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 matches 1-50 of 982)

Label	Polynomial	Discriminant	Galois group	Class group
9.9.62523502209.1	x^9 - 15x^7 - 4x^6 + 54x^5 + 12x^4 - 38x^3 - 9x^2 + 6x + 1	\( 3^{12}\cdot 7^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.567869252041.1	x^9 - 20x^7 - 8x^6 + 103x^5 + 46x^4 - 157x^3 - 32x^2 + 60x + 8	\( 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.2565164201769.1	x^9 - 3x^8 - 18x^7 + 38x^6 + 93x^5 - 147x^4 - 161x^3 + 201x^2 + 57x - 53	\( 3^{12}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.5534900853769.1	x^9 - 26x^7 - 14x^6 + 181x^5 + 154x^4 - 295x^3 - 224x^2 + 84x + 56	\( 7^{6}\cdot 19^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.25002110044521.1	x^9 - 3x^8 - 24x^7 + 74x^6 + 117x^5 - 429x^4 + 119x^3 + 243x^2 - 69x - 37	\( 3^{12}\cdot 19^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.104413920565969.1	x^9 - 38x^7 - 13x^6 + 409x^5 + 257x^4 - 1333x^3 - 832x^2 + 1143x + 433	\( 7^{6}\cdot 31^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.227081481823729.1	x^9 - 32x^7 - 22x^6 + 259x^5 + 140x^4 - 787x^3 - 88x^2 + 804x - 248	\( 13^{6}\cdot 19^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.301855146292441.1	x^9 - 44x^7 - 46x^6 + 559x^5 + 1004x^4 - 1711x^3 - 4600x^2 - 2172x + 232	\( 7^{6}\cdot 37^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.471655843734321.1	x^9 - 3x^8 - 36x^7 + 101x^6 + 327x^5 - 921x^4 - 575x^3 + 1632x^2 + 480x - 449	\( 3^{12}\cdot 31^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.743702041351801.1	x^9 - 50x^7 - 39x^6 + 733x^5 + 999x^4 - 3097x^3 - 5616x^2 + 279x + 2619	\( 7^{6}\cdot 43^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.1363532208525369.2	x^9 - 3x^8 - 42x^7 + 56x^6 + 585x^5 - 51x^4 - 2707x^3 - 1683x^2 + 1659x + 593	\( 3^{12}\cdot 37^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.3359431500123609.1	x^9 - 3x^8 - 48x^7 + 77x^6 + 735x^5 - 333x^4 - 3903x^3 - 1452x^2 + 4476x + 2971	\( 3^{12}\cdot 43^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.4283810754983929.1	x^9 - 44x^7 - 21x^6 + 511x^5 + 213x^4 - 1993x^3 - 756x^2 + 2277x + 1269	\( 13^{6}\cdot 31^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.6061320523197289.1	x^9 - 68x^7 - 6x^6 + 1399x^5 + 272x^4 - 9467x^3 - 1944x^2 + 15100x - 8	\( 7^{6}\cdot 61^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.10642338203800681.1	x^9 - 74x^7 - 38x^6 + 1669x^5 + 1562x^4 - 12043x^3 - 15200x^2 + 12932x + 11864	\( 7^{6}\cdot 67^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.12384271322498881.1	x^9 - 50x^7 - 38x^6 + 673x^5 + 946x^4 - 1387x^3 - 2432x^2 - 540x + 248	\( 13^{6}\cdot 37^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.17804320388674561.1	x^9 - 80x^7 - 56x^6 + 1963x^5 + 2646x^4 - 14757x^3 - 27104x^2 + 5964x + 11816	\( 7^{6}\cdot 73^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.27380039270784201.1	x^9 - 3x^8 - 66x^7 + 164x^6 + 1281x^5 - 2619x^4 - 7815x^3 + 10197x^2 + 14175x - 1467	\( 3^{12}\cdot 61^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.28598996054590129.1	x^9 - 86x^7 - 150x^6 + 2281x^5 + 7494x^4 - 12883x^3 - 86400x^2 - 124308x - 54216	\( 7^{6}\cdot 79^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.30512012057180641.1	x^9 - 56x^7 - 31x^6 + 859x^5 + 971x^4 - 3037x^3 - 3100x^2 + 2157x + 967	\( 13^{6}\cdot 43^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.41753392563387961.1	x^9 - 50x^7 - x^6 + 637x^5 - 163x^4 - 1837x^3 - 16x^2 + 1107x + 349	\( 19^{6}\cdot 31^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.48073293078275529.1	x^9 - 3x^8 - 72x^7 + 134x^6 + 1629x^5 - 1341x^4 - 12749x^3 - 2013x^2 + 24255x + 12471	\( 3^{12}\cdot 67^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.80425212553252449.3	x^9 - 3x^8 - 78x^7 + 242x^6 + 1725x^5 - 5823x^4 - 9253x^3 + 36933x^2 - 8679x - 9809	\( 3^{12}\cdot 73^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.97998323407891921.1	x^9 - 104x^7 - 204x^6 + 3379x^5 + 12786x^4 - 22081x^3 - 183600x^2 - 320652x - 178632	\( 7^{6}\cdot 97^{6} \)	$C_3^2$ (as 9T2)	$[2, 2]$ (GRH)
9.9.120706859316371329.1	x^9 - 56x^7 - 60x^6 + 811x^5 + 834x^4 - 4393x^3 - 2160x^2 + 8532x - 2376	\( 19^{6}\cdot 37^{6} \)	$C_3^2$ (as 9T2)	$[2, 2]$
9.9.129186640449535761.1	x^9 - 3x^8 - 84x^7 + 50x^6 + 2445x^5 + 3303x^4 - 21345x^3 - 64641x^2 - 53817x - 9197	\( 3^{12}\cdot 79^{6} \)	$C_3^2$ (as 9T2)	$[2, 2]$ (GRH)
9.9.140479058634340321.1	x^9 - 110x^7 - 148x^6 + 3793x^5 + 9892x^4 - 35773x^3 - 151552x^2 - 138256x - 10688	\( 7^{6}\cdot 103^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.197309150940332809.1	x^9 - 116x^7 - 25x^6 + 4231x^5 + 1679x^4 - 51103x^3 - 28900x^2 + 92067x + 32089	\( 7^{6}\cdot 109^{6} \)	$C_3^2$ (as 9T2)	$[2, 2]$ (GRH)
9.9.248679006649044049.1	x^9 - 74x^7 - 14x^6 + 1561x^5 + 162x^4 - 10743x^3 - 3584x^2 + 23412x + 14936	\( 13^{6}\cdot 61^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.297394093761051169.1	x^9 - 62x^7 - 53x^6 + 1009x^5 + 829x^4 - 5833x^3 - 3392x^2 + 10515x + 4169	\( 19^{6}\cdot 43^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.301789003173921081.1	x^9 - 3x^8 - 120x^7 + 14x^6 + 5109x^5 + 12303x^4 - 59793x^3 - 316281x^2 - 504861x - 269801	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.3	x^9 - 60x^7 - 66x^6 + 927x^5 + 1002x^4 - 5092x^3 - 2376x^2 + 10272x - 4096	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.4	x^9 - 60x^7 - 45x^6 + 927x^5 + 981x^4 - 2593x^3 - 1620x^2 + 2061x - 99	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$
9.9.301789003173921081.5	x^9 - 60x^7 - 6x^6 + 927x^5 + 240x^4 - 4075x^3 - 216x^2 + 3036x - 8	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$
9.9.301789003173921081.6	x^9 - 60x^7 - 27x^6 + 927x^5 + 261x^4 - 4663x^3 - 972x^2 + 5787x + 2547	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$
9.9.301789003173921081.7	x^9 - 3x^8 - 72x^7 + 62x^6 + 1701x^5 + 1023x^4 - 12993x^3 - 19497x^2 + 4083x + 5095	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.8	x^9 - 3x^8 - 72x^7 + 83x^6 + 1659x^5 + 267x^4 - 12923x^3 - 13218x^2 + 15024x + 16561	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.9	x^9 - 3x^8 - 120x^7 + 209x^6 + 4719x^5 - 2127x^4 - 63433x^3 - 40746x^2 + 100224x + 24389	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.10	x^9 - 3x^8 - 96x^7 + 116x^6 + 3057x^5 + 1179x^4 - 32635x^3 - 54633x^2 + 18465x + 51661	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.301789003173921081.12	x^9 - 3x^8 - 96x^7 + 389x^6 + 2511x^5 - 14109x^4 - 5335x^3 + 132372x^2 - 234060x + 113723	\( 3^{12}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2$ (as 9T2)	$[3]$ (GRH)
9.9.436625333178768721.1	x^9 - 80x^7 - 30x^6 + 1843x^5 + 1600x^4 - 12695x^3 - 9720x^2 + 23356x - 1000	\( 13^{6}\cdot 67^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.442675475271472689.1	x^9 - 3x^8 - 102x^7 + 446x^6 + 2805x^5 - 17991x^4 - 1257x^3 + 185757x^2 - 412611x + 273043	\( 3^{12}\cdot 97^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.493640252540246161.1	x^9 - 134x^7 - 283x^6 + 5689x^5 + 23207x^4 - 54253x^3 - 452800x^2 - 838713x - 470681	\( 7^{6}\cdot 127^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.634568346519668289.1	x^9 - 3x^8 - 108x^7 + 404x^6 + 3321x^5 - 15921x^4 - 18635x^3 + 171075x^2 - 218979x + 57237	\( 3^{12}\cdot 103^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.730461405459781801.1	x^9 - 86x^7 - 64x^6 + 2149x^5 + 2404x^4 - 17377x^3 - 25600x^2 + 30032x + 46528	\( 13^{6}\cdot 73^{6} \)	$C_3^2$ (as 9T2)	$[2, 2]$ (GRH)
9.9.848549225908978489.1	x^9 - 146x^7 - 356x^6 + 6781x^5 + 32056x^4 - 63325x^3 - 689216x^2 - 1538736x - 1112896	\( 7^{6}\cdot 139^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.891279760005451881.2	x^9 - 3x^8 - 114x^7 + 245x^6 + 4095x^5 - 5487x^4 - 49615x^3 + 21474x^2 + 119118x + 26333	\( 3^{12}\cdot 109^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.1173336718095862489.1	x^9 - 92x^7 - 142x^6 + 2479x^5 + 7340x^4 - 11887x^3 - 68728x^2 - 86076x - 32408	\( 13^{6}\cdot 79^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.1394600844463789249.1	x^9 - 158x^7 - 318x^6 + 7969x^5 + 31382x^4 - 99263x^3 - 732672x^2 - 1280612x - 649832	\( 7^{6}\cdot 151^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)
9.9.1761919874898143401.1	x^9 - 164x^7 - 245x^6 + 8599x^5 + 24955x^4 - 130579x^3 - 612500x^2 - 638925x - 35875	\( 7^{6}\cdot 157^{6} \)	$C_3^2$ (as 9T2)	Trivial (GRH)