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 10 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.4558310746519570263.1	x^18 + 6x^16 - 2x^15 + 15x^14 - 10x^13 + 22x^12 - 20x^11 + 23x^10 - 20x^9 + 18x^8 - 10x^7 + 9x^6 - 2x^5 + 2x^4 - x^3 - x + 1	\( -\,3^{9}\cdot 229\cdot 433^{3}\cdot 12457 \)	18T951	Trivial
18.4.214098808754763671875.1	x^18 - 4x^16 - 6x^15 + 7x^14 + 20x^13 + 7x^12 - 28x^11 - 35x^10 + 4x^9 + 39x^8 + 30x^7 - 8x^6 - 25x^5 - 15x^4 + 2x^3 + 7x^2 + 4x + 1	\( -\,5^{9}\cdot 109\cdot 409^{3}\cdot 14699 \)	18T951	Trivial
18.6.357298468475369140625.1	x^18 - 5x^16 - 6x^15 + 8x^14 + 25x^13 + 9x^12 - 32x^11 - 44x^10 - 2x^9 + 44x^8 + 38x^7 - 4x^6 - 28x^5 - 19x^4 + 8x^2 + 5x + 1	\( 5^{9}\cdot 71\cdot 941\cdot 1399^{3} \)	18T951	Trivial
18.2.5092753852060837890625.1	x^18 - x^17 + 2x^16 - 6x^15 + 4x^14 - 7x^13 + 14x^12 - 8x^11 + 11x^10 - 20x^9 + 9x^8 - 8x^7 + 15x^6 - 5x^5 + 2x^4 - 6x^3 + x^2 + 1	\( 5^{9}\cdot 241^{3}\cdot 186282269 \)	18T951	Trivial
18.10.3241716400658576603515625.1	x^18 - 3x^16 - 6x^15 - 2x^14 + 15x^13 + 23x^12 + 8x^11 - 28x^10 - 44x^9 - 16x^8 + 26x^7 + 38x^6 + 12x^5 - 13x^4 - 14x^3 - 2x^2 + 3x + 1	\( 5^{9}\cdot 3881^{3}\cdot 28393181 \)	18T951	Trivial (GRH)
18.8.5277455674211775935546875.1	x^18 - 9x^16 - 6x^15 + 31x^14 + 45x^13 - 35x^12 - 124x^11 - 57x^10 + 130x^9 + 190x^8 + 24x^7 - 146x^6 - 128x^5 - 12x^4 + 44x^3 + 31x^2 + 9x + 1	\( -\,5^{9}\cdot 11^{3}\cdot 109^{3}\cdot 1567606321 \)	18T951	Trivial (GRH)
18.12.1512887191404113585568359375.1	x^18 - 15x^16 - 6x^15 + 88x^14 + 75x^13 - 241x^12 - 352x^11 + 236x^10 + 748x^9 + 244x^8 - 622x^7 - 674x^6 - 68x^5 + 311x^4 + 250x^3 + 88x^2 + 15x + 1	\( -\,5^{9}\cdot 29^{2}\cdot 3881^{3}\cdot 15756131 \)	18T951	Trivial (GRH)
18.16.46565137128897741068083984375.1	x^18 - 21x^16 - 6x^15 + 178x^14 + 105x^13 - 763x^12 - 712x^11 + 1637x^10 + 2314x^9 - 1189x^8 - 3484x^7 - 1210x^6 + 1545x^5 + 1742x^4 + 772x^3 + 178x^2 + 21x + 1	\( -\,5^{9}\cdot 89\cdot 3881^{3}\cdot 4582578491 \)	18T951	Trivial (GRH)
18.14.75920134215510255381541015625.1	x^18 - 17x^16 - 6x^15 + 114x^14 + 85x^13 - 369x^12 - 456x^11 + 512x^10 + 1132x^9 + 80x^8 - 1194x^7 - 928x^6 + 148x^5 + 597x^4 + 378x^3 + 114x^2 + 17x + 1	\( 5^{9}\cdot 11\cdot 191\cdot 1021\cdot 7841^{3}\cdot 37589 \)	18T951	Trivial (GRH)
18.18.2503257203269486434420666015625.1	x^18 - 23x^16 - 6x^15 + 214x^14 + 115x^13 - 1015x^12 - 856x^11 + 2473x^10 + 3070x^9 - 2383x^8 - 5176x^7 - 1064x^6 + 2811x^5 + 2588x^4 + 1024x^3 + 214x^2 + 23x + 1	\( 5^{9}\cdot 821\cdot 7841^{3}\cdot 3238306241 \)	18T951	Trivial (GRH)