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 25 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.784827703284623883644266441.1	x^20 - 8x^19 + 21x^18 - 111x^16 + 173x^15 + 144x^14 - 649x^13 + 397x^12 + 839x^11 - 1816x^10 + 800x^9 + 1134x^8 - 1848x^7 + 716x^6 + 421x^5 - 727x^4 + 330x^3 - 78x^2 - 3x + 1	\( 11^{18}\cdot 109^{4} \)	20T331	Trivial (GRH)
20.8.784827703284623883644266441.1	x^20 - 5x^19 + 4x^18 + 19x^17 - 36x^16 - 21x^15 + 124x^14 - 168x^13 - 70x^12 + 897x^11 - 1200x^10 - 1238x^9 + 3967x^8 - 679x^7 - 5024x^6 + 3123x^5 + 2714x^4 - 2681x^3 - 293x^2 + 720x - 131	\( 11^{18}\cdot 109^{4} \)	20T331	Trivial (GRH)
20.12.50522262278163705147147943936.4	x^20 - 8x^18 + 13x^16 + 8x^14 + 35x^12 - 66x^10 - 31x^8 + 52x^6 + 2x^4 - 8x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.12.50522262278163705147147943936.5	x^20 - 10x^18 + 43x^16 - 104x^14 + 149x^12 - 110x^10 + 8x^8 + 40x^6 - 15x^4 - 2x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.4.50522262278163705147147943936.13	x^20 + 8x^18 + 13x^16 - 8x^14 + 35x^12 + 66x^10 - 31x^8 - 52x^6 + 2x^4 + 8x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.8.50522262278163705147147943936.13	x^20 + 2x^18 - 15x^16 + 4x^14 + 41x^12 - 88x^10 + 28x^8 + 60x^6 - 23x^4 - 12x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.4.50522262278163705147147943936.14	x^20 + 10x^18 + 43x^16 + 104x^14 + 149x^12 + 110x^10 + 8x^8 - 40x^6 - 15x^4 + 2x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.8.50522262278163705147147943936.14	x^20 - 2x^18 - 15x^16 - 4x^14 + 41x^12 + 88x^10 + 28x^8 - 60x^6 - 23x^4 + 12x^2 + 1	\( 2^{40}\cdot 11^{16} \)	20T331	Trivial (GRH)
20.8.6113193735657808322804901216256.5	x^20 + 8x^18 + 9x^16 - 38x^14 - 51x^12 + 54x^10 + 14x^8 - 64x^6 + 159x^4 - 26x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.8.6113193735657808322804901216256.6	x^20 - 4x^18 - 17x^16 + 24x^14 + 25x^12 - 34x^10 + 37x^8 - 126x^6 + 130x^4 - 36x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.4.6113193735657808322804901216256.7	x^20 + 10x^18 + 45x^16 + 120x^14 + 122x^12 - 276x^10 - 967x^8 - 1068x^6 - 461x^4 - 34x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.8.6113193735657808322804901216256.7	x^20 + 2x^18 - 18x^16 - 36x^14 + 93x^12 + 164x^10 - 211x^8 - 180x^6 + 377x^4 - 126x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.4.6113193735657808322804901216256.8	x^20 + 10x^18 + x^16 - 122x^14 + 111x^12 + 274x^10 - 208x^8 + 10x^6 + x^4 - 12x^2 + 1	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.4.6113193735657808322804901216256.9	x^20 + 2x^18 - 7x^16 - 14x^14 - 72x^12 - 56x^10 + 625x^8 + 282x^6 - 1251x^4 - 412x^2 + 529	\( 2^{40}\cdot 11^{18} \)	20T331	Trivial (GRH)
20.0.14138200398183609412083027778994176.3	x^20 - 8x^18 + 24x^16 + 96x^14 + 640x^12 + 2112x^10 + 14016x^8 + 53248x^6 + 199168x^4 + 329728x^2 + 541696	\( 2^{40}\cdot 11^{16}\cdot 23^{4} \)	20T331	$[4]$ (GRH)
20.0.14138200398183609412083027778994176.4	x^20 + 12x^18 + 89x^16 + 210x^14 + x^12 - 2848x^10 - 109x^8 - 8040x^6 + 58444x^4 - 152030x^2 + 279841	\( 2^{40}\cdot 11^{16}\cdot 23^{4} \)	20T331	$[4]$ (GRH)
20.0.142074815881149027354713197399801593856.1	x^20 + 121x^18 + 5932x^16 + 152482x^14 + 2232986x^12 + 19074528x^10 + 94432719x^8 + 264094303x^6 + 392014338x^4 + 267981054x^2 + 54302161	\( 2^{20}\cdot 11^{16}\cdot 7369^{4} \)	20T331	$[2, 4, 21684]$ (GRH)
20.0.142074815881149027354713197399801593856.2	x^20 + 103x^18 + 4218x^16 + 91023x^14 + 1151428x^12 + 8938062x^10 + 42995286x^8 + 125455236x^6 + 209321704x^4 + 176362277x^2 + 54302161	\( 2^{20}\cdot 11^{16}\cdot 7369^{4} \)	20T331	$[2, 2, 50316]$ (GRH)
20.16.3956448137628099441486726576701509206016.1	x^20 - 80x^18 + 2341x^16 - 29870x^14 + 151221x^12 - 175704x^10 - 874464x^8 + 2802780x^6 - 2229321x^4 - 595654x^2 + 978121	\( 2^{40}\cdot 11^{16}\cdot 23^{8} \)	20T331	Trivial (GRH)
20.16.3956448137628099441486726576701509206016.2	x^20 - 24x^18 - 188x^16 + 9328x^14 - 69680x^12 - 126848x^10 + 3090432x^8 - 10103808x^6 + 10698496x^4 - 4333568x^2 + 541696	\( 2^{40}\cdot 11^{16}\cdot 23^{8} \)	20T331	Trivial (GRH)
20.20.17191052721619032309920296885375992856576.1	x^20 - 143x^18 + 8437x^16 - 270083x^14 + 5181616x^12 - 62146183x^10 + 472121067x^8 - 2248682392x^6 + 6447181169x^4 - 10085441839x^2 + 6570561481	\( 2^{20}\cdot 11^{18}\cdot 7369^{4} \)	20T331	Trivial (GRH)
20.20.17191052721619032309920296885375992856576.2	x^20 - 165x^18 + 11473x^16 - 438383x^14 + 10041889x^12 - 140937236x^10 + 1188999845x^8 - 5709838629x^6 + 14341314097x^4 - 16233361694x^2 + 6570561481	\( 2^{20}\cdot 11^{18}\cdot 7369^{4} \)	20T331	Trivial (GRH)
20.8.17165941082918625907388507845862234378814751768576.1	x^20 + 48x^18 - 66884x^16 - 7164256x^14 + 490247200x^12 + 63743484160x^10 + 99168290752x^8 - 51749801951232x^6 - 623091135441152x^4 - 584275946368000x^2 + 2350270064813056	\( 2^{40}\cdot 11^{16}\cdot 23^{8}\cdot 199^{2}\cdot 331^{2} \)	20T331	$[2, 2, 2]$ (GRH)
20.8.17165941082918625907388507845862234378814751768576.2	x^20 + 80x^18 - 54002x^16 - 3480624x^14 + 566715315x^12 + 6739768564x^10 - 1371610846859x^8 + 8416391205200x^6 + 450513883311701x^4 + 701568715396758x^2 + 277717458830449	\( 2^{40}\cdot 11^{16}\cdot 23^{8}\cdot 199^{2}\cdot 331^{2} \)	20T331	$[2, 2, 2]$ (GRH)
20.8.74478300488702629539932974793088386039042768856289940340736.1	x^20 - 1120x^18 - 5285397x^16 - 2948764734x^14 + 1452248809698x^12 + 1562655693365106x^10 + 302048559639192771x^8 - 33560109862573395248x^6 - 10712944772094516747441x^4 - 147763063047639772279068x^2 + 18412673999053943482324441	\( 2^{40}\cdot 11^{16}\cdot 23^{8}\cdot 199^{4}\cdot 331^{4} \)	20T331	$[2, 2, 2, 2, 2]$ (GRH)