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 249)

Label	Polynomial	Discriminant	Galois group	Class group
9.9.164648481361.1	x^9 - 14x^7 + 63x^5 - 98x^3 + 42x - 7	\( 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.3063651608241.1	x^9 - 21x^7 - 7x^6 + 126x^5 + 105x^4 - 189x^3 - 252x^2 - 63x + 7	\( 3^{12}\cdot 7^{8} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.19708707423601.1	x^9 - x^8 - 26x^7 + 56x^6 + 154x^5 - 546x^4 + 154x^3 + 1074x^2 - 1368x + 503	\( 7^{8}\cdot 43^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.433512750098961.1	x^9 - 39x^7 - 13x^6 + 234x^5 - 39x^4 - 429x^3 + 234x^2 + 117x - 65	\( 3^{12}\cdot 13^{8} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.510353687638081.1	x^9 - 4x^8 - 38x^7 + 175x^6 + 266x^5 - 1750x^4 - 7x^3 + 5570x^2 - 2239x - 3991	\( 7^{8}\cdot 97^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.753344451188641.1	x^9 - 2x^8 - 30x^7 + 17x^6 + 250x^5 + 73x^4 - 513x^3 - 239x^2 + 235x + 125	\( 13^{8}\cdot 31^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.1499682086581441.1	x^9 - 2x^8 - 48x^7 + 91x^6 + 707x^5 - 1386x^4 - 2877x^3 + 6873x^2 - 3757x + 601	\( 7^{8}\cdot 127^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.2152006214457841.1	x^9 - 3x^8 - 52x^7 + 49x^6 + 1001x^5 + 770x^4 - 5908x^3 - 10008x^2 + 2528x + 8933	\( 7^{8}\cdot 139^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.4089611069304489.1	x^9 - 72x^7 - 135x^6 + 1539x^5 + 5472x^4 - 5016x^3 - 48735x^2 - 77976x - 39349	\( 3^{22}\cdot 19^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.4089611069304489.2	x^9 - 72x^7 - 45x^6 + 1539x^5 + 1197x^4 - 11343x^3 - 9747x^2 + 19494x + 13357	\( 3^{22}\cdot 19^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.9025761726072081.3	x^9 - 57x^7 - 38x^6 + 342x^5 + 57x^4 - 684x^3 + 171x^2 + 342x - 133	\( 3^{12}\cdot 19^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$
9.9.9025761726072081.4	x^9 - 57x^7 - 76x^6 + 855x^5 + 1482x^4 - 4218x^3 - 7866x^2 + 3591x + 6289	\( 3^{12}\cdot 19^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$
9.9.11426524135596241.1	x^9 - 4x^8 - 73x^7 + 168x^6 + 1750x^5 - 2569x^4 - 16933x^3 + 17008x^2 + 56260x - 40979	\( 7^{8}\cdot 211^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.23165317606061761.1	x^9 - 4x^8 - 42x^7 + 214x^6 + 178x^5 - 2045x^4 + 2021x^3 + 2558x^2 - 4411x + 1405	\( 13^{8}\cdot 73^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.31772777657138401.1	x^9 - 65x^7 - 143x^6 + 507x^5 + 585x^4 - 2028x^3 + 1261x^2 - 52x - 65	\( 13^{8}\cdot 79^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.51208000923838801.1	x^9 - 2x^8 - 90x^7 + 133x^6 + 2618x^5 - 2317x^4 - 25851x^3 + 7860x^2 + 24376x - 11047	\( 7^{8}\cdot 307^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.58813158057863049.2	x^9 - 117x^7 - 72x^6 + 3996x^5 + 6993x^4 - 39738x^3 - 110889x^2 - 24642x + 72557	\( 3^{22}\cdot 37^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.58813158057863049.3	x^9 - 117x^7 - 9x^6 + 3996x^5 - 999x^4 - 45399x^3 + 160173x + 121841	\( 3^{22}\cdot 37^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.85523610698528401.1	x^9 - 112x^7 - 77x^6 + 3864x^5 + 6013x^4 - 39655x^3 - 99176x^2 - 32648x + 8323	\( 7^{8}\cdot 349^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.87500953582971201.2	x^9 - 105x^7 - 210x^6 + 3276x^5 + 11739x^4 - 22750x^3 - 159705x^2 - 241332x - 114751	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.87500953582971201.4	x^9 - 105x^7 - 105x^6 + 3276x^5 + 7917x^4 - 28483x^3 - 127764x^2 - 145509x - 34307	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.87500953582971201.5	x^9 - 105x^7 + 3276x^5 - 1365x^4 - 33124x^3 + 31941x^2 + 14196x - 15379	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.87500953582971201.9	x^9 - 105x^7 - 147x^6 + 3276x^5 + 7644x^4 - 30121x^3 - 95823x^2 + 3549x + 133679	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.87500953582971201.10	x^9 - 105x^7 - 147x^6 + 3276x^5 + 6279x^4 - 35581x^3 - 63882x^2 + 131313x + 164437	\( 3^{12}\cdot 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.115147048447564081.1	x^9 - 65x^7 - 39x^6 + 1378x^5 + 1859x^4 - 9464x^3 - 21112x^2 - 6240x + 5057	\( 13^{8}\cdot 109^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.118943622204325681.1	x^9 - 119x^7 - 84x^6 + 3927x^5 + 2268x^4 - 42406x^3 - 16583x^2 + 83832x + 45773	\( 7^{8}\cdot 379^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.180905563815022809.1	x^9 - 63x^7 + 1323x^5 - 10290x^3 + 21609x - 12005	\( 3^{22}\cdot 7^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$
9.9.180905563815022809.2	x^9 - 63x^7 + 1323x^5 - 10290x^3 + 21609x - 11564	\( 3^{22}\cdot 7^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.202645006049665921.1	x^9 - 4x^8 - 122x^7 + 147x^6 + 4487x^5 + 588x^4 - 51569x^3 + 3764x^2 + 207418x - 157151	\( 7^{8}\cdot 433^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.424086656141248321.1	x^9 - 2x^8 - 82x^7 - 48x^6 + 1706x^5 + 2049x^4 - 12798x^3 - 16307x^2 + 29017x + 26645	\( 13^{8}\cdot 151^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.453261265828682481.1	x^9 - 93x^7 - 124x^6 + 2232x^5 + 2976x^4 - 19344x^3 - 17856x^2 + 53568x + 7936	\( 3^{12}\cdot 31^{8} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.495616125312007921.1	x^9 - 4x^8 - 94x^7 + 500x^6 + 1920x^5 - 15331x^4 + 14618x^3 + 59888x^2 - 134918x + 77195	\( 13^{8}\cdot 157^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.516099722371854481.1	x^9 - 4x^8 - 136x^7 + 616x^6 + 4634x^5 - 21371x^4 - 38500x^3 + 192925x^2 + 8597x - 257881	\( 7^{8}\cdot 547^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.562900392725468161.1	x^9 - 4x^8 - 136x^7 + 203x^6 + 5768x^5 - 2226x^4 - 92211x^3 + 2392x^2 + 493333x - 23521	\( 7^{8}\cdot 13^{4}\cdot 43^{4} \)	$C_9:C_3$ (as 9T6)	$[3, 3]$ (GRH)
9.9.562900392725468161.3	x^9 - 133x^7 - 28x^6 + 5593x^5 + 567x^4 - 89817x^3 - 14945x^2 + 487298x + 195307	\( 7^{8}\cdot 13^{4}\cdot 43^{4} \)	$C_9:C_3$ (as 9T6)	$[3, 3]$ (GRH)
9.9.562900392725468161.5	x^9 - 3x^8 - 143x^7 + 735x^6 + 5390x^5 - 43064x^4 + 10143x^3 + 556537x^2 - 1421552x + 903673	\( 7^{8}\cdot 13^{4}\cdot 43^{4} \)	$C_9:C_3$ (as 9T6)	$[3, 3]$ (GRH)
9.9.752111463475447201.1	x^9 - x^8 - 159x^7 + 399x^6 + 6748x^5 - 17878x^4 - 97909x^3 + 180134x^2 + 530513x - 204751	\( 7^{8}\cdot 601^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.875510014130460241.1	x^9 - 2x^8 - 82x^7 + 199x^6 + 1888x^5 - 5296x^4 - 7949x^3 + 22628x^2 - 10295x + 125	\( 13^{8}\cdot 181^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.891166893611747769.3	x^9 - 189x^7 - 396x^6 + 9855x^5 + 24966x^4 - 173010x^3 - 287766x^2 + 1103103x - 474281	\( 3^{22}\cdot 73^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.891166893611747769.4	x^9 - 189x^7 - 234x^6 + 9855x^5 + 13140x^4 - 180894x^3 - 287766x^2 + 1103103x + 2115613	\( 3^{22}\cdot 73^{4} \)	$C_9:C_3$ (as 9T6)	$[3]$ (GRH)
9.9.913906480870362721.1	x^9 - 168x^7 - 378x^6 + 8505x^5 + 33810x^4 - 97426x^3 - 597296x^2 - 527058x + 315259	\( 7^{8}\cdot 631^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.985435518764720401.1	x^9 - 2x^8 - 146x^7 + 168x^6 + 7112x^5 - 3871x^4 - 129045x^3 + 20628x^2 + 639221x + 260903	\( 7^{8}\cdot 643^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.1257791680575160641.1	x^9 - 4x^8 - 20x^7 + 84x^6 - 56x^5 - 70x^4 + 84x^3 - 16x^2 - 5x + 1	\( 3^{8}\cdot 61^{8} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.1610356251405500641.1	x^9 - x^8 - 166x^7 - 21x^6 + 8806x^5 + 13818x^4 - 162365x^3 - 462879x^2 + 287613x + 1336453	\( 7^{8}\cdot 727^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.1866675593471230161.3	x^9 - 111x^7 - 148x^6 + 3663x^5 + 9546x^4 - 25530x^3 - 119214x^2 - 142857x - 53021	\( 3^{12}\cdot 37^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$
9.9.1866675593471230161.4	x^9 - 111x^7 - 148x^6 + 666x^5 + 555x^4 - 1554x^3 - 333x^2 + 1332x - 407	\( 3^{12}\cdot 37^{8} \)	$C_9:C_3$ (as 9T6)	$[3]$
9.9.1893075078005641201.1	x^9 - 3x^8 - 164x^7 + 546x^6 + 8127x^5 - 23072x^4 - 156324x^3 + 267654x^2 + 1048615x - 278879	\( 7^{8}\cdot 757^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.2664210032449121601.1	x^9 - 2x^8 - 28x^7 + 84x^6 - 28x^5 - 98x^4 + 84x^3 - 8x^2 - 7x + 1	\( 3^{8}\cdot 67^{8} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.4429692664637819049.1	x^9 - 216x^7 - 567x^6 + 14715x^5 + 71613x^4 - 251463x^3 - 2245509x^2 - 4277160x - 1508887	\( 3^{22}\cdot 109^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)
9.9.4429692664637819049.4	x^9 - 216x^7 - 495x^6 + 14715x^5 + 57879x^4 - 300513x^3 - 1603935x^2 + 213858x + 6213763	\( 3^{22}\cdot 109^{4} \)	$C_9:C_3$ (as 9T6)	Trivial (GRH)