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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.9686159036696250915921.1	x^20 - 2x^19 + 3x^18 - 3x^16 + 4x^15 - x^14 - 5x^13 + 6x^12 - 7x^11 + 3x^10 + x^9 - 5x^8 + 10x^7 - 5x^6 - 3x^5 + 7x^4 - 2x^3 - 2x + 1	\( 3^{10}\cdot 47^{8}\cdot 83^{2} \)	20T141	Trivial
20.0.16097667994068134233761.1	x^20 - x^19 + x^18 + 2x^17 - 3x^16 + 2x^15 - x^14 - x^13 - 2x^12 - 2x^11 + 2x^10 - 4x^9 + 2x^8 + 3x^7 + x^6 + 6x^4 - 6x^3 + 2x^2 - 2x + 1	\( 3^{10}\cdot 47^{8}\cdot 107^{2} \)	20T141	Trivial
20.0.123009478946011416015625.1	x^20 - x^19 + 5x^18 - 6x^17 + 26x^16 - 21x^15 + 71x^14 - 30x^13 + 112x^12 - 42x^11 + 159x^10 + 42x^9 + 112x^8 + 30x^7 + 71x^6 + 21x^5 + 26x^4 + 6x^3 + 5x^2 + x + 1	\( 5^{10}\cdot 23^{2}\cdot 47^{8} \)	20T141	Trivial
20.4.1239163541216058291015625.1	x^20 - 3x^19 + 7x^17 - 13x^16 + 29x^15 - 7x^14 - 68x^13 + 75x^12 - 83x^11 + 39x^10 + 196x^9 - 157x^8 + 111x^7 - 172x^6 - 239x^5 + 215x^4 - 59x^3 + 9x^2 - 15x - 5	\( 5^{10}\cdot 47^{8}\cdot 73^{2} \)	20T141	Trivial
20.0.1601913611453823525390625.1	x^20 - 2x^19 - x^18 - 2x^17 + 9x^16 - 18x^15 + 17x^14 - 31x^13 + 96x^12 + 53x^11 - 5x^10 + 123x^9 + 49x^8 + 24x^7 + 21x^6 + 21x^5 + 19x^4 + 4x^3 + 8x^2 + 2x + 1	\( 5^{10}\cdot 47^{8}\cdot 83^{2} \)	20T141	Trivial
20.4.8661588055311870009765625.1	x^20 - x^19 - 4x^18 + 11x^17 + 3x^16 - 29x^15 + 34x^14 + 15x^13 - 67x^12 - 52x^11 - 97x^10 - 33x^9 + 57x^8 + 76x^7 + 8x^6 - 23x^5 - 20x^4 - 4x^3 + 3x^2 + 1	\( 5^{10}\cdot 47^{8}\cdot 193^{2} \)	20T141	Trivial (GRH)
20.0.6309535724727483864248745984.1	x^20 + x^18 - 4x^16 + 2x^14 + 4x^12 - 7x^10 + 4x^8 + 2x^6 - 4x^4 + x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T141	$[5]$ (GRH)
20.0.6671972272300106674226558481.1	x^20 - 3x^19 + 11x^18 - 16x^17 + 42x^16 - 48x^15 + 105x^14 - 29x^13 + 42x^12 + 141x^11 + 72x^10 + 27x^9 + 280x^8 - 69x^7 + 522x^6 - 385x^5 + 519x^4 - 79x^3 + 70x^2 - 3x + 9	\( 3^{10}\cdot 13^{2}\cdot 401^{8} \)	20T141	$[2, 2]$
20.8.58762130557815394031337890625.1	x^20 - x^19 - x^18 - 14x^16 + 3x^15 - 29x^14 - 22x^13 + 4x^12 - 78x^11 + 87x^10 + 78x^9 + 4x^8 + 22x^7 - 29x^6 - 3x^5 - 14x^4 - x^2 + x + 1	\( 3^{2}\cdot 5^{10}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.0.146901827368217141626017894129.1	x^20 - 2x^19 + 16x^18 - 20x^17 + 147x^16 - 167x^15 + 778x^14 - 604x^13 + 2611x^12 - 1801x^11 + 4764x^10 - 740x^9 + 3010x^8 - 371x^7 + 1283x^6 + 51x^5 + 222x^4 + 36x^3 + 33x^2 + 5x + 1	\( 3^{10}\cdot 61^{2}\cdot 401^{8} \)	20T141	$[2, 4]$
20.0.199014273518726850560805214809.1	x^20 - 4x^19 + 10x^18 - 6x^17 - 10x^16 + 15x^15 - 3x^14 - 7x^13 + 7x^12 - 5x^10 + 7x^8 - 7x^7 - 3x^6 + 15x^5 - 10x^4 - 6x^3 + 10x^2 - 4x + 1	\( 3^{10}\cdot 71^{2}\cdot 401^{8} \)	20T141	$[2, 4]$ (GRH)
20.0.199014273518726850560805214809.2	x^20 - x^19 + 11x^18 - 22x^17 + 95x^16 - 165x^15 + 405x^14 - 553x^13 + 1044x^12 - 1174x^11 + 1819x^10 - 1557x^9 + 2016x^8 - 1316x^7 + 1529x^6 - 677x^5 + 542x^4 - 174x^3 + 127x^2 - 30x + 9	\( 3^{10}\cdot 71^{2}\cdot 401^{8} \)	20T141	$[2, 2, 2]$
20.12.1103422229363422399032900390625.1	x^20 - 3x^19 - 15x^18 + 38x^17 + 68x^16 - 38x^15 - 169x^14 - 767x^13 + 182x^12 + 2827x^11 + 372x^10 - 3149x^9 - 436x^8 + 687x^7 - 668x^6 + 487x^5 + 769x^4 - 181x^3 - 208x^2 + 3x + 9	\( 5^{10}\cdot 13^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.8.2357014347930150805034775390625.1	x^20 - 5x^19 + 26x^18 - 67x^17 + 125x^16 - 168x^15 + 10x^14 - 122x^13 - 174x^12 + 244x^11 - 203x^10 - 50x^9 + 90x^8 + 309x^7 + 536x^6 + 161x^5 - 88x^4 - 74x^3 - 9x^2 + 6x + 1	\( 5^{10}\cdot 19^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.0.2899386483136048131727057286409.1	x^20 - 2x^19 + 17x^18 - 4x^17 + 155x^16 - 50x^15 + 621x^14 - 17x^13 + 1572x^12 + 87x^11 + 2525x^10 + 811x^9 + 2589x^8 + 1042x^7 + 1857x^6 + 907x^5 + 667x^4 + 142x^3 + 44x^2 - 4x + 1	\( 3^{10}\cdot 271^{2}\cdot 401^{8} \)	20T141	$[2, 12]$ (GRH)
20.16.4759732575183046916538369140625.1	x^20 - x^19 - 7x^18 + 34x^17 - 95x^16 - 233x^15 + 728x^14 + 663x^13 - 1076x^12 - 1191x^11 - 1181x^10 + 2409x^9 + 3191x^8 - 3047x^7 - 1811x^6 + 1548x^5 + 311x^4 - 242x^3 - 31x^2 + 10x + 1	\( 3^{6}\cdot 5^{10}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.12.8938372970405474936544619140625.1	x^20 - 25x^18 + 216x^16 - 940x^14 + 3318x^12 - 10296x^10 + 21832x^8 - 27353x^6 + 18774x^4 - 6237x^2 + 729	\( 5^{10}\cdot 37^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.16.32913322237994155701330478515625.1	x^20 - x^19 - 31x^18 + 54x^17 + 295x^16 - 593x^15 - 1341x^14 + 2743x^13 + 3556x^12 - 6400x^11 - 6059x^10 + 8079x^9 + 6400x^8 - 5702x^7 - 3903x^6 + 2227x^5 + 1254x^4 - 438x^3 - 181x^2 + 30x + 9	\( 5^{10}\cdot 71^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.4.61432542935387226937873134765625.1	x^20 - 2x^19 - 4x^18 + 40x^17 - 24x^16 + 47x^15 + 208x^14 + 622x^13 + 421x^12 - 222x^11 - 1478x^10 - 1369x^9 - 659x^8 + 246x^7 + 268x^6 + 55x^5 + 12x^4 + 43x^3 - 16x^2 - x + 1	\( 5^{10}\cdot 97^{2}\cdot 401^{8} \)	20T141	$[9]$ (GRH)
20.20.1029048959454080715320570400390625.1	x^20 - 37x^18 + 526x^16 - 3728x^14 + 14503x^12 - 32241x^10 + 41027x^8 - 28660x^6 + 9799x^4 - 1190x^2 + 9	\( 5^{10}\cdot 397^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.20.1967884990250679730715474619140625.1	x^20 - 41x^18 + 668x^16 - 5534x^14 + 25006x^12 - 62974x^10 + 90469x^8 - 73305x^6 + 30966x^4 - 5336x^2 + 81	\( 3^{4}\cdot 5^{10}\cdot 61^{2}\cdot 401^{8} \)	20T141	Trivial (GRH)
20.0.3222585556571212807579035957723136.1	x^20 - 8x^19 + 22x^18 - 16x^17 + 15x^16 - 222x^15 + 390x^14 + 1598x^13 - 6037x^12 + 1344x^11 + 20357x^10 - 23534x^9 + 9710x^8 - 42100x^7 + 33296x^6 + 22698x^5 + 17985x^4 + 33158x^3 + 16835x^2 - 150018x + 145247	\( 2^{30}\cdot 67^{2}\cdot 401^{8} \)	20T141	$[39]$ (GRH)
20.4.31514842292848707138778668056640625.1	x^20 - 6x^19 + 15x^18 + 14x^17 - 193x^16 + 360x^15 - 488x^14 - 4116x^13 + 8622x^12 + 12570x^11 - 35089x^10 - 31355x^9 + 56360x^8 + 89618x^7 - 11621x^6 - 132550x^5 + 27869x^4 + 102969x^3 - 66339x^2 + 40581x - 21951	\( 5^{10}\cdot 13^{6}\cdot 401^{8} \)	20T141	$[2, 2]$ (GRH)
20.0.42390388623295510152536086938648576.1	x^20 - 10x^19 + 86x^18 - 468x^17 + 2186x^16 - 8164x^15 + 26400x^14 - 74414x^13 + 180306x^12 - 389440x^11 + 740054x^10 - 1218710x^9 + 1791009x^8 - 2307508x^7 + 2518702x^6 - 2490132x^5 + 2265462x^4 - 1623348x^3 + 964152x^2 - 615708x + 244053	\( 2^{30}\cdot 3^{10}\cdot 401^{8} \)	20T141	$[2, 2, 48]$ (GRH)