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
18.2.2389861611358642578125.1	x^18 - 4x^17 + 5x^16 - x^15 - 4x^13 + 6x^12 + 15x^11 - x^10 + 60x^7 + 25x^6 + 64x^3 + 64x^2 + 20x + 1	\( 5^{15}\cdot 23^{8} \)	$D_{18}$ (as 18T13)	Trivial
18.0.2463405967062215950336.1	x^18 + x^16 - 2x^14 - 7x^12 + 10x^10 + 33x^8 + 13x^6 + 20x^4 + 16x^2 + 4	\( -\,2^{24}\cdot 59^{8} \)	$D_{18}$ (as 18T13)	Trivial
18.0.5232754168105857064083.1	x^18 - 3x^17 + 6x^16 - 23x^15 + 36x^14 - 69x^13 + 124x^12 - 87x^11 + 237x^10 - 80x^9 + 306x^8 - 24x^7 + 173x^6 + 75x^5 + 51x^4 + 33x^3 + 27x^2 + 3x + 1	\( -\,3^{21}\cdot 29^{8} \)	$D_{18}$ (as 18T13)	Trivial
18.2.50583290291689951619469.1	x^18 - x^15 + 4x^12 + 4x^9 + 11x^6 - 13x^3 - 1	\( 3^{20}\cdot 29^{9} \)	$D_{18}$ (as 18T13)	Trivial
18.2.4768875488962616064464333777.1	x^18 - 2x^17 + 17x^15 - 17x^14 + 51x^13 + 119x^12 - 476x^11 + 493x^10 + 1632x^9 - 3638x^8 - 3502x^7 + 6936x^6 + 1972x^5 - 3451x^4 + 3264x^3 + 17x^2 - 750x + 225	\( 7^{8}\cdot 17^{17} \)	$D_{18}$ (as 18T13)	Trivial
18.0.33382128422738312451250336439.1	x^18 - 4x^17 + 17x^16 - 51x^15 + 170x^14 - 408x^13 + 918x^12 - 1445x^11 + 1870x^10 - 1887x^9 + 3672x^8 - 5797x^7 + 8058x^6 - 8143x^5 + 9044x^4 - 6851x^3 + 5916x^2 - 2826x + 1971	\( -\,7^{9}\cdot 17^{17} \)	$D_{18}$ (as 18T13)	$[10]$ (GRH)
18.0.51956851764606118870683564963.1	x^18 - 3x^17 + 19x^16 - 46x^15 + 209x^14 - 457x^13 + 1289x^12 - 2046x^11 + 4263x^10 - 5541x^9 + 9392x^8 - 9256x^7 + 11934x^6 - 8321x^5 + 9457x^4 - 4564x^3 + 3678x^2 + 60x + 1	\( -\,3^{9}\cdot 1129^{8} \)	$D_{18}$ (as 18T13)	$[2, 38]$ (GRH)
18.0.691976677792049302709773533184.1	x^18 + 29x^16 + 338x^14 + 2070x^12 + 7345x^10 + 15603x^8 + 19532x^6 + 13258x^4 + 3756x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	$D_{18}$ (as 18T13)	$[178]$ (GRH)
18.18.354292059029529242987404048990208.1	x^18 - 6x^17 - 29x^16 + 232x^15 + 122x^14 - 2972x^13 + 2218x^12 + 15816x^11 - 21375x^10 - 33384x^9 + 61321x^8 + 17204x^7 - 59508x^6 + 13790x^5 + 7002x^4 - 1052x^3 - 340x^2 - 8x + 1	\( 2^{27}\cdot 1129^{8} \)	$D_{18}$ (as 18T13)	Trivial (GRH)
18.18.13620176948980906425236472453660672.1	x^18 - 6x^17 - 38x^16 + 280x^15 + 350x^14 - 4460x^13 + 932x^12 + 30696x^11 - 23739x^10 - 93216x^9 + 86432x^8 + 120652x^7 - 101484x^6 - 59266x^5 + 34798x^4 + 12148x^3 - 3288x^2 - 564x + 109	\( 2^{18}\cdot 3^{9}\cdot 1129^{8} \)	$D_{18}$ (as 18T13)	Trivial (GRH)