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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.14861658978964734748713.1	x^20 - 5x^19 + 16x^18 - 46x^17 + 108x^16 - 214x^15 + 395x^14 - 698x^13 + 1123x^12 - 1588x^11 + 2057x^10 - 2588x^9 + 3128x^8 - 3348x^7 + 2932x^6 - 1996x^5 + 1016x^4 - 371x^3 + 92x^2 - 14x + 1	\( 3^{5}\cdot 11^{19} \)	$C_5\times D_4$ (as 20T12)	Trivial
20.0.17374741604663223378125.1	x^20 - 5x^19 + 15x^18 - 36x^17 + 74x^16 - 131x^15 + 201x^14 - 267x^13 + 304x^12 - 291x^11 + 230x^10 - 116x^9 - 15x^8 + 80x^7 - 63x^6 + 21x^5 + 8x^4 - 19x^3 + 15x^2 - 6x + 1	\( 5^{5}\cdot 11^{18} \)	$C_5\times D_4$ (as 20T12)	Trivial
20.10.3611383131888430543937259.1	x^20 - 3x^19 - 7x^18 + 25x^17 + 4x^16 - 27x^15 + 17x^14 - 191x^13 + 37x^12 + 613x^11 - 33x^10 - 796x^9 - 208x^8 + 490x^7 + 329x^6 - 71x^5 - 145x^4 - 46x^3 + 5x^2 + 6x + 1	\( -\,3^{10}\cdot 11^{19} \)	$C_5\times D_4$ (as 20T12)	Trivial
20.10.4936006137688415732421875.1	x^20 - 4x^19 - x^18 + 28x^17 - 60x^16 + 45x^15 + 65x^14 - 215x^13 + 233x^12 - x^11 - 318x^10 + 407x^9 - 158x^8 - 175x^7 + 270x^6 - 75x^5 - 110x^4 + 46x^3 + 24x^2 - 2x - 1	\( -\,5^{10}\cdot 11^{17} \)	$C_5\times D_4$ (as 20T12)	Trivial (GRH)
20.0.81693426134005631737181457408.1	x^20 - 8x^19 + 40x^18 - 117x^17 + 251x^16 - 300x^15 + 303x^14 - 64x^13 + 654x^12 - 836x^11 + 1629x^10 + 352x^9 - 442x^8 + 1545x^7 + 3077x^6 + 1939x^5 + 1665x^4 + 2206x^3 + 406x^2 + 95x + 661	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	$C_5\times D_4$ (as 20T12)	$[10]$
20.20.81693426134005631737181457408.1	x^20 - 5x^19 - 18x^18 + 118x^17 + 63x^16 - 1022x^15 + 498x^14 + 4100x^13 - 4382x^12 - 7485x^11 + 12429x^10 + 3921x^9 - 14821x^8 + 3875x^7 + 6273x^6 - 3851x^5 - 190x^4 + 641x^3 - 150x^2 + 5x + 1	\( 2^{10}\cdot 3^{15}\cdot 11^{18} \)	$C_5\times D_4$ (as 20T12)	Trivial (GRH)
20.0.118337802465720092063736102912.1	x^20 - 4x^19 + 12x^18 - 32x^17 + 91x^16 - 126x^15 + 349x^14 - 606x^13 + 1765x^12 - 3140x^11 + 5896x^10 - 8688x^9 + 11729x^8 - 12648x^7 + 11673x^6 - 7892x^5 + 4643x^4 - 688x^3 - 849x^2 + 428x + 463	\( 2^{15}\cdot 3^{10}\cdot 11^{19} \)	$C_5\times D_4$ (as 20T12)	$[2, 4]$
20.20.118337802465720092063736102912.1	x^20 - 8x^19 + 4x^18 + 118x^17 - 260x^16 - 490x^15 + 1920x^14 + 114x^13 - 5672x^12 + 3567x^11 + 7304x^10 - 8202x^9 - 3013x^8 + 6759x^7 - 980x^6 - 1898x^5 + 680x^4 + 134x^3 - 83x^2 + 5x + 1	\( 2^{15}\cdot 3^{10}\cdot 11^{19} \)	$C_5\times D_4$ (as 20T12)	Trivial (GRH)