Global number field search results

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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
18.2.30729754039387186164357.1	x^18 - 6x^15 + 13x^12 - 4x^9 - 113x^6 - 99x^3 + 1	\( 3^{19}\cdot 31^{9} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial
18.4.1399463681474351289249792.1	x^18 + 6x^16 - 21x^14 - 71x^12 + 327x^10 - 228x^8 - 36x^6 + 3x^4 - 45x^2 + 3	\( -\,2^{12}\cdot 3^{15}\cdot 47^{8} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial
18.2.4610950813345280000000000.1	x^18 - 4x^17 + 24x^15 - 47x^14 + 64x^13 + 136x^12 - 462x^11 + 30x^10 + 562x^9 + 216x^8 - 416x^7 - 583x^6 - 30x^5 + 418x^4 + 320x^3 - 28x^2 - 152x - 56	\( 2^{18}\cdot 5^{10}\cdot 23^{9} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial (GRH)
18.4.21481164688288963759058944.1	x^18 - x^17 + 7x^16 - 24x^15 + 3x^14 - 27x^13 + 21x^12 + 309x^11 - 32x^10 - 190x^9 - 1125x^8 + 323x^7 + 763x^6 + 1551x^5 - 901x^4 - 693x^3 - 197x^2 + 254x + 65	\( -\,2^{12}\cdot 7^{9}\cdot 37^{9} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial (GRH)
18.0.2083629921519675807054655488.1	x^18 - 3x^17 + 21x^16 - 54x^15 + 195x^14 - 471x^13 + 1077x^12 - 2142x^11 + 3306x^10 - 5050x^9 + 6096x^8 - 8646x^7 + 9585x^6 - 9465x^5 + 9138x^4 - 1689x^3 + 19827x^2 + 11898x + 10104	\( -\,2^{12}\cdot 3^{24}\cdot 23^{9} \)	$C_3:S_3:S_4$ (as 18T155)	$[14]$
18.0.2407618658213698882221637632.1	x^18 - 21x^14 + 3x^12 + 81x^10 - 18x^8 + 234x^6 + 297x^4 + 135x^2 + 27	\( -\,2^{30}\cdot 3^{21}\cdot 11^{8} \)	$C_3:S_3:S_4$ (as 18T155)	$[2]$ (GRH)
18.0.4001925539052664141228388352.1	x^18 - 6x^17 + 25x^16 - 101x^15 + 323x^14 - 917x^13 + 2199x^12 - 4227x^11 + 7049x^10 - 9906x^9 + 12946x^8 - 17477x^7 + 22549x^6 - 26741x^5 + 27005x^4 - 18930x^3 + 14889x^2 - 5565x + 877	\( -\,2^{12}\cdot 3^{12}\cdot 107^{9} \)	$C_3:S_3:S_4$ (as 18T155)	$[2, 6]$ (GRH)
18.0.8055620642901114529869201408.1	x^18 - 18x^16 - 22x^15 + 153x^14 + 300x^13 - 416x^12 - 1926x^11 - 1308x^10 + 4148x^9 + 10962x^8 + 7584x^7 - 13782x^6 - 39294x^5 - 36777x^4 + 9544x^3 + 67788x^2 + 78738x + 34061	\( -\,2^{18}\cdot 3^{19}\cdot 31^{9} \)	$C_3:S_3:S_4$ (as 18T155)	$[2]$ (GRH)
18.6.202979709877915393317843809755697.1	x^18 - 7x^17 - 25x^16 + 180x^15 + 285x^14 - 1852x^13 - 1969x^12 + 11030x^11 + 8177x^10 - 41562x^9 - 22879x^8 + 106680x^7 + 41661x^6 - 182058x^5 - 51154x^4 + 187467x^3 + 47036x^2 - 90508x - 25432	\( 11^{8}\cdot 17^{9}\cdot 41^{8} \)	$C_3:S_3:S_4$ (as 18T155)	$[9]$ (GRH)
18.6.315293840660890978521435310500347904.1	x^18 - 12x^16 - 78x^15 + 198x^14 + 1128x^13 - 3323x^12 + 7344x^11 - 27270x^10 + 752x^9 + 37062x^8 + 339900x^7 - 830151x^6 + 1196208x^5 - 2067246x^4 + 1256326x^3 + 492588x^2 - 316380x - 21697	\( 2^{33}\cdot 3^{24}\cdot 37^{9} \)	$C_3:S_3:S_4$ (as 18T155)	$[6]$ (GRH)
18.18.4121927399946666429876786747200000000.1	x^18 - 2x^17 - 58x^16 + 101x^15 + 1142x^14 - 1882x^13 - 9654x^12 + 15098x^11 + 37144x^10 - 48401x^9 - 77790x^8 + 65634x^7 + 93720x^6 - 30410x^5 - 58390x^4 - 5767x^3 + 12788x^2 + 5170x + 595	\( 2^{12}\cdot 5^{8}\cdot 7^{8}\cdot 197^{9} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial (GRH)
18.18.5703857685299429613102692113176969216.1	x^18 - 99x^16 - 34x^15 + 3936x^14 + 2910x^13 - 80911x^12 - 91218x^11 + 908568x^10 + 1336398x^9 - 5362239x^8 - 9346950x^7 + 14757756x^6 + 28021338x^5 - 17858889x^4 - 32457542x^3 + 9855147x^2 + 10514490x - 1319078	\( 2^{14}\cdot 3^{21}\cdot 11^{12}\cdot 13^{9} \)	$C_3:S_3:S_4$ (as 18T155)	Trivial (GRH)