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
20.6.18783695020114406357421875.1	x^20 - 3x^19 + 3x^18 - 10x^17 + 18x^16 - 12x^15 + 27x^14 - 18x^13 + 32x^12 - 59x^11 - 5x^10 - 29x^9 - 66x^8 + 26x^7 - 4x^6 + 15x^5 + 39x^4 + 3x^3 - 15x^2 - 3x + 1	\( -\,5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T547	Trivial (GRH)
20.6.2272827097433843169248046875.1	x^20 - x^19 + 4x^18 - 12x^17 - 4x^16 + 3x^15 - x^14 + 59x^13 - 29x^12 + 21x^11 - 20x^10 - 28x^9 - 29x^8 - 3x^7 + 4x^6 - 54x^5 - 2x^4 + 25x^3 + 8x^2 - 1	\( -\,5^{10}\cdot 11^{11}\cdot 13^{8} \)	20T547	Trivial (GRH)
20.0.76214743566869006476722044928.1	x^20 - 4x^18 + 12x^16 - 24x^14 + 39x^12 - 48x^10 + 54x^8 - 12x^6 + 57x^4 + 16x^2 + 8	\( 2^{59}\cdot 3^{8}\cdot 67^{4} \)	20T547	Trivial (GRH)
20.0.76214743566869006476722044928.2	x^20 + 4x^18 + 12x^16 + 24x^14 + 39x^12 + 48x^10 + 54x^8 + 12x^6 + 57x^4 - 16x^2 + 8	\( 2^{59}\cdot 3^{8}\cdot 67^{4} \)	20T547	Trivial (GRH)
20.0.96479729228174488169059713024.1	x^20 - 4x^19 + 8x^18 + 8x^17 - 62x^16 + 160x^15 - 136x^14 - 104x^13 + 748x^12 - 1200x^11 + 1416x^10 - 456x^9 - 294x^8 + 1848x^7 - 1008x^6 + 1104x^5 + 2097x^4 - 60x^3 + 1128x^2 + 1464x + 564	\( 2^{63}\cdot 3^{21} \)	20T547	$[2]$ (GRH)
20.4.96479729228174488169059713024.1	x^20 - 4x^19 - 2x^18 + 36x^17 - 69x^16 + 24x^15 + 84x^14 - 120x^13 - 102x^12 + 488x^11 - 704x^10 + 488x^9 - 102x^8 - 120x^7 + 84x^6 + 24x^5 - 69x^4 + 36x^3 - 2x^2 - 4x + 1	\( 2^{63}\cdot 3^{21} \)	20T547	Trivial (GRH)
20.0.385918916912697952676238852096.1	x^20 - 8x^19 + 32x^18 - 108x^17 + 309x^16 - 720x^15 + 1576x^14 - 2792x^13 + 4544x^12 - 6144x^11 + 7296x^10 - 7368x^9 + 6312x^8 - 4608x^7 + 2784x^6 - 1384x^5 + 533x^4 - 152x^3 + 32x^2 - 4x + 1	\( 2^{65}\cdot 3^{21} \)	20T547	$[2]$ (GRH)
20.4.385918916912697952676238852096.1	x^20 - 8x^19 + 28x^18 - 44x^17 - 23x^16 + 208x^15 - 236x^14 - 272x^13 + 982x^12 - 864x^11 - 384x^10 + 1632x^9 - 1494x^8 - 384x^7 + 2952x^6 - 4416x^5 + 3810x^4 - 2064x^3 + 672x^2 - 120x + 6	\( 2^{65}\cdot 3^{21} \)	20T547	Trivial (GRH)
20.12.16060561821304241463001418628595712.1	x^20 - 44x^18 - 2x^17 + 647x^16 + 472x^15 - 4513x^14 - 6682x^13 + 13040x^12 + 30916x^11 + 637x^10 - 41708x^9 - 18688x^8 - 39492x^7 - 27384x^6 + 75968x^5 + 40636x^4 - 32512x^3 - 12576x^2 + 2816x - 64	\( 2^{34}\cdot 2657^{7} \)	20T547	Trivial (GRH)
20.12.16060561821304241463001418628595712.2	x^20 - 36x^18 - 12x^17 + 522x^16 + 500x^15 - 5592x^14 - 2892x^13 + 45225x^12 - 40956x^11 - 126598x^10 + 271060x^9 - 6853x^8 - 443464x^7 + 315634x^6 + 197948x^5 - 164472x^4 - 209264x^3 + 234632x^2 - 72472x + 7081	\( 2^{34}\cdot 2657^{7} \)	20T547	Trivial (GRH)
20.0.4111503826253885814528363168920502272.1	x^20 - 8x^19 + 92x^18 - 508x^17 + 3536x^16 - 15820x^15 + 80556x^14 - 301748x^13 + 1180861x^12 - 3705440x^11 + 11379146x^10 - 29303884x^9 + 69078496x^8 - 138934976x^7 + 247514958x^6 - 378201868x^5 + 495962812x^4 - 543999108x^3 + 473508600x^2 - 276218960x + 90850706	\( 2^{42}\cdot 2657^{7} \)	20T547	$[12]$ (GRH)
20.0.4111503826253885814528363168920502272.2	x^20 - 4x^19 + 50x^18 - 116x^17 + 1199x^16 - 1900x^15 + 18668x^14 - 21488x^13 + 215087x^12 - 232900x^11 + 1626322x^10 - 1503972x^9 + 9654213x^8 - 9065852x^7 + 41595536x^6 - 46839408x^5 + 156661796x^4 - 190676344x^3 + 317189688x^2 - 239357408x + 177738116	\( 2^{42}\cdot 2657^{7} \)	20T547	$[2, 12]$ (GRH)