750x^7 + 28608x^6 - 22919x^5 - 4516x^4 + 28591x^3 - 11528x^2 - 4741x + 1921	\( 2^{4}\cdot 5^{18}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.16.133572012199627601368564605712890625.1	x^20 - x^19 - 35x^18 + 48x^17 + 371x^16 - 720x^15 - 1072x^14 + 3390x^13 - 1550x^12 - 4400x^11 + 11484x^10 - 4579x^9 - 21055x^8 + 17107x^7 + 19669x^6 - 16970x^5 - 10688x^4 + 7275x^3 + 3345x^2 - 1150x - 475	\( 5^{18}\cdot 11^{6}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.4.222590582974652144958325347900390625.1	x^20 - x^19 - 2x^18 + 33x^17 - 81x^16 - 115x^15 + 454x^14 - 2019x^13 - 623x^12 + 737x^11 - 14501x^10 - 4126x^9 + 3362x^8 - 64205x^7 + 40793x^6 - 54693x^5 + 4194x^4 - 1786x^3 - 11914x^2 + 12730x + 6137	\( 5^{16}\cdot 11^{4}\cdot 71^{6}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.16.2893810046781750242410000000000000000.1	x^20 - 23x^18 + 187x^16 - 711x^14 + 1320x^12 - 1015x^10 - 39x^8 + 331x^6 - 23x^4 - 10x^2 + 1	\( 2^{16}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.4.2893810046781750242410000000000000000.1	x^20 + 29x^18 + 258x^16 + 870x^14 + 546x^12 - 2830x^10 - 5713x^8 - 3481x^6 - 645x^4 - 27x^2 + 1	\( 2^{16}\cdot 5^{16}\cdot 11^{4}\cdot 71^{4}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.0.26933460539932909539957367095947265625.1	x^20 - 2x^19 + 21x^18 + 3x^17 + 214x^16 - 170x^15 + 2576x^14 - 755x^13 + 13339x^12 + 19832x^11 + 149025x^10 + 275981x^9 + 581614x^8 + 755443x^7 + 883394x^6 + 1008224x^5 + 1010770x^4 + 873795x^3 + 491090x^2 + 490795x + 536845	\( 5^{16}\cdot 11^{6}\cdot 71^{6}\cdot 167^{4} \)	20T1100	$[1588]$ (GRH)
20.20.135771574581801796990925087530670166015625.1	x^20 - x^19 - 114x^18 + 146x^17 + 5261x^16 - 8086x^15 - 127004x^14 + 222110x^13 + 1735841x^12 - 3298366x^11 - 13694442x^10 + 27051188x^9 + 61475933x^8 - 119264556x^7 - 150754758x^6 + 255705133x^5 + 192822823x^4 - 201595569x^3 - 116462395x^2 + 511167x + 667999	\( 5^{16}\cdot 11^{6}\cdot 71^{8}\cdot 167^{4} \)	20T1100	Trivial (GRH)
20.20.253416930220228745861458867005767822265625.1	x^20 - x^19 - 101x^18 + 128x^17 + 4008x^16 - 5805x^15 - 81655x^14 + 126810x^13 + 948445x^12 - 1524673x^11 - 6577211x^10 + 10786542x^9 + 27350617x^8 - 45881421x^7 - 65289834x^6 + 114875447x^5 + 77439919x^4 - 155522891x^3 - 22316787x^2 + 87698196x - 21505501	\( 5^{16}\cdot 11^{6}\cdot 71^{6}\cdot 97^{2}\cdot 167^{4} \)	20T1100	Trivial (GRH)