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
18.0.1198241002273018867.1	x^18 - 4x^17 + 9x^16 - 14x^15 + 17x^14 - 16x^13 + 15x^12 - 23x^11 + 45x^10 - 65x^9 + 62x^8 - 40x^7 + 29x^6 - 39x^5 + 49x^4 - 41x^3 + 22x^2 - 7x + 1	\( -\,31^{6}\cdot 67^{5} \)	18T284	Trivial
18.0.3221287037577650765824.1	x^18 + 5x^16 + 11x^14 + 25x^12 + 51x^10 + 65x^8 + 59x^6 + 40x^4 + 13x^2 + 1	\( -\,2^{18}\cdot 31^{6}\cdot 61^{4} \)	18T284	Trivial
18.6.35696797698715505066797.1	x^18 - 2x^17 - 5x^16 + 26x^15 - 33x^14 - 64x^13 + 213x^12 - 159x^11 - 271x^10 + 761x^9 - 287x^8 - 735x^7 + 1010x^6 - 19x^5 - 1218x^4 + 81x^3 + 744x^2 + 209x - 79	\( 31^{9}\cdot 67^{5} \)	18T284	Trivial
18.6.196498509292236696715264.1	x^18 - x^16 - 9x^14 - 29x^12 + 84x^10 + 22x^8 + 202x^6 + 61x^4 + 61x^2 - 61	\( 2^{18}\cdot 31^{6}\cdot 61^{5} \)	18T284	Trivial (GRH)
18.12.640031705538953992499008.1	x^18 - 6x^17 + 3x^16 + 34x^15 - 74x^14 + 68x^13 - 8x^12 - 160x^11 + 395x^10 - 474x^9 + 187x^8 + 270x^7 - 312x^6 + 6x^5 + 101x^4 - 24x^3 - 13x^2 + 4x + 1	\( -\,2^{6}\cdot 37^{5}\cdot 229^{6} \)	18T284	Trivial
18.12.640031705538953992499008.2	x^18 - 9x^17 + 30x^16 - 22x^15 - 145x^14 + 446x^13 - 269x^12 - 972x^11 + 1981x^10 - 378x^9 - 2497x^8 + 2227x^7 + 548x^6 - 1285x^5 + 199x^4 + 193x^3 - 43x^2 - 5x + 1	\( -\,2^{6}\cdot 37^{5}\cdot 229^{6} \)	18T284	Trivial
18.6.776560801327854853887973.1	x^18 - 3x^17 + 3x^16 + 4x^15 - 47x^14 + 80x^13 + 63x^12 - 192x^11 - 99x^10 + 528x^9 - 529x^8 + 209x^7 - 75x^6 + 44x^5 + 112x^4 - 114x^3 + 21x^2 - 4x - 1	\( 11^{6}\cdot 37^{5}\cdot 43^{6} \)	18T284	Trivial
18.0.1107081869040352851890176.1	x^18 + 17x^16 + 115x^14 + 404x^12 + 802x^10 + 911x^8 + 568x^6 + 176x^4 + 24x^2 + 1	\( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T284	$[2]$
18.6.13690678201294187745799093.1	x^18 - 4x^17 + 2x^16 + 16x^15 + 7x^14 - 90x^13 - 30x^12 + 193x^11 + 38x^10 - 358x^9 - 279x^8 + 759x^7 - 276x^6 - 456x^5 + 597x^4 - 263x^3 + 26x^2 + 24x - 8	\( 37^{7}\cdot 229^{6} \)	18T284	Trivial
18.18.23380151989531222748958669.1	x^18 - 4x^17 - 14x^16 + 71x^15 + 53x^14 - 472x^13 + 33x^12 + 1522x^11 - 555x^10 - 2661x^9 + 1098x^8 + 2705x^7 - 839x^6 - 1574x^5 + 194x^4 + 435x^3 + 27x^2 - 22x + 1	\( 3^{9}\cdot 7^{5}\cdot 643^{6} \)	18T284	Trivial (GRH)
18.0.631264103717343014221884063.1	x^18 - 2x^17 - 9x^16 + 30x^15 + 26x^14 - 97x^13 + 184x^12 + 231x^11 - 384x^10 + 978x^9 + 1461x^8 - 279x^7 + 2232x^6 + 2772x^5 - 243x^4 + 405x^3 + 4050x^2 - 2970x + 1431	\( -\,3^{12}\cdot 7^{5}\cdot 643^{6} \)	18T284	$[2, 2]$
18.18.56077017912500993006793084928.1	x^18 - 5x^17 - 29x^16 + 174x^15 + 257x^14 - 2275x^13 - 342x^12 + 14348x^11 - 5814x^10 - 48471x^9 + 33485x^8 + 89506x^7 - 78846x^6 - 84548x^5 + 90666x^4 + 30849x^3 - 45350x^2 + 1420x + 4973	\( 2^{12}\cdot 37^{7}\cdot 229^{6} \)	18T284	Trivial (GRH)