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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.62703695411604830748672.1	x^20 - 2x^19 + 5x^17 - x^16 - 6x^15 - 8x^14 + 22x^13 + 4x^12 - 32x^11 + 16x^10 + 10x^9 + 3x^8 - 30x^7 + 22x^6 + 5x^5 - 12x^4 + 4x^3 - 2x^2 + 3x - 1	\( -\,2^{16}\cdot 3^{5}\cdot 13^{14} \)	$C_2^2:F_5$ (as 20T22)	Trivial
20.2.640000000000000000000000.1	x^20 - 5x^18 + 5x^16 - 10x^14 + 45x^12 + x^10 - 45x^8 - 10x^6 - 5x^4 - 5x^2 - 1	\( -\,2^{28}\cdot 5^{22} \)	$C_2^2:F_5$ (as 20T22)	Trivial
20.4.3204867031250000000000000000.1	x^20 - 72x^15 - 712x^10 + 288x^5 + 16	\( 2^{16}\cdot 5^{22}\cdot 29^{5} \)	$C_2^2:F_5$ (as 20T22)	Trivial
20.0.16024335156250000000000000000.1	x^20 - 5x^19 + 10x^18 - 25x^17 + 70x^16 - 51x^15 - 50x^14 - 235x^13 + 895x^12 - 180x^11 - 384x^10 - 1430x^9 + 2595x^8 + 2575x^7 + 5100x^6 + 3749x^5 + 5420x^4 + 2385x^3 + 1760x^2 + 445x + 431	\( 2^{16}\cdot 5^{23}\cdot 29^{5} \)	$C_2^2:F_5$ (as 20T22)	$[2]$
20.4.19102496095001697540283203125.1	x^20 - 4x^15 - 183x^10 + 104x^5 + 1	\( 5^{30}\cdot 29^{5} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.0.95512480475008487701416015625.1	x^20 - 6x^15 - 439x^10 + 5344x^5 + 161051	\( 5^{31}\cdot 29^{5} \)	$C_2^2:F_5$ (as 20T22)	$[2]$ (GRH)
20.10.3689472640000000000000000000000.1	x^20 - 5x^18 - 115x^16 - 250x^14 + 525x^12 + 1201x^10 - 525x^8 - 250x^6 + 115x^4 - 5x^2 - 1	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.10.18447363200000000000000000000000.1	x^20 - 160x^16 + 2360x^12 - 4240x^8 + 1520x^4 - 80	\( -\,2^{28}\cdot 5^{23}\cdot 7^{8} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.2.1907348632812500000000000000000000.1	x^20 - 5	\( -\,2^{20}\cdot 5^{39} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.20.18475420666617031250000000000000000.1	x^20 - 5x^19 - 30x^18 + 160x^17 + 330x^16 - 1933x^15 - 1700x^14 + 11500x^13 + 4245x^12 - 36760x^11 - 5160x^10 + 65020x^9 + 4050x^8 - 63410x^7 - 3400x^6 + 31774x^5 + 1655x^4 - 6755x^3 + 100x^2 + 460x - 41	\( 2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 29^{5} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.0.19379770369172092530288888794611712.1	x^20 - 5x^19 - 11x^18 + 83x^17 + 56x^16 - 700x^15 + 105x^14 + 2882x^13 - 1781x^12 - 5757x^11 + 7777x^10 + 3940x^9 - 13469x^8 - 7812x^7 + 52825x^6 - 87721x^5 + 99762x^4 - 30932x^3 + 54617x^2 - 18028x + 20591	\( 2^{15}\cdot 17^{14}\cdot 37^{8} \)	$C_2^2:F_5$ (as 20T22)	$[4, 20]$ (GRH)
20.20.128406412316224387779791991644684288.1	x^20 - 3x^19 - 38x^18 + 109x^17 + 461x^16 - 1366x^15 - 2392x^14 + 7958x^13 + 5346x^12 - 23708x^11 - 2958x^10 + 37354x^9 - 7565x^8 - 29683x^7 + 13316x^6 + 9335x^5 - 6991x^4 + 252x^3 + 780x^2 - 208x + 16	\( 2^{16}\cdot 17^{5}\cdot 53^{14} \)	$C_2^2:F_5$ (as 20T22)	Trivial (GRH)
20.0.1854949516446736210185316359063535616.1	x^20 - 3x^19 - 8x^18 + 28x^17 - x^16 - 28x^15 + 212x^14 - 658x^13 + 2547x^12 - 587x^11 + 12252x^10 + 10456x^9 + 54982x^8 + 70259x^7 + 186965x^6 + 205103x^5 + 344870x^4 + 251547x^3 + 274509x^2 + 116534x + 141499	\( 2^{16}\cdot 29^{5}\cdot 53^{14} \)	$C_2^2:F_5$ (as 20T22)	$[2, 410]$ (GRH)