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 )

Label	Polynomial	Discriminant	Galois group	Class group
9.1.479966398994267136000.1	x^9 - 3x^8 - 36x^7 - 1254x^6 + 5916x^5 + 33258x^4 + 548766x^3 - 719928x^2 + 759141x + 95444679	\( 2^{13}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3}\cdot 137^{3} \)	$S_3^2$ (as 9T8)	$[9, 216]$ (GRH)
9.3.961258003845861719744.1	x^9 - x^8 - 69x^7 + 692x^6 - 3420x^5 + 9735x^4 - 16479x^3 + 16347x^2 - 8784x + 1979	\( -\,2^{6}\cdot 17^{3}\cdot 163^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 806]$ (GRH)
9.1.1564474192453606883904.1	x^9 - 54x^6 - 1212x^3 - 5832	\( 2^{6}\cdot 3^{16}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 18, 54]$ (GRH)
9.3.3789758442045443136192.2	x^9 - 9x^7 - 25x^6 + 159x^5 + 216x^4 - 794x^3 - 3525x^2 - 75x + 14299	\( -\,2^{6}\cdot 3^{9}\cdot 7^{4}\cdot 11^{6}\cdot 29^{4} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 387]$ (GRH)
9.1.4828914945396284659776.3	x^9 - 246x^6 + 181548x^3 - 551368	\( 2^{6}\cdot 3^{18}\cdot 41^{7} \)	$S_3^2$ (as 9T8)	$[3, 6, 84]$ (GRH)
9.3.8666121461345916813504.1	x^9 - 3x^8 - 117x^7 - 1068x^6 - 5292x^5 - 15255x^4 - 26055x^3 - 25947x^2 - 13932x - 3123	\( -\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 31^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 819]$ (GRH)
9.1.9351388785251241000000.1	x^9 - 561x^6 + 867x^3 - 4913	\( 2^{6}\cdot 3^{18}\cdot 5^{6}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6, 6, 12]$ (GRH)
9.3.9946239527177597280448.1	x^9 - x^8 - 93x^7 - 876x^6 - 4320x^5 - 12363x^4 - 21015x^3 - 20883x^2 - 11214x - 2519	\( -\,2^{6}\cdot 7^{7}\cdot 19^{3}\cdot 31^{7} \)	$S_3\times C_3$ (as 9T4)	$[4, 12, 156]$ (GRH)
9.1.11500045118399169000000.3	x^9 - 72x^7 - 746x^6 + 1728x^5 + 35808x^4 + 168128x^3 - 429696x^2 - 4366848x - 9021088	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 41^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 270]$ (GRH)
9.1.12307133121875361000000.1	x^9 - 275x^6 + 81675x^3 + 4492125	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 3, 9, 36]$ (GRH)
9.1.13557996409720545000000.1	x^9 - 810x^6 + 210060x^3 - 19683000	\( 2^{6}\cdot 3^{10}\cdot 5^{7}\cdot 3581^{3} \)	$S_3^2$ (as 9T8)	$[3, 6, 72]$ (GRH)
9.3.14060953235879331005952.1	x^9 - 273x^7 - 1001x^6 + 26208x^5 + 197652x^4 - 516516x^3 - 10434060x^2 - 41140008x - 54787096	\( -\,2^{9}\cdot 3^{12}\cdot 7^{7}\cdot 13^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 12, 12]$ (GRH)
9.1.14795701528018641274944.1	x^9 - 3x^8 + 6x^7 - 405x^6 + 1596x^5 - 1197x^4 + 52275x^3 - 51876x^2 + 52272x + 2299968	\( 2^{6}\cdot 3^{10}\cdot 397^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6, 18, 18]$ (GRH)
9.1.18226538222455809000000.2	x^9 - 195x^6 - 15825x^3 - 274625	\( 2^{6}\cdot 3^{18}\cdot 5^{6}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 9, 54]$ (GRH)
9.1.22963746932945280000000.2	x^9 - 120x^6 + 266160x^3 - 64000	\( 2^{13}\cdot 3^{10}\cdot 5^{7}\cdot 7^{3}\cdot 11^{6} \)	$S_3^2$ (as 9T8)	$[3, 3, 126]$ (GRH)
9.1.28392734312005734425664.1	x^9 - 3x^8 + 6x^7 + 245x^6 - 498x^5 + 207x^4 + 37955x^3 - 37842x^2 - 19236x + 607446	\( 2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 13^{6}\cdot 307^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 9, 18]$ (GRH)
9.3.42156337503708731671875.2	x^9 - 36x^7 - 147x^6 + 3942x^5 - 10512x^4 - 122640x^3 + 575532x^2 - 767376x - 5329	\( -\,3^{9}\cdot 5^{6}\cdot 13^{6}\cdot 73^{4} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 3, 126]$ (GRH)
9.1.62984024442172500245568.1	x^9 - 1243x^6 - 55869x^3 - 2924207	\( 2^{6}\cdot 3^{9}\cdot 11^{7}\cdot 37^{6} \)	$S_3^2$ (as 9T8)	$[3, 18, 36]$ (GRH)
9.3.74211952229135601401024.1	x^9 - 287x^7 - 445x^6 + 25039x^5 + 96194x^4 - 488422x^3 - 2638405x^2 - 3176523x - 10543679	\( -\,2^{6}\cdot 7^{6}\cdot 37^{7}\cdot 47^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 111]$ (GRH)
9.3.77080003669746653832704.1	x^9 - x^8 - 259x^7 + 2834x^6 - 15538x^5 + 59769x^4 - 127105x^3 + 190071x^2 - 166668x + 114449	\( -\,2^{9}\cdot 7^{7}\cdot 109^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 474]$ (GRH)
9.3.81483030856958691870000.1	x^9 - 273x^7 - 101x^6 + 24570x^5 + 16380x^4 - 737370x^3 - 737100x^2 - 245700x - 327300	\( -\,2^{4}\cdot 3^{15}\cdot 5^{4}\cdot 7^{6}\cdot 13^{6} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 18, 126]$ (GRH)
9.1.85626986126302659544128.2	x^9 + 54x^7 - 645x^6 + 972x^5 + 11934x^4 + 156225x^3 - 208980x^2 - 5061960x - 11203919	\( 2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 31^{7} \)	$S_3^2$ (as 9T8)	$[9, 9, 54]$ (GRH)
9.1.85626986126302659544128.3	x^9 - 3x^8 - 209x^6 - 6x^5 + 645x^4 + 16283x^3 + 15624x^2 - 16278x + 390818	\( 2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 31^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 9, 27]$ (GRH)
9.3.95886440685214498936512.4	x^9 - 21x^7 - 978x^6 + 13167x^5 - 43596x^4 - 362895x^3 + 2433690x^2 - 3643164x - 32428236	\( -\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 31^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 78]$ (GRH)
9.3.108943453504735227000000.3	x^9 - 60x^6 - 251500x^3 - 8000	\( -\,2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 7^{6}\cdot 19^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 63]$ (GRH)
9.1.112966347984842801097792.1	x^9 - 3x^8 - 49x^6 + 108x^5 - 573x^4 + 48859x^3 - 48606x^2 + 26328x - 11292	\( 2^{6}\cdot 3^{10}\cdot 11^{3}\cdot 13^{7}\cdot 71^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 42]$ (GRH)
9.3.121356276492224600216523.2	x^9 - 24x^6 - 1761x^3 - 512	\( -\,3^{19}\cdot 7^{6}\cdot 31^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 9, 90]$ (GRH)
9.3.127317235713997956046875.1	x^9 - 108x^7 - 195x^6 + 3888x^5 + 14040x^4 - 36711x^3 - 252720x^2 - 358020x - 42120	\( -\,3^{15}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[6, 234]$ (GRH)
9.1.129197726101491786058752.1	x^9 - 48x^6 - 956x^3 - 4096	\( 2^{10}\cdot 3^{9}\cdot 431^{6} \)	$S_3^2$ (as 9T8)	$[2, 2, 2, 12, 24]$ (GRH)
9.1.147960417197346328355328.1	x^9 - 3x^8 + 18x^7 - 1531x^6 + 3090x^5 + 5391x^4 + 1083109x^3 - 1120128x^2 - 7085514x - 121416404	\( 2^{9}\cdot 3^{3}\cdot 523^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 135]$ (GRH)
9.1.165109609889173909757952.1	x^9 - 48x^6 - 926x^3 - 4096	\( 2^{13}\cdot 3^{9}\cdot 7^{6}\cdot 11^{6}\cdot 17^{3} \)	$S_3^2$ (as 9T8)	$[6, 6, 30]$ (GRH)
9.1.181530127723340313000000.1	x^9 + 48x^7 - 135x^6 + 768x^5 - 5040x^4 + 16921x^3 - 34560x^2 + 129600x - 70645	\( 2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 67^{3}\cdot 313^{3} \)	$S_3^2$ (as 9T8)	$[3, 6, 60]$ (GRH)
9.3.200566492330693110797824.1	x^9 - 4x^8 - 129x^7 - 1167x^6 - 5805x^5 - 16800x^4 - 28764x^3 - 28677x^2 - 15399x - 3449	\( -\,2^{9}\cdot 11^{3}\cdot 313^{7} \)	$S_3\times C_3$ (as 9T4)	$[9, 189]$ (GRH)
9.3.240836286342118785100992.1	x^9 - 147x^7 - 759x^6 + 8721x^5 + 118404x^4 + 400242x^3 - 967725x^2 - 4041675x - 94875	\( -\,2^{6}\cdot 3^{15}\cdot 11^{6}\cdot 23^{6} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[9, 351]$ (GRH)
9.1.259932343846602632901696.1	x^9 - 3x^8 - 83x^6 - 6x^5 + 267x^4 + 3011x^3 + 2730x^2 - 3006x + 30122	\( 2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 11^{3}\cdot 13^{7} \)	$S_3^2$ (as 9T8)	$[9, 9, 54]$ (GRH)
9.1.268548467233795126572096.1	x^9 + 48x^7 - 645x^6 + 768x^5 + 10608x^4 + 154489x^3 - 165120x^2 - 4499520x - 10827207	\( 2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 19^{3}\cdot 31^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 180]$ (GRH)
9.1.273919266332571877019712.6	x^9 - 18x^7 - 711x^6 + 2736x^5 + 7218x^4 - 2529x^3 + 250344x^2 + 1568340x - 3346531	\( 2^{6}\cdot 3^{18}\cdot 73^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 18, 18]$ (GRH)
9.1.273919266332571877019712.7	x^9 - 36x^7 - 267x^6 + 1746x^5 + 3780x^4 - 20013x^3 - 29250x^2 + 74880x + 115113	\( 2^{6}\cdot 3^{18}\cdot 73^{7} \)	$S_3^2$ (as 9T8)	$[6, 18, 18]$ (GRH)
9.1.308955633348850571290176.1	x^9 - 3x^8 + 24x^7 + 35x^6 + 12x^5 + 3603x^4 + 80571x^3 - 79218x^2 + 114300x - 22500	\( 2^{6}\cdot 3^{10}\cdot 43^{7}\cdot 67^{3} \)	$S_3^2$ (as 9T8)	$[3, 6, 6, 12]$ (GRH)
9.1.321931368581771643444288.1	x^9 - 2508x^6 - 1508144x^3 - 584277056	\( 2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 11^{6}\cdot 19^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 198]$ (GRH)
9.3.374418025971689252058688.1	x^9 - 4x^8 - 194x^7 + 703x^6 + 3393x^5 - 54925x^4 + 263003x^3 - 776932x^2 + 1275105x - 1241227	\( -\,2^{6}\cdot 7^{3}\cdot 13^{7}\cdot 43^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 12, 36]$ (GRH)
9.1.460783890475548460173504.1	x^9 - x^8 + 210x^7 - 1652x^6 + 8392x^5 - 219078x^4 + 401771x^3 - 2902963x^2 + 37229388x + 196442864	\( 2^{6}\cdot 3^{3}\cdot 17^{6}\cdot 73^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 126]$ (GRH)
9.1.502729509987688558288896.1	x^9 - 3x^8 + 135x^7 - 239x^6 + 8982x^5 - 26062x^4 + 205304x^3 + 229684x^2 - 6773468x + 13907244	\( 2^{13}\cdot 3^{3}\cdot 7^{7}\cdot 13^{6}\cdot 83^{3} \)	$S_3^2$ (as 9T8)	$[6, 6, 72]$ (GRH)
9.3.528604308547604359881408.2	x^9 - 81x^7 - 786x^6 - 14661x^5 - 58644x^4 - 830247x^3 - 5307282x^2 - 10614564x - 13890664	\( -\,2^{6}\cdot 3^{13}\cdot 13^{6}\cdot 181^{4} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 9, 63]$ (GRH)
9.1.531635482684868000145408.1	x^9 - 856x^6 + 343470x^3 + 9800344	\( 2^{13}\cdot 3^{9}\cdot 13^{3}\cdot 107^{6} \)	$S_3^2$ (as 9T8)	$[9, 198]$ (GRH)
9.1.538122447811291702464000.1	x^9 - 3x^8 - 87x^7 - 10x^6 + 2988x^5 + 10362x^4 - 13847x^3 - 195867x^2 - 492093x - 399406	\( 2^{9}\cdot 3^{9}\cdot 5^{3}\cdot 7^{6}\cdot 29^{3}\cdot 53^{3} \)	$S_3^2$ (as 9T8)	$[6, 12, 24]$ (GRH)
9.3.545622717609851839474608.1	x^9 - 3x^8 - 159x^7 + 1025x^6 + 4095x^5 - 28674x^4 - 259386x^3 + 3671649x^2 - 15308946x + 20976129	\( -\,2^{4}\cdot 3^{15}\cdot 7^{6}\cdot 13^{4}\cdot 29^{4} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[6, 234]$ (GRH)
9.3.679386010623941601864000.1	x^9 - 3x^8 - 252x^7 + 470x^6 + 20757x^5 - 70659x^4 - 426106x^3 - 316368x^2 + 3830112x + 38431744	\( -\,2^{6}\cdot 3^{9}\cdot 5^{3}\cdot 13^{6}\cdot 19^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 45]$ (GRH)
9.3.710632240764767196320448.2	x^9 - 27x^7 - 19x^6 + 243x^5 + 342x^4 - 26x^3 - 1539x^2 - 6327x + 7353	\( -\,2^{6}\cdot 3^{13}\cdot 19^{6}\cdot 23^{6} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 9, 54]$ (GRH)
9.1.710723455359858596021625.1	x^9 - 3x^8 + 4x^7 + 819x^6 - 48503x^5 - 514094x^4 + 3139612x^3 + 61428264x^2 + 283397584x + 434263712	\( 3^{3}\cdot 5^{3}\cdot 7^{6}\cdot 151^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 54]$ (GRH)

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