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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.132745109443598544921875.1	x^20 - 3x^19 + x^18 - x^17 + 14x^16 - 8x^15 - 9x^14 - 10x^13 + 6x^12 + 15x^11 - 24x^10 + 16x^9 + 31x^8 - 29x^7 + 3x^6 + 7x^5 - 24x^4 - 7x^3 + 3x^2 - 2x + 1	\( -\,5^{10}\cdot 7^{8}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial
20.2.6504510362736328701171875.1	x^20 - 4x^19 + 11x^18 - 28x^17 + 57x^16 - 95x^15 + 115x^14 - 79x^13 - 5x^12 + 136x^11 - 271x^10 + 247x^9 + 30x^8 - 395x^7 + 602x^6 - 575x^5 + 396x^4 - 194x^3 + 63x^2 - 12x + 1	\( -\,5^{10}\cdot 7^{10}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial
20.0.139193335879930787840000000000.1	x^20 - x^18 + 6x^16 + 27x^14 - 7x^12 + 98x^10 + 143x^8 + 22x^6 - 44x^4 - 11x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 7^{8}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[2]$
20.4.139193335879930787840000000000.1	x^20 + x^18 + 6x^16 - 27x^14 - 7x^12 - 98x^10 + 143x^8 - 22x^6 - 44x^4 + 11x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 7^{8}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)
20.0.6820473458116608604160000000000.1	x^20 - 14x^16 + 49x^14 - 27x^12 - 259x^10 + 1001x^8 - 1925x^6 + 2277x^4 - 1617x^2 + 539	\( 2^{20}\cdot 5^{10}\cdot 7^{10}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[2, 4]$ (GRH)
20.4.6820473458116608604160000000000.1	x^20 - 14x^16 - 49x^14 - 27x^12 + 259x^10 + 1001x^8 + 1925x^6 + 2277x^4 + 1617x^2 + 539	\( 2^{20}\cdot 5^{10}\cdot 7^{10}\cdot 11^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)
20.0.16294596052685417602356719970703125.1	x^20 - 3x^19 - 7x^18 + 20x^17 + 17x^16 + 2x^15 - 183x^14 - 994x^13 + 1277x^12 + 6377x^11 + 6339x^10 + 16463x^9 + 37015x^8 + 31607x^7 + 25138x^6 + 8148x^5 + 11280x^4 + 8667x^3 + 3708x^2 + 810x + 81	\( 3^{8}\cdot 5^{17}\cdot 71^{10} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[7]$ (GRH)
20.0.16294596052685417602356719970703125.2	x^20 - 6x^19 + 32x^18 - 53x^17 + 33x^16 + 456x^15 - 1283x^14 + 2494x^13 - 561x^12 - 5839x^11 + 18597x^10 - 25026x^9 + 12058x^8 + 36503x^7 - 77348x^6 + 88536x^5 + 54681x^4 - 177390x^3 + 387585x^2 - 291600x + 273375	\( 3^{8}\cdot 5^{17}\cdot 71^{10} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[7]$ (GRH)
20.10.8925264962285150499914914463751340032.1	x^20 - 4x^19 - 26x^18 + 116x^17 + 147x^16 - 1168x^15 + 1262x^14 + 4360x^13 - 20145x^12 + 18456x^11 + 145308x^10 - 283164x^9 - 958240x^8 + 755896x^7 + 3904306x^6 + 2146840x^5 - 4193927x^4 - 6818088x^3 - 3970514x^2 - 996780x - 78119	\( -\,2^{20}\cdot 3^{10}\cdot 7^{8}\cdot 11^{9}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)
20.10.8925264962285150499914914463751340032.2	x^20 - 4x^19 - 28x^18 + 82x^17 + 227x^16 + 150x^15 + 165x^14 - 12260x^13 - 15111x^12 + 57640x^11 + 79121x^10 + 238244x^9 + 9741x^8 - 1466670x^7 + 764544x^6 + 2289288x^5 - 2361935x^4 - 523652x^3 + 1541335x^2 - 635210x + 69001	\( -\,2^{20}\cdot 3^{10}\cdot 7^{8}\cdot 11^{9}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)
20.0.830861029216363101082988400989215653888.1	x^20 - 50x^17 + 45x^16 - 1954x^15 + 1146x^14 - 8728x^13 + 35720x^12 + 63452x^11 + 399454x^10 + 1381924x^9 + 4593593x^8 + 10877422x^7 + 18625392x^6 + 18362518x^5 + 8907493x^4 + 1360618x^3 + 2035604x^2 + 3955342x + 2849617	\( 2^{30}\cdot 3^{10}\cdot 7^{8}\cdot 11^{8}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[1102]$ (GRH)
20.20.830861029216363101082988400989215653888.1	x^20 - 2x^19 - 70x^18 + 130x^17 + 1884x^16 - 3176x^15 - 26030x^14 + 38676x^13 + 204088x^12 - 258790x^11 - 929382x^10 + 972558x^9 + 2376321x^8 - 1981016x^7 - 3070474x^6 + 1939996x^5 + 1575260x^4 - 643258x^3 - 248460x^2 + 15576x + 6157	\( 2^{30}\cdot 3^{10}\cdot 7^{8}\cdot 11^{8}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)
20.0.830861029216363101082988400989215653888.2	x^20 - 2x^19 + 10x^18 - 18x^17 + 177x^16 - 298x^15 + 684x^14 - 1574x^13 - 11369x^12 + 20752x^11 - 138456x^10 + 250450x^9 - 413105x^8 - 313688x^7 + 3541782x^6 - 3181752x^5 + 24408428x^4 + 3387604x^3 + 45176274x^2 + 4594876x + 17487613	\( 2^{30}\cdot 3^{10}\cdot 7^{8}\cdot 11^{8}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	$[5, 290]$ (GRH)
20.20.830861029216363101082988400989215653888.2	x^20 - 84x^18 - 8x^17 + 2529x^16 - 800x^15 - 36852x^14 + 32222x^13 + 265203x^12 - 384760x^11 - 789498x^10 + 1688544x^9 + 475396x^8 - 2699058x^7 + 1031692x^6 + 1263226x^5 - 1003929x^4 + 81360x^3 + 87522x^2 - 13042x - 1367	\( 2^{30}\cdot 3^{10}\cdot 7^{8}\cdot 11^{8}\cdot 13^{9} \)	$C_{10}^2:C_2^2$ (as 20T106)	Trivial (GRH)