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Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. \(p\)

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Results (19 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.3.178...427.1	$x^{9} - 1305 x^{6} - 709614 x^{3} - 82312875$	$9$	[3,3]	$-\,3^{19}\cdot 13^{6}\cdot 1213^{6}$	$3$	$6394.28639832702$	$6796.711263034178$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 54, 1045170]$	$2$	$5$	$250762.4844980746$
9.3.221...536.1	$x^{9} - 20307 x^{7} - 643055 x^{6} + 138412512 x^{5} + 8796667488 x^{4} - 176694943488 x^{3} - 30297960822528 x^{2} - 967845661396992 x - 10323499378798592$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 7^{7}\cdot 967^{7}$	$4$	$6548.55050078$	$13467.761918306092$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 7801212]$	$2$	$5$	$374306.60136712604$
9.3.257...787.1	$x^{9} - 363 x^{6} - 1252683960 x^{3} - 1771561$	$9$	[3,3]	$-\,3^{15}\cdot 11^{6}\cdot 3169^{6}$	$3$	$6659.046395606023$	$7078.133949383966$			?	$S_3\times C_3$ (as 9T4)	$[7, 21, 1661688]$	$2$	$5$	$385398.4204609144$
9.3.370...963.1	$x^{9} - 363 x^{6} - 1330954746 x^{3} - 1771561$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 11^{6}\cdot 13^{6}\cdot 37^{6}$	$5$	$6933.608121097081$	$7369.975236400984$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 18, 32526]$	$2$	$5$	$393142.3779935802$
9.3.372...368.1	$x^{9} - 1308 x^{6} - 712896 x^{3} - 82881856$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 19^{6}\cdot 67^{6}$	$5$	$6937.882522124614$	$7374.518647158151$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 9, 61047]$	$2$	$5$	$597706.0055074854$
9.3.610...136.1	$x^{9} - 2 x^{8} - 12783 x^{7} - 655523 x^{6} - 8351247 x^{5} - 109011858 x^{4} - 648630606 x^{3} - 3516028401 x^{2} - 9062063283 x - 22186138127$	$9$	[3,3]	$-\,2^{9}\cdot 7^{7}\cdot 43^{7}\cdot 127^{7}$	$4$	$7329.86067396$	$18628.88409487867$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 6, 6, 78876]$	$2$	$5$	$852760.0283206603$
9.3.145...616.1	$x^{9} - 9507 x^{7} - 205985 x^{6} + 30431907 x^{5} + 1325408898 x^{4} - 18341132568 x^{3} - 2154460739013 x^{2} - 47277836420067 x - 346690767098467$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 11^{3}\cdot 3169^{7}$	$4$	$8070.84024931$	$18835.618198946016$			?	$S_3\times C_3$ (as 9T4)	$[3, 93510522]$	$2$	$5$	$342732.7478730024$
9.3.385...728.1	$x^{9} - 6 x^{6} - 2954976 x^{3} - 8$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 27361^{6}$	$3$	$8994.493916135887$	$9560.5630240597$			?	$S_3\times C_3$ (as 9T4)	$[15, 13262760]$	$2$	$5$	$932233.0211215143$
9.3.436...032.1	$x^{9} - 6 x^{6} - 3017184 x^{3} - 8$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 13^{6}\cdot 307^{6}$	$5$	$9120.288997507569$	$9694.275027734873$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 18, 18, 27972]$	$2$	$5$	$937599.0387526765$
9.3.535...427.1	$x^{9} - 507 x^{6} - 3429205026 x^{3} - 4826809$	$9$	[3,3]	$-\,3^{15}\cdot 13^{6}\cdot 4447^{6}$	$3$	$9329.873292496624$	$9917.049525086115$			?	$S_3\times C_3$ (as 9T4)	$[12, 36, 1510848]$	$2$	$5$	$447510.71870329685$
9.3.728...803.1	$x^{9} - 507 x^{6} - 3609653424 x^{3} - 4826809$	$9$	[3,3]	$-\,3^{15}\cdot 13^{6}\cdot 31^{6}\cdot 151^{6}$	$4$	$9654.358466762505$	$10261.956196641762$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 3509262]$	$2$	$5$	$454884.82024610945$
9.3.798...875.1	$x^{9} - 20025 x^{6} - 167096250 x^{3} - 297408796875$	$9$	[3,3]	$-\,3^{19}\cdot 5^{6}\cdot 13^{6}\cdot 457^{6}$	$4$	$9753.092728372458$	$10366.90430595812$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 12, 1305612]$	$2$	$5$	$506767.73832978925$
9.3.936...136.1	$x^{9} - 25761 x^{7} - 918809 x^{6} + 222575040 x^{5} + 15926171508 x^{4} - 359711868708 x^{3} - 69450114770892 x^{2} - 2496333846718440 x - 29955576128950872$	$9$	[3,3]	$-\,2^{9}\cdot 3^{12}\cdot 31^{7}\cdot 277^{7}$	$4$	$9927.64273279$	$23222.44192902505$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 1036659]$	$2$	$5$	$3839173.315130516$
9.3.104...875.1	$x^{9} - 20475 x^{6} - 174690000 x^{3} - 317912765625$	$9$	[3,3]	$-\,3^{19}\cdot 5^{6}\cdot 6211^{6}$	$3$	$10046.39704347429$	$10678.667748782753$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 126, 256410]$	$2$	$5$	$513819.9883304559$
9.3.205...088.2	$x^{9} - 588 x^{6} - 5359262496 x^{3} - 7529536$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 5167^{6}$	$4$	$10833.773609655149$	$11515.597914596217$			?	$S_3\times C_3$ (as 9T4)	$[3, 12, 72, 317016]$	$2$	$5$	$477471.86340433825$
9.3.257...864.1	$x^{9} - 13341 x^{7} - 342419 x^{6} + 59834385 x^{5} + 3084679338 x^{4} - 50395467408 x^{3} - 7008408278937 x^{2} - 181827588181005 x - 1575795650116337$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 13^{3}\cdot 4447^{7}$	$4$	$11105.761244695568$	$27156.63493277724$			?	$S_3\times C_3$ (as 9T4)	$[3, 18, 15087618]$	$2$	$5$	$397802.9321759621$
9.3.477...875.1	$x^{9} - 15 x^{6} - 11239350 x^{3} - 125$	$9$	[3,3]	$-\,3^{15}\cdot 5^{6}\cdot 16651^{6}$	$3$	$11898.045935472348$	$12646.850294175258$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 30382596]$	$2$	$5$	$770712.1309455266$
9.3.917...688.1	$x^{9} - 15501 x^{7} - 428861 x^{6} + 80729208 x^{5} + 4484811324 x^{4} - 78874606356 x^{3} - 11820864125196 x^{2} - 330324864438744 x - 3082958809087528$	$9$	[3,3]	$-\,2^{9}\cdot 3^{12}\cdot 7^{3}\cdot 5167^{7}$	$4$	$12792.793048431276$	$40236.58104865605$			?	$S_3\times C_3$ (as 9T4)	$[39, 4036071]$	$2$	$5$	$4284814.681888726$
9.3.648...000.1	$x^{9} - 31863 x^{7} - 1263899 x^{6} + 340296840 x^{5} + 27072079320 x^{4} - 679127982000 x^{3} - 145790010428400 x^{2} - 5823478410984000 x - 77645476367992000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 13^{7}\cdot 19^{7}\cdot 43^{7}$	$6$	$15896.4563857367$	$43834.343995711555$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 153, 20349]$	$2$	$5$	$3906388.442798904$

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