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
18.0.343180490848379918163.1	x^18 - 2x^16 - 6x^15 + x^14 + 10x^13 + 9x^12 - 3x^11 - 11x^10 + 3x^8 - 4x^7 - 7x^6 - x^5 + 6x^4 + 2x^3 + 2x + 1	\( -\,3^{9}\cdot 11491^{4} \)	18T888	Trivial
18.0.2236733441516513787904.1	x^18 - 6x^16 + 13x^14 - 9x^12 - 2x^10 - x^8 + 11x^6 - 8x^4 + x^2 + 1	\( -\,2^{18}\cdot 7^{4}\cdot 1373^{4} \)	18T888	Trivial
18.2.16664962779853595703125.1	x^18 - 2x^17 + 11x^16 - 18x^15 + 39x^14 - 70x^13 + 71x^12 - 86x^11 + 117x^10 + 2x^9 + 67x^8 + 21x^7 - 17x^6 - 8x^5 - 16x^4 - 16x^3 - 3x^2 - 3x - 1	\( 5^{9}\cdot 7^{4}\cdot 1373^{4} \)	18T888	Trivial
18.0.120334583646716719921875.1	x^18 - 2x^17 + 4x^16 + 2x^15 - 2x^14 + 6x^13 + 15x^12 - 4x^11 + 17x^10 + 10x^9 + 32x^8 + 9x^7 + 15x^6 + 34x^5 + 13x^4 + 8x^3 + 7x^2 + 3x + 1	\( -\,3^{17}\cdot 5^{8}\cdot 13^{4}\cdot 17^{4} \)	18T888	$[2]$
18.10.1547512649777735595703125.1	x^18 - 2x^17 - 4x^16 - 4x^15 - 6x^14 + 66x^13 + 101x^12 - 36x^11 - 195x^10 - 246x^9 - 144x^8 - 39x^7 + 19x^6 + 70x^5 + 29x^4 - 10x^3 + 3x^2 + 3x - 1	\( 3^{12}\cdot 5^{13}\cdot 13^{4}\cdot 17^{4} \)	18T888	Trivial (GRH)
18.0.2685200750332540417736704.1	x^18 + 3x^16 - 3x^14 - 12x^12 - 6x^10 + 14x^8 + 40x^6 + 33x^4 + 10x^2 + 1	\( -\,2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4} \)	18T888	Trivial
18.10.710305959195813821519073637.1	x^18 - 4x^17 - 20x^16 + 72x^15 + 136x^14 - 533x^13 - 349x^12 + 1958x^11 - 20x^10 - 3498x^9 + 1205x^8 + 2685x^7 - 50x^6 - 1829x^5 - 2161x^4 + 3167x^3 - 645x^2 - 185x + 37	\( 11^{4}\cdot 37^{9}\cdot 139^{4} \)	18T888	Trivial (GRH)
18.2.1842046168626834314431823872.1	x^18 - 14x^14 - 77x^12 - 245x^10 + 4116x^8 + 31213x^6 + 16807x^4 - 117649x^2 - 823543	\( 2^{18}\cdot 7^{11}\cdot 1373^{4} \)	18T888	Trivial (GRH)
18.0.56388376477809160462736031744.1	x^18 + 33x^16 + 400x^14 + 2320x^12 + 6854x^10 + 9894x^8 + 6064x^6 + 1648x^4 + 201x^2 + 9	\( -\,2^{42}\cdot 3^{4}\cdot 3547^{4} \)	18T888	$[6]$ (GRH)
18.0.214099616939181656131950870528.1	x^18 - x^17 + 17x^16 - 32x^15 + 232x^14 - 360x^13 + 1208x^12 - 1088x^11 + 3453x^10 - 2429x^9 + 5853x^8 - 648x^7 + 3040x^6 - 736x^5 + 904x^4 - 96x^3 + 105x^2 - 9x + 9	\( -\,2^{36}\cdot 3^{9}\cdot 3547^{4} \)	18T888	$[79]$ (GRH)
18.18.13702375484107625992444855713792.1	x^18 - 6x^17 - 28x^16 + 224x^15 + 44x^14 - 2264x^13 + 1808x^12 + 8380x^11 - 8701x^10 - 11562x^9 + 8914x^8 + 8156x^7 - 3036x^6 - 2792x^5 + 218x^4 + 388x^3 + 33x^2 - 14x - 2	\( 2^{42}\cdot 3^{9}\cdot 3547^{4} \)	18T888	Trivial (GRH)
18.18.9540369687303470979346612772502997.1	x^18 - 4x^17 - 56x^16 + 212x^15 + 1215x^14 - 4267x^13 - 13496x^12 + 42867x^11 + 82703x^10 - 233941x^9 - 272786x^8 + 700492x^7 + 423035x^6 - 1066391x^5 - 159932x^4 + 624213x^3 - 145537x^2 + 7505x - 25	\( 37^{9}\cdot 151^{4}\cdot 613^{4} \)	18T888	Trivial (GRH)