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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.173777417066788218208256.1	x^20 - 2x^19 + 4x^17 + 10x^16 - 14x^15 - 14x^14 + 16x^13 + 67x^12 + 6x^11 - 54x^10 - 40x^9 + 129x^8 + 186x^7 + 192x^6 + 206x^5 + 293x^4 + 250x^3 + 128x^2 + 36x + 5	\( 2^{30}\cdot 29^{5}\cdot 53^{4} \)	20T168	Trivial
20.0.317593210501371571208192.1	x^20 - 4x^18 + 4x^16 + 2x^14 + 16x^12 - 30x^10 - 35x^8 + 104x^6 - 30x^4 - 80x^2 + 53	\( 2^{30}\cdot 29^{4}\cdot 53^{5} \)	20T168	Trivial
20.2.1335973502986240000000000.1	x^20 + 4x^18 + 5x^16 + 4x^14 + 5x^12 + 6x^10 - x^8 - 13x^4 + x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T168	Trivial
20.2.1335973502986240000000000.2	x^20 - 4x^18 + 5x^16 - 4x^14 + 5x^12 - 6x^10 - x^8 - 13x^4 - x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T168	Trivial
20.10.201484463662828739248046875.1	x^20 - 2x^19 - 11x^18 + 16x^17 + 40x^16 - 41x^15 - 71x^14 + 42x^13 + 39x^12 - 27x^11 + 159x^10 + 4x^9 - 369x^8 - 61x^7 + 444x^6 + 7x^5 - 200x^4 + 2x^3 + 29x^2 - x - 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T168	Trivial (GRH)
20.10.1242593181789399040000000000.1	x^20 - 7x^18 + 20x^16 - 8x^14 - 145x^12 + 486x^10 - 688x^8 + 468x^6 - 146x^4 + 21x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T168	Trivial (GRH)
20.2.1242593181789399040000000000.1	x^20 + 7x^18 + 20x^16 + 8x^14 - 145x^12 - 486x^10 - 688x^8 - 468x^6 - 146x^4 - 21x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T168	Trivial (GRH)
20.10.1303586853480048640000000000.1	x^20 - 8x^18 + 14x^16 + 29x^14 - 105x^12 + 88x^10 - 13x^8 + 8x^6 - 21x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3359^{4} \)	20T168	Trivial (GRH)
20.2.1303586853480048640000000000.1	x^20 + 8x^18 + 14x^16 - 29x^14 - 105x^12 - 88x^10 - 13x^8 - 8x^6 - 21x^4 - 9x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3359^{4} \)	20T168	Trivial (GRH)
20.10.18016952829639264630654296875.1	x^20 - x^19 - 11x^18 + 16x^17 + 24x^16 - 47x^15 + 56x^14 + 12x^13 - 287x^12 - 486x^11 + 1015x^10 + 1549x^9 - 2096x^8 + 713x^7 + 922x^6 - 2653x^5 + 1445x^4 + 757x^3 - 944x^2 + 295x - 29	\( -\,5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T168	Trivial (GRH)
20.0.4124166770359015413760000000000.1	x^20 + 10x^18 - 31x^16 - 390x^14 + 476x^12 + 4449x^10 - 4671x^8 - 4287x^6 + 17411x^4 + 15564x^2 + 3319	\( 2^{20}\cdot 5^{10}\cdot 3319^{5} \)	20T168	$[28]$ (GRH)
20.12.4124166770359015413760000000000.1	x^20 - 10x^18 - 31x^16 + 390x^14 + 476x^12 - 4449x^10 - 4671x^8 + 4287x^6 + 17411x^4 - 15564x^2 + 3319	\( 2^{20}\cdot 5^{10}\cdot 3319^{5} \)	20T168	Trivial (GRH)
20.0.4378748240839483381760000000000.1	x^20 + 10x^18 + 29x^16 + 10x^14 - 44x^12 + 381x^10 + 4489x^8 + 18337x^6 + 30671x^4 + 17956x^2 + 3359	\( 2^{20}\cdot 5^{10}\cdot 3359^{5} \)	20T168	$[20]$ (GRH)
20.12.4378748240839483381760000000000.1	x^20 - 10x^18 + 29x^16 - 10x^14 - 44x^12 - 381x^10 + 4489x^8 - 18337x^6 + 30671x^4 - 17956x^2 + 3359	\( 2^{20}\cdot 5^{10}\cdot 3359^{5} \)	20T168	Trivial (GRH)
20.0.211271772969714308085760000000000.1	x^20 + 29x^18 + 320x^16 + 1804x^14 + 5753x^12 + 10700x^10 + 11469x^8 + 6802x^6 + 2144x^4 + 330x^2 + 19	\( 2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T168	$[178]$ (GRH)
20.20.211271772969714308085760000000000.1	x^20 - 29x^18 + 320x^16 - 1804x^14 + 5753x^12 - 10700x^10 + 11469x^8 - 6802x^6 + 2144x^4 - 330x^2 + 19	\( 2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T168	Trivial (GRH)
20.0.18892144330291821549352960000000000.1	x^20 + 44x^18 + 646x^16 + 4788x^14 + 20635x^12 + 54632x^10 + 89857x^8 + 89868x^6 + 51571x^4 + 15088x^2 + 1699	\( 2^{20}\cdot 5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T168	$[1246]$ (GRH)
20.20.18892144330291821549352960000000000.1	x^20 - 44x^18 + 646x^16 - 4788x^14 + 20635x^12 - 54632x^10 + 89857x^8 - 89868x^6 + 51571x^4 - 15088x^2 + 1699	\( 2^{20}\cdot 5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T168	Trivial (GRH)
20.0.10800753337779736826690692535166015625.1	x^20 - 3x^19 + 120x^18 - 311x^17 + 6424x^16 - 14503x^15 + 202822x^14 - 400895x^13 + 4194686x^12 - 7251477x^11 + 59444659x^10 - 88813431x^9 + 583819605x^8 - 732444355x^7 + 3910053860x^6 - 3897482918x^5 + 17011183013x^4 - 12094971499x^3 + 43219440899x^2 - 16688451949x + 48517907351	\( 5^{10}\cdot 31^{4}\cdot 71^{4}\cdot 2161^{5} \)	20T168	$[2, 22]$ (GRH)
20.0.10800753337779736826690692535166015625.2	x^20 - 7x^19 + 139x^18 - 782x^17 + 8304x^16 - 38164x^15 + 282210x^14 - 1066070x^13 + 6059682x^12 - 18764856x^11 + 86065041x^10 - 215819750x^9 + 820377495x^8 - 1623921679x^7 + 5194846005x^6 - 7728153702x^5 + 20977732177x^4 - 21172817140x^3 + 48965425278x^2 - 25512798670x + 50483698079	\( 5^{10}\cdot 31^{4}\cdot 71^{4}\cdot 2161^{5} \)	20T168	$[11]$ (GRH)
20.4.20496413448242187500000000000000000000.1	x^20 + 20x^18 + 170x^16 + 800x^14 + 2275x^12 + 3972x^10 + 3970x^8 + 1520x^6 - 775x^4 - 700x^2 + 176	\( 2^{20}\cdot 5^{30}\cdot 11^{5}\cdot 19^{4} \)	20T168	Trivial (GRH)
20.4.177014479780273437500000000000000000000.1	x^20 - 20x^18 + 255x^16 - 2070x^14 + 10740x^12 - 24045x^10 - 9775x^8 + 152600x^6 + 758075x^4 - 2663025x^2 + 969095	\( 2^{20}\cdot 5^{31}\cdot 11^{4}\cdot 19^{5} \)	20T168	$[2, 2]$ (GRH)