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
18.0.1963375693486812487.1	x^18 - x^17 - 7x^15 + 5x^14 + 6x^13 + 21x^12 - 29x^11 - 13x^10 - 11x^9 + 49x^8 - 8x^7 - 3x^6 - 24x^5 + 14x^4 + 3x^3 - 3x + 1	\( -\,31^{6}\cdot 1303^{3} \)	18T314	Trivial
18.0.2745546730527991447.1	x^18 - 5x^17 + 12x^16 - 17x^15 + 12x^14 - 2x^13 + 8x^12 - 46x^11 + 111x^10 - 168x^9 + 188x^8 - 173x^7 + 137x^6 - 102x^5 + 70x^4 - 40x^3 + 19x^2 - 5x + 1	\( -\,23^{6}\cdot 2647^{3} \)	18T314	Trivial
18.0.36182713571708760064.1	x^18 - x^17 + 2x^16 - 8x^15 + 11x^14 - 11x^13 + 16x^12 - 17x^11 + 8x^10 - x^9 + 8x^8 - 17x^7 + 16x^6 - 11x^5 + 11x^4 - 8x^3 + 2x^2 - x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 151^{3} \)	18T314	Trivial
18.0.195675021953328640000.1	x^18 - x^17 + 2x^16 - 12x^15 + 27x^14 - 45x^13 + 72x^12 - 85x^11 + 92x^10 - 101x^9 + 92x^8 - 85x^7 + 72x^6 - 45x^5 + 27x^4 - 12x^3 + 2x^2 - x + 1	\( -\,2^{12}\cdot 5^{4}\cdot 31^{3}\cdot 37^{6} \)	18T314	Trivial
18.6.203534156411299994041.1	x^18 - 5x^17 + 2x^16 + 29x^15 - 41x^14 - 77x^13 + 166x^12 + 107x^11 - 338x^10 - 67x^9 + 383x^8 + x^7 - 234x^6 + 4x^5 + 96x^4 - 10x^3 - 23x^2 + 4x + 1	\( 31^{6}\cdot 6121^{3} \)	18T314	Trivial
18.6.262059590501480557297.1	x^18 - 10x^16 - 6x^15 + 23x^14 + 13x^13 + 11x^12 + 72x^11 - 45x^10 - 265x^9 - 99x^8 + 246x^7 + 227x^6 - 3x^5 - 87x^4 - 37x^3 + 2x^2 + 5x + 1	\( 23^{6}\cdot 12097^{3} \)	18T314	Trivial
18.6.677646828706763608064.1	x^18 - 3x^17 + 2x^16 + 8x^15 - 19x^14 + 21x^13 - 10x^12 + 9x^11 - 78x^10 + 109x^9 - 46x^8 + 33x^7 - 50x^6 + 13x^5 + 25x^4 - 22x^3 + 8x^2 - 3x + 1	\( 2^{12}\cdot 37^{6}\cdot 401^{3} \)	18T314	Trivial
18.6.2377371204272673094736.1	x^18 - 4x^17 + 20x^15 - 27x^14 - x^13 + 36x^12 - 96x^11 + 107x^10 + 97x^9 - 218x^8 - 18x^7 + 137x^6 + 12x^5 - 38x^4 - 13x^3 + 2x^2 + 3x + 1	\( 2^{4}\cdot 101^{3}\cdot 229^{6} \)	18T314	Trivial
18.12.244708287054102675846827.1	x^18 - 10x^16 - 8x^15 + 28x^14 + 52x^13 - 82x^12 - 73x^11 + 312x^10 - 112x^9 - 460x^8 + 429x^7 + 171x^6 - 365x^5 + 62x^4 + 91x^3 - 36x^2 + 1	\( -\,257^{6}\cdot 947^{3} \)	18T314	Trivial
18.12.264502279525614257635328.1	x^18 - 4x^17 - 3x^16 + 40x^15 - 54x^14 - 116x^13 + 358x^12 + 8x^11 - 904x^10 + 556x^9 + 1244x^8 - 1152x^7 - 1146x^6 + 1076x^5 + 690x^4 - 512x^3 - 169x^2 + 104x - 1	\( -\,2^{16}\cdot 37^{6}\cdot 1163^{3} \)	18T314	Trivial
18.18.46025638949152433124675584.1	x^18 - 7x^17 - 6x^16 + 144x^15 - 189x^14 - 975x^13 + 2404x^12 + 1953x^11 - 10054x^10 + 3451x^9 + 15638x^8 - 14529x^7 - 5420x^6 + 10671x^5 - 2089x^4 - 1318x^3 + 248x^2 + 75x + 1	\( 2^{12}\cdot 37^{6}\cdot 16361^{3} \)	18T314	Trivial (GRH)
18.18.314080936086007337997242368.1	x^18 - 9x^17 + 12x^16 + 102x^15 - 283x^14 - 341x^13 + 1564x^12 + 355x^11 - 3972x^10 - 17x^9 + 5382x^8 + 199x^7 - 3798x^6 - 569x^5 + 1139x^4 + 236x^3 - 114x^2 - 25x - 1	\( 2^{12}\cdot 37^{6}\cdot 31033^{3} \)	18T314	Trivial (GRH)