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
20.0.66045000696445844586496.1	x^20 - 2x^16 + 3x^14 + x^12 - 2x^10 + x^8 + 3x^6 - 2x^4 + 1	\( 2^{24}\cdot 89^{8} \)	20T226	Trivial (GRH)
20.0.68020707707819889350409.1	x^20 - 2x^19 + 3x^18 - 2x^16 - x^15 - 6x^14 + 4x^13 - x^12 - x^11 + 11x^10 - x^9 - x^8 + 4x^7 - 6x^6 - x^5 - 2x^4 + 3x^2 - 2x + 1	\( 3^{10}\cdot 181^{8} \)	20T226	Trivial (GRH)
20.0.4226880044572534053535744.1	x^20 - 10x^19 + 50x^18 - 162x^17 + 381x^16 - 696x^15 + 1032x^14 - 1242x^13 + 1134x^12 - 648x^11 + 484x^9 - 611x^8 + 428x^7 - 136x^6 - 84x^5 + 164x^4 - 136x^3 + 72x^2 - 24x + 4	\( 2^{30}\cdot 89^{8} \)	20T226	$[2]$
20.4.6887475360000000000000000.1	x^20 - 20x^16 + 100x^12 - 124x^10 + 60x^8 - 40x^6 + 40x^4 - 20x^2 + 4	\( 2^{20}\cdot 3^{16}\cdot 5^{16} \)	20T226	Trivial (GRH)
20.4.11654783511381160590876241.1	x^20 - 4x^19 + 4x^18 + 2x^17 - 9x^16 + 2x^15 + 26x^14 + 35x^13 - 106x^12 - 103x^11 + 122x^10 + 153x^9 + 16x^8 - 22x^7 - 108x^6 - 153x^5 - 12x^4 + 63x^3 + 56x^2 + 55x + 25	\( 13^{12}\cdot 29^{8} \)	20T226	Trivial (GRH)
20.0.870517771377771111824490496.1	x^20 - 4x^18 + 2x^16 + 6x^14 + 5x^12 - 4x^10 + 5x^8 + 6x^6 + 2x^4 - 4x^2 + 1	\( 2^{36}\cdot 103^{8} \)	20T226	$[2]$ (GRH)
20.12.17031712842465295728640000000000.1	x^20 - 3x^18 - 139x^16 - 156x^14 + 1424x^12 - 132x^10 - 2468x^8 + 720x^6 + 736x^4 - 240x^2 + 16	\( 2^{32}\cdot 5^{10}\cdot 67^{8} \)	20T226	Trivial (GRH)
20.12.28800379907535799561915674394624.1	x^20 - 10x^19 + 23x^18 + 78x^17 - 393x^16 + 84x^15 + 1948x^14 - 2458x^13 - 3419x^12 + 8112x^11 - 73x^10 - 9398x^9 + 4651x^8 + 3002x^7 - 1744x^6 - 708x^5 + 141x^4 + 140x^3 + 27x^2 - 4x - 1	\( 2^{20}\cdot 13^{14}\cdot 17^{8} \)	20T226	Trivial (GRH)
20.4.460806078520572792990650790313984.1	x^20 - 10x^19 + 39x^18 - 66x^17 + 55x^16 - 236x^15 + 876x^14 - 778x^13 - 921x^12 - 844x^11 + 5685x^10 + 5394x^9 - 19361x^8 - 13338x^7 + 25610x^6 + 54392x^5 - 13091x^4 - 122148x^3 - 60515x^2 + 139256x + 118469	\( 2^{24}\cdot 13^{14}\cdot 17^{8} \)	20T226	Trivial (GRH)
20.4.4360118487671115706531840000000000.1	x^20 + 12x^18 - 82x^16 - 1392x^14 - 4669x^12 - 3648x^10 + 7790x^8 + 16884x^6 + 11585x^4 + 3024x^2 + 256	\( 2^{40}\cdot 5^{10}\cdot 67^{8} \)	20T226	$[2]$ (GRH)
20.20.17859045325500889933954416640000000000.1	x^20 - 37x^18 + 517x^16 - 3516x^14 + 12606x^12 - 24810x^10 + 26734x^8 - 14804x^6 + 3461x^4 - 133x^2 + 1	\( 2^{52}\cdot 5^{10}\cdot 67^{8} \)	20T226	Trivial (GRH)
20.20.125265573758493326836079165440000000000.1	x^20 - 77x^18 + 2475x^16 - 43054x^14 + 439496x^12 - 2669912x^10 + 9338864x^8 - 17142880x^6 + 13155456x^4 - 1740160x^2 + 6400	\( 2^{24}\cdot 5^{10}\cdot 967^{8} \)	20T226	Trivial (GRH)