Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.32289424279912035447849.1	x^20 - 3x^15 + 9x^14 - 6x^12 + 6x^10 - 9x^8 + 9x^7 - 9x^5 + 18x^4 - 27x^3 + 36x^2 - 27x + 9	\( 3^{18}\cdot 11^{6}\cdot 19^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.0.47644389152686853402121.1	x^20 - x^19 + 4x^18 - 3x^17 + 9x^16 + 9x^14 + 9x^13 + 6x^12 + 23x^11 + 7x^10 + 23x^9 + 6x^8 + 9x^7 + 9x^6 + 9x^4 - 3x^3 + 4x^2 - x + 1	\( 3^{18}\cdot 223^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.0.118438005369159252085761.1	x^20 - x^19 + 5x^17 - 2x^16 - 4x^15 + 14x^14 - 3x^13 - x^12 + 19x^11 - 9x^10 + x^9 + 12x^8 - 11x^7 + 6x^6 + 7x^5 - 4x^4 + 5x^3 + 2x^2 - x + 1	\( 3^{10}\cdot 1123^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.4.223904745130829775390625.1	x^20 - 4x^18 - 4x^17 - x^16 + 15x^15 + 33x^14 - 21x^13 - 80x^12 + 16x^11 + 108x^10 - 15x^9 - 97x^8 + 34x^7 + 55x^6 - 35x^5 - 15x^4 + 13x^3 + 2x^2 - 5x + 1	\( 5^{10}\cdot 13^{6}\cdot 41^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.0.874231651432481601634281.1	x^20 - 2x^19 - x^18 + 6x^17 - 5x^16 - 4x^15 + 9x^14 - 8x^13 + 5x^12 + 6x^11 - 13x^10 + 6x^9 + 5x^8 - 8x^7 + 9x^6 - 4x^5 - 5x^4 + 6x^3 - x^2 - 2x + 1	\( 3^{10}\cdot 1567^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.4.1679266481181638363313121.1	x^20 - 3x^19 - 5x^18 + 16x^17 + 18x^16 - 37x^15 - 38x^14 + 21x^13 + 35x^12 + 60x^11 - 5x^10 - 82x^9 + 10x^8 + x^7 - 53x^6 + 32x^5 + 21x^4 - 22x^3 + 11x^2 + x + 1	\( 17^{10}\cdot 97^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.8.29160000000000000000000000.1	x^20 - 10x^18 - 10x^17 + 25x^16 + 36x^15 - 25x^14 - 40x^13 - 45x^12 - 50x^11 + 97x^10 + 50x^9 - 45x^8 + 40x^7 - 25x^6 - 36x^5 + 25x^4 + 10x^3 - 10x^2 + 1	\( 2^{24}\cdot 3^{6}\cdot 5^{22} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.8.47136806640625000000000000.1	x^20 - 5x^18 - 5x^17 + 20x^16 + 13x^15 - 70x^14 + 110x^12 + 5x^11 - 116x^10 - 5x^9 + 110x^8 - 70x^6 - 13x^5 + 20x^4 + 5x^3 - 5x^2 + 1	\( 2^{12}\cdot 5^{22}\cdot 13^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.0.11011450072223110345423202389329.1	x^20 - x^19 + 4x^18 + 3x^17 - 15x^16 + 24x^15 - 51x^14 - 27x^13 + 72x^12 - 135x^11 + 405x^10 - 405x^9 + 648x^8 - 729x^7 - 4131x^6 + 5832x^5 - 10935x^4 + 6561x^3 + 26244x^2 - 19683x + 59049	\( 3^{14}\cdot 11491^{6} \)	$C_2\times S_5$ (as 20T62)	$[9]$ (GRH)
20.0.11803130064401712301503252791296.1	x^20 - 2x^19 + x^18 - 2x^17 + 6x^16 - 12x^15 + 18x^14 - 24x^13 + 32x^12 - 48x^11 + 80x^10 - 96x^9 + 128x^8 - 192x^7 + 288x^6 - 384x^5 + 384x^4 - 256x^3 + 256x^2 - 1024x + 1024	\( 2^{28}\cdot 13^{6}\cdot 457^{6} \)	$C_2\times S_5$ (as 20T62)	$[42]$ (GRH)
20.20.19356024941343968143360000000000.1	x^20 - 2x^19 - 32x^18 + 50x^17 + 396x^16 - 494x^15 - 2496x^14 + 2434x^13 + 8869x^12 - 6324x^11 - 18596x^10 + 8580x^9 + 23081x^8 - 5240x^7 - 16182x^6 + 300x^5 + 5588x^4 + 832x^3 - 634x^2 - 140x + 5	\( 2^{20}\cdot 5^{10}\cdot 17^{6}\cdot 23^{8} \)	$C_2\times S_5$ (as 20T62)	Trivial (GRH)
20.20.201997953325162874882560000000000.1	x^20 - 8x^19 - 7x^18 + 219x^17 - 387x^16 - 1897x^15 + 6363x^14 + 4692x^13 - 39284x^12 + 18927x^11 + 114437x^10 - 137699x^9 - 143822x^8 + 309409x^7 + 15158x^6 - 295673x^5 + 105445x^4 + 103459x^3 - 55470x^2 - 9313x + 5431	\( 2^{18}\cdot 5^{10}\cdot 307^{8} \)	$C_2\times S_5$ (as 20T62)	Trivial (GRH)