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 matches 1-50 of 651)

Label	Polynomial	Discriminant	Galois group	Class group
9.9.5609891727441.1	x^9 - 3x^8 - 15x^7 + 51x^6 + 39x^5 - 219x^4 + 81x^3 + 204x^2 - 132x - 8	\( 3^{16}\cdot 19^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.15091989595281.1	x^9 - 3x^8 - 18x^7 + 40x^6 + 123x^5 - 141x^4 - 373x^3 + 57x^2 + 339x + 127	\( 3^{12}\cdot 73^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.25002110044521.2	x^9 - 24x^7 - 23x^6 + 135x^5 + 159x^4 - 209x^3 - 180x^2 + 141x + 11	\( 3^{12}\cdot 19^{6} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.80676485676081.1	x^9 - 3x^8 - 21x^7 + 63x^6 + 141x^5 - 435x^4 - 273x^3 + 996x^2 - 192x - 64	\( 3^{16}\cdot 37^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.126270685902529.1	x^9 - x^8 - 34x^7 - 3x^6 + 350x^5 + 330x^4 - 729x^3 - 718x^2 + 356x + 344	\( 7^{6}\cdot 181^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.290942852360209.1	x^9 - 2x^8 - 43x^7 + 46x^6 + 626x^5 - 148x^4 - 3168x^3 - 779x^2 + 3052x - 97	\( 7^{6}\cdot 223^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.543261605368729.1	x^9 - 2x^8 - 26x^7 + 54x^6 + 211x^5 - 456x^4 - 585x^3 + 1360x^2 + 308x - 1000	\( 13^{6}\cdot 103^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.992903858682129.1	x^9 - 28x^7 - 9x^6 + 237x^5 + 95x^4 - 613x^3 - 54x^2 + 405x - 27	\( 3^{8}\cdot 73^{6} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.1363532208525369.1	x^9 - 39x^7 - 50x^6 + 396x^5 + 930x^4 - 636x^3 - 3825x^2 - 4050x - 1375	\( 3^{12}\cdot 37^{6} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.1517427126663889.1	x^9 - 3x^8 - 53x^7 + 207x^6 + 613x^5 - 3243x^4 - 22x^3 + 13140x^2 - 13923x + 2619	\( 7^{6}\cdot 337^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.1785733746591249.1	x^9 - 57x^7 - 94x^6 + 936x^5 + 2886x^4 - 2418x^3 - 19773x^2 - 27378x - 11999	\( 3^{12}\cdot 7^{6}\cdot 13^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.1785733746591249.2	x^9 - 57x^7 - 20x^6 + 936x^5 + 858x^4 - 4446x^3 - 7605x^2 - 3042x - 169	\( 3^{12}\cdot 7^{6}\cdot 13^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.1785733746591249.3	x^9 - 57x^7 - 74x^6 + 936x^5 + 2028x^4 - 3783x^3 - 12168x^2 - 6084x + 1352	\( 3^{12}\cdot 7^{6}\cdot 13^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.2025170913606201.1	x^9 - 3x^8 - 33x^7 + 96x^6 + 327x^5 - 912x^4 - 1116x^3 + 2904x^2 + 768x - 1664	\( 3^{16}\cdot 19^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.2025170913606201.2	x^9 - 3x^8 - 33x^7 + 114x^6 + 291x^5 - 1326x^4 + 9x^3 + 4290x^2 - 4812x + 1405	\( 3^{16}\cdot 19^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.2866369804403121.1	x^9 - 3x^8 - 45x^7 + 137x^6 + 651x^5 - 1953x^4 - 3861x^3 + 11268x^2 + 8160x - 22976	\( 3^{12}\cdot 271^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.3695869460957569.1	x^9 - 2x^8 - 64x^7 + 199x^6 + 961x^5 - 3839x^4 - 2045x^3 + 18840x^2 - 16975x + 727	\( 7^{6}\cdot 421^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.4720723441965441.1	x^9 - 3x^8 - 54x^7 + 55x^6 + 903x^5 + 243x^4 - 4817x^3 - 4902x^2 + 2454x + 1853	\( 3^{12}\cdot 307^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.5406450165073489.1	x^9 - x^8 - 62x^7 - 11x^6 + 1277x^5 + 1255x^4 - 9101x^3 - 11442x^2 + 20534x + 26417	\( 7^{6}\cdot 463^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.6076395973440081.1	x^9 - 3x^8 - 54x^7 + 51x^6 + 927x^5 + 315x^4 - 5373x^3 - 6390x^2 + 3258x + 4857	\( 3^{16}\cdot 109^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.11198373780772161.1	x^9 - 3x^8 - 54x^7 + 69x^6 + 1035x^5 + 279x^4 - 6561x^3 - 8064x^2 + 3042x + 4479	\( 3^{16}\cdot 127^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.11487763116846289.2	x^9 - 71x^7 - 104x^6 + 1608x^5 + 4316x^4 - 9654x^3 - 44887x^2 - 41948x - 757	\( 7^{6}\cdot 13^{4}\cdot 43^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.11487763116846289.3	x^9 - 3x^8 - 75x^7 + 59x^6 + 1925x^5 + 2217x^4 - 12881x^3 - 31750x^2 - 17852x + 2792	\( 7^{6}\cdot 13^{4}\cdot 43^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.11487763116846289.4	x^9 - x^8 - 84x^7 + 25x^6 + 1968x^5 - 276x^4 - 16400x^3 - 1664x^2 + 41472x + 27712	\( 7^{6}\cdot 13^{4}\cdot 43^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.13274007026617129.1	x^9 - 43x^7 - 2x^6 + 638x^5 + 14x^4 - 3889x^3 + 8x^2 + 8064x + 512	\( 13^{6}\cdot 229^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.24135066344494609.2	x^9 - x^8 - 79x^7 + 169x^6 + 1967x^5 - 6811x^4 - 10892x^3 + 78008x^2 - 118237x + 56987	\( 7^{6}\cdot 673^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.24458476118259481.1	x^9 - 3x^8 - 57x^7 + 125x^6 + 995x^5 - 1567x^4 - 5164x^3 + 6948x^2 + 1261x - 467	\( 19^{6}\cdot 151^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.30387186626385681.1	x^9 - 3x^8 - 60x^7 + 141x^6 + 1173x^5 - 2055x^4 - 7317x^3 + 10500x^2 + 3774x - 4913	\( 3^{16}\cdot 163^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.34103327641164769.1	x^9 - x^8 - 57x^7 + 75x^6 + 827x^5 - 1099x^4 - 3585x^3 + 4222x^2 + 2676x - 8	\( 13^{4}\cdot 103^{6} \)	$C_3^2:C_3$ (as 9T7)	Trivial
9.9.39761413237774881.1	x^9 - 75x^7 - 68x^6 + 1530x^5 + 2184x^4 - 7399x^3 - 16302x^2 - 5568x + 3448	\( 3^{12}\cdot 523^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.41142776764733329.2	x^9 - 2x^8 - 87x^7 + 272x^6 + 2256x^5 - 10378x^4 - 9344x^3 + 115983x^2 - 211778x + 121709	\( 7^{6}\cdot 769^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.46201319063696241.2	x^9 - 3x^8 - 81x^7 + 339x^6 + 1665x^5 - 9855x^4 + 54x^3 + 70524x^2 - 125631x + 64419	\( 3^{16}\cdot 181^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.50894594316479809.1	x^9 - 4x^8 - 84x^7 + 186x^6 + 2601x^5 - 692x^4 - 29609x^3 - 41306x^2 + 5524x + 11752	\( 7^{6}\cdot 811^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.58905834008868081.1	x^9 - 75x^7 - 50x^6 + 1890x^5 + 2256x^4 - 16912x^3 - 23745x^2 + 28992x + 9811	\( 3^{12}\cdot 577^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.62285128497192769.1	x^9 - 2x^8 - 98x^7 + 235x^6 + 2907x^5 - 8083x^4 - 23323x^3 + 72818x^2 - 3197x - 65647	\( 7^{6}\cdot 853^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.67507555346709921.1	x^9 - 3x^8 - 87x^7 + 303x^6 + 1533x^5 - 3819x^4 - 10269x^3 + 5982x^2 + 21720x + 10216	\( 3^{16}\cdot 199^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.71520584390288929.1	x^9 - x^8 - 105x^7 - 53x^6 + 3287x^5 + 5559x^4 - 26661x^3 - 72326x^2 - 48824x - 7288	\( 7^{6}\cdot 883^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.75040713495231201.1	x^9 - 78x^7 - 52x^6 + 1845x^5 + 1632x^4 - 14625x^3 - 13056x^2 + 16908x - 1592	\( 3^{12}\cdot 613^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.80425212553252449.1	x^9 - 3x^8 - 54x^7 + 137x^6 + 759x^5 - 1971x^4 - 2178x^3 + 5625x^2 + 1608x - 3284	\( 3^{12}\cdot 73^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.80425212553252449.2	x^9 - 3x^8 - 54x^7 + 95x^6 + 843x^5 - 417x^4 - 3347x^3 + 1278x^2 + 3204x - 1457	\( 3^{12}\cdot 73^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.84423549813321481.1	x^9 - 2x^8 - 45x^7 - 11x^6 + 595x^5 + 1092x^4 - 776x^3 - 3297x^2 - 2653x - 665	\( 7^{4}\cdot 181^{6} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.104318309619869401.2	x^9 - x^8 - 81x^7 - 11x^6 + 1893x^5 + 1771x^4 - 9137x^3 - 1218x^2 + 13552x - 6776	\( 7^{4}\cdot 19^{6}\cdot 31^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.104318309619869401.3	x^9 - 61x^7 - 60x^6 + 740x^5 + 578x^4 - 670x^3 - 341x^2 + 110x - 1	\( 7^{4}\cdot 19^{6}\cdot 31^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.104318309619869401.4	x^9 - x^8 - 81x^7 + 8x^6 + 1950x^5 + 99x^4 - 17877x^3 - 2529x^2 + 55200x + 16157	\( 7^{4}\cdot 19^{6}\cdot 31^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.110446108890554889.1	x^9 - 3x^8 - 57x^7 + 162x^6 + 906x^5 - 2433x^4 - 2901x^3 + 5496x^2 + 1203x - 1990	\( 3^{16}\cdot 37^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.110446108890554889.2	x^9 - 3x^8 - 57x^7 + 126x^6 + 978x^5 - 1029x^4 - 6717x^3 + 465x^2 + 15756x + 9989	\( 3^{16}\cdot 37^{6} \)	$C_3^2:C_3$ (as 9T7)	$[3]$
9.9.127847196324051169.1	x^9 - 4x^8 - 102x^7 + 445x^6 + 2869x^5 - 15551x^4 - 10175x^3 + 157160x^2 - 271691x + 139399	\( 7^{6}\cdot 1021^{4} \)	$C_3^2:C_3$ (as 9T7)	Trivial (GRH)
9.9.129800497404846321.2	x^9 - 81x^7 - 94x^6 + 2148x^5 + 5274x^4 - 15806x^3 - 71859x^2 - 85950x - 31641	\( 3^{12}\cdot 19^{4}\cdot 37^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.129800497404846321.3	x^9 - 3x^8 - 87x^7 + 257x^6 + 2037x^5 - 6885x^4 - 10825x^3 + 57330x^2 - 60840x + 17576	\( 3^{12}\cdot 19^{4}\cdot 37^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)
9.9.129800497404846321.4	x^9 - 3x^8 - 90x^7 + 22x^6 + 2709x^5 + 4893x^4 - 18513x^3 - 47211x^2 + 26685x + 93419	\( 3^{12}\cdot 19^{4}\cdot 37^{4} \)	$C_3^2:C_3$ (as 9T7)	$[3]$ (GRH)