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Results (48 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.3.161...776.2	$x^{9} - 3 x^{8} - 1221 x^{7} - 33360 x^{6} - 468492 x^{5} - 4028151 x^{4} - 21971391 x^{3} - 74216559 x^{2} - 141693072 x - 116934011$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 19^{3}\cdot 307^{7}$	$4$	$2272.9030635$	$5424.848382525166$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 42, 34398]$	$2$	$5$	$55601.09550130088$
9.3.387...632.1	$x^{9} - x^{8} - 1045 x^{7} + 29560 x^{6} - 417628 x^{5} + 3585287 x^{4} - 19479671 x^{3} + 65515343 x^{2} - 124577908 x + 102451091$	$9$	[3,3]	$-\,2^{6}\cdot 7^{7}\cdot 53^{3}\cdot 337^{7}$	$4$	$2504.25258006$	$7471.902840325843$	?	$S_3\times C_3$ (as 9T4)	$[6, 6, 283896]$	$2$	$5$	$50251.72122232476$
9.3.100...384.2	$x^{9} - 3 x^{8} - 1365 x^{7} - 10410 x^{6} + 646854 x^{5} + 11394435 x^{4} - 48531561 x^{3} - 2802169227 x^{2} - 26368099602 x - 83468320741$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 13^{3}\cdot 67^{7}$	$5$	$2784.72352314$	$6387.700371233269$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 113868]$	$2$	$5$	$134850.14021681162$
9.3.111...347.2	$x^{9} - 3 x^{7} - x^{6} + 41472 x^{5} + 27648 x^{4} - 191098368 x^{3} - 191102976 x^{2} - 63700992 x - 7077888$	$9$	[3,3]	$-\,3^{13}\cdot 23^{6}\cdot 601^{6}$	$3$	$2815.6371348384487$	$2992.839456171486$	?	$S_3\times C_3$ (as 9T4)	$[2, 4, 3444252]$	$2$	$5$	$90213.24712093834$
9.3.209...107.1	$x^{9} - 1389 x^{7} - 1452 x^{6} + 2016828 x^{5} - 29169 x^{4} - 1314060 x^{3} + 91674 x^{2} - 704223 x + 21297$	$9$	[3,3]	$-\,3^{15}\cdot 23^{6}\cdot 463^{6}$	$3$	$3020.4708066410126$	$3210.5643495314985$	?	$S_3\times C_3$ (as 9T4)	$[2, 6, 1493142]$	$2$	$5$	$80324.60848047983$
9.3.272...568.1	$x^{9} - 4 x^{8} - 1313 x^{7} + 44491 x^{6} - 733595 x^{5} + 7301738 x^{4} - 45971710 x^{3} + 179531183 x^{2} - 397550999 x + 381879679$	$9$	[3,3]	$-\,2^{6}\cdot 13^{7}\cdot 59^{3}\cdot 229^{7}$	$4$	$3110.27400156$	$9570.36199585062$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 2581830]$	$2$	$5$	$58281.10858602539$
9.3.465...712.1	$x^{9} + 3102 x^{7} - 1518 x^{6} + 2404512 x^{5} - 2336268 x^{4} - 1536216 x^{3} + 2204136 x^{2} - 702768 x - 10648$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 11^{6}\cdot 79^{6}$	$5$	$3300.9121478514057$	$3508.6552862971384$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 9, 30366]$	$2$	$5$	$85708.1998325773$
9.3.471...592.1	$x^{9} - 17346 x^{6} - 125562696 x^{3} - 193301071768$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 13^{6}\cdot 67^{6}$	$5$	$3305.9748977840454$	$3514.036660753263$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 6, 18, 5328]$	$2$	$5$	$112605.1854345681$
9.3.498...816.1	$x^{9} - 2 x^{8} - 1417 x^{7} + 47083 x^{6} - 773167 x^{5} + 7694710 x^{4} - 48508270 x^{3} + 189764407 x^{2} - 420948217 x + 405005803$	$9$	[3,3]	$-\,2^{6}\cdot 7^{7}\cdot 61^{3}\cdot 457^{7}$	$4$	$3325.97358344$	$10332.294619825148$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 1635606]$	$2$	$5$	$60963.2262314742$
9.3.509...872.1	$x^{9} - 3 x^{8} - 1845 x^{7} + 70446 x^{6} - 1318464 x^{5} + 14917527 x^{4} - 106922079 x^{3} + 476252001 x^{2} - 1205266068 x + 1325705823$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 23^{3}\cdot 463^{7}$	$4$	$3334.47674792$	$8405.758372963333$	?	$S_3\times C_3$ (as 9T4)	$[3, 11362932]$	$2$	$5$	$71695.60842587455$
9.3.597...843.2	$x^{9} - 12675 x^{6} - 67004106 x^{3} - 75418890625$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 13^{6}\cdot 67^{6}$	$4$	$3393.6478824679234$	$3607.2273509013676$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 18, 7722]$	$2$	$5$	$151265.99885256487$
9.3.668...664.1	$x^{9} - x^{8} - 1469 x^{7} + 48382 x^{6} - 793070 x^{5} + 7893095 x^{4} - 49792969 x^{3} + 194960777 x^{2} - 432853214 x + 416791129$	$9$	[3,3]	$-\,2^{9}\cdot 31^{3}\cdot 3313^{7}$	$3$	$3436.37511968$	$13512.7488086505$	?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 320454]$	$2$	$5$	$140165.5057770597$
9.3.753...128.2	$x^{9} - 390 x^{6} - 63384 x^{3} - 2197000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 3169^{6}$	$3$	$3482.497436615358$	$3701.6686579950615$	?	$S_3\times C_3$ (as 9T4)	$[546, 22932]$	$2$	$5$	$382549.892745197$
9.3.860...043.1	$x^{9} - 3 x^{6} - 524904 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 19441^{6}$	$2$	$3534.44216204$	$3756.8825283686483$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 252, 8316]$	$2$	$5$	$272823.291028714$
9.3.986...128.1	$x^{9} - 2 x^{8} - 5111 x^{7} - 98827 x^{6} + 1155889 x^{5} - 18079154 x^{4} + 108296402 x^{3} - 612717833 x^{2} + 1613120173 x - 3927745279$	$9$	[3,3]	$-\,2^{9}\cdot 15259^{7}$	$2$	$3588.25755575$	$8665.960816334924$	?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 752618]$	$2$	$5$	$383749.96312639443$
9.3.998...347.1	$x^{9} - 3 x^{6} - 538026 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 19927^{6}$	$2$	$3593.10376688$	$3819.2360054459764$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 58590]$	$2$	$5$	$274734.5123921934$
9.3.103...027.1	$x^{9} - 28611 x^{6} - 341266806 x^{3} - 867431817153$	$9$	[3,3]	$-\,3^{15}\cdot 17^{6}\cdot 19^{6}\cdot 43^{6}$	$4$	$3605.643155737152$	$4330.150112902169$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 2147418]$	$2$	$5$	$202070.6599011665$
9.3.156...000.1	$x^{9} - 2 x^{8} - 1625 x^{7} - 52291 x^{6} - 853247 x^{5} - 8495846 x^{4} - 53712742 x^{3} - 210868919 x^{2} - 469393757 x - 453036163$	$9$	[3,3]	$-\,2^{6}\cdot 5^{3}\cdot 13^{3}\cdot 19^{7}\cdot 193^{7}$	$5$	$3777.74756961$	$11950.950118785335$	?	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 1449426]$	$2$	$5$	$66330.15527875583$
9.3.217...728.1	$x^{9} - 1278 x^{6} - 680616 x^{3} - 77308776$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 19^{6}\cdot 199^{6}$	$4$	$3917.5429287781585$	$4164.09376883914$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 54, 54, 54]$	$2$	$5$	$416837.13531478605$
9.3.267...992.2	$x^{9} - 25506 x^{6} - 491854896 x^{3} - 614558602008$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 13^{6}\cdot 43^{6}$	$5$	$4008.1984082293184$	$4260.454657272707$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 9, 23751]$	$2$	$5$	$316974.1489414114$
9.3.270...544.1	$x^{9} - 4 x^{8} - 1729 x^{7} - 54907 x^{6} - 893755 x^{5} - 8904010 x^{4} - 56380654 x^{3} - 221740207 x^{2} - 494442079 x - 477940399$	$9$	[3,3]	$-\,2^{6}\cdot 7^{7}\cdot 13^{7}\cdot 43^{7}\cdot 67^{3}$	$5$	$4013.77100016$	$12808.028099513633$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 57, 35568]$	$2$	$5$	$69013.40411574923$
9.3.303...352.1	$x^{9} - 1314 x^{6} - 719496 x^{3} - 84027672$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 571^{6}$	$4$	$4065.357520043332$	$4321.211081813369$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 117, 4914]$	$2$	$5$	$424389.4831120638$
9.3.485...875.1	$x^{9} - 15450 x^{6} - 105219375 x^{3} - 136590875000$	$9$	[3,3]	$-\,3^{19}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}$	$5$	$4283.176594043372$	$4552.738614572471$		$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 9, 9, 1512]$	$2$	$5$	$4824737.00413184$
9.3.505...000.1	$x^{9} - 300 x^{6} - 704940000 x^{3} - 1000000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 7^{6}\cdot 373^{6}$	$5$	$4302.422541390596$	$4573.195806971121$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 315, 10395]$	$2$	$5$	$353135.65621737204$
9.3.552...672.2	$x^{9} - 17052 x^{6} - 121240896 x^{3} - 183637853504$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 631^{6}$	$4$	$4345.37817548737$	$4618.854856924327$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 18, 285138]$	$2$	$5$	$173531.71890901978$
9.3.619...875.2	$x^{9} - 735 x^{6} - 225150 x^{3} - 14706125$	$9$	[3,3]	$-\,3^{19}\cdot 5^{6}\cdot 1801^{6}$	$3$	$4401.274547370881$	$4678.269070908049$	?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 2, 6, 129402]$	$2$	$5$	$297351.2982801563$
9.3.681...672.1	$x^{9} - 4 x^{8} - 9033 x^{7} - 359861 x^{6} - 2910119 x^{5} - 41373100 x^{4} - 151418854 x^{3} - 1012666779 x^{2} - 1671033865 x - 6584680237$	$9$	[3,3]	$-\,2^{6}\cdot 27067^{7}$	$2$	$4447.74717729$	$7841.276463162858$	?	$S_3\times C_3$ (as 9T4)	$[2, 12114970]$	$2$	$5$	$199449.4196881334$
9.3.753...000.1	$x^{9} - 300 x^{6} - 753540000 x^{3} - 1000000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 2791^{6}$	$4$	$4497.954280158571$	$4781.033349486053$	?	$S_3\times C_3$ (as 9T4)	$[4, 36, 241704]$	$2$	$5$	$361086.1575274617$
9.3.765...136.1	$x^{9} - x^{8} - 1965 x^{7} + 73862 x^{6} - 1377684 x^{5} + 15584739 x^{4} - 111818439 x^{3} + 498777897 x^{2} - 1264170258 x + 1392458831$	$9$	[3,3]	$-\,2^{6}\cdot 43^{7}\cdot 71^{3}\cdot 103^{7}$	$4$	$4505.97013684$	$14618.536789485457$	?	$S_3\times C_3$ (as 9T4)	$[2, 2, 42, 558516]$	$2$	$5$	$74376.1833618562$
9.3.109...000.1	$x^{9} - 2 x^{8} - 4905 x^{7} - 71331 x^{6} + 1753533 x^{5} - 26039686 x^{4} + 196483798 x^{3} - 1074133819 x^{2} + 3296384083 x - 6648336463$	$9$	[3,3]	$-\,2^{6}\cdot 5^{3}\cdot 73^{7}\cdot 199^{7}$	$4$	$4687.32013328$	$10438.82490543639$	?	$S_3\times C_3$ (as 9T4)	$[18, 234, 14274]$	$2$	$5$	$145060.64716551403$
9.3.125...112.1	$x^{9} - x^{8} - 2085 x^{7} - 77286 x^{6} - 1437264 x^{5} - 16258695 x^{4} - 116782119 x^{3} - 521681457 x^{2} - 1324203408 x - 1460616767$	$9$	[3,3]	$-\,2^{6}\cdot 37^{7}\cdot 73^{3}\cdot 127^{7}$	$4$	$4762.10008618$	$15572.295322709964$	?	$S_3\times C_3$ (as 9T4)	$[3, 18, 1524510]$	$2$	$5$	$77054.60654044396$
9.3.160...088.1	$x^{9} - 2 x^{8} - 2145 x^{7} - 79001 x^{6} - 1467189 x^{5} - 16598202 x^{4} - 119289204 x^{3} - 533274861 x^{2} - 1354643343 x - 1495222583$	$9$	[3,3]	$-\,2^{9}\cdot 7^{7}\cdot 37^{3}\cdot 691^{7}$	$4$	$4892.66302044$	$20236.058598873537$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 1160481]$	$2$	$5$	$1760806.0863588715$
9.3.467...000.2	$x^{9} - 6150 x^{6} - 15765000 x^{3} - 8615125000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 5^{6}\cdot 13^{6}\cdot 97^{6}$	$5$	$5508.914599650231$	$5855.618527867704$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 18, 10512]$	$2$	$5$	$247513.39839609378$
9.1.525...336.1	$x^{9} - 3 x^{8} + 66 x^{7} + 26333 x^{6} - 51534 x^{5} - 505365 x^{4} + 234481891 x^{3} - 222820542 x^{2} - 9591070860 x + 691037609738$	$9$	[1,4]	$2^{6}\cdot 3^{9}\cdot 7^{7}\cdot 13^{7}\cdot 97^{7}$	$5$	$5581.79244627$	$11104.671944723488$	?	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 18, 72, 72]$	$2$	$4$	$9434745.489555798$
9.3.605...712.1	$x^{9} - 2166 x^{6} - 3380005456 x^{3} - 376367048$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 13^{6}\cdot 19^{6}\cdot 499^{6}$	$5$	$5670.117794304793$	$6809.453999381672$	?	$S_3\times C_3$ (as 9T4)	$[3, 18, 18, 18648]$	$2$	$5$	$1729708.1921366968$
9.3.105...952.1	$x^{9} - 2 x^{8} - 3575 x^{7} + 7821 x^{6} + 1971289 x^{5} - 46669722 x^{4} + 524651850 x^{3} - 3436972865 x^{2} + 12798407621 x - 22633585879$	$9$	[3,3]	$-\,2^{9}\cdot 13^{3}\cdot 9907^{7}$	$3$	$6029.75216455$	$21800.601287267342$	?	$S_3\times C_3$ (as 9T4)	$[2, 8, 2303672]$	$2$	$5$	$670690.3151139264$
9.3.127...664.2	$x^{9} - 3 x^{8} - 11778 x^{7} - 343563 x^{6} + 6802959 x^{5} - 118025175 x^{4} + 976314459 x^{3} - 6434869944 x^{2} + 22446840324 x - 58194334529$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 3907^{7}$	$3$	$6159.48981572$	$13059.954561196577$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 84, 27468]$	$2$	$5$	$762839.4307937925$
9.3.155...808.1	$x^{9} - 1299 x^{7} - 28041 x^{6} + 4119129 x^{5} - 102698940 x^{4} + 236156898 x^{3} + 33422281461 x^{2} - 466410575739 x + 1437983022635$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 37^{6}\cdot 433^{6}$	$4$	$6295.281699827852$	$6691.475696863939$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 42, 38430]$	$2$	$5$	$1695385.4013192279$
9.3.179...528.1	$x^{9} - 18057 x^{7} - 475501 x^{6} + 146478384 x^{5} - 1403751180 x^{4} - 46876525748 x^{3} + 22126109197140 x^{2} - 1477617177418200 x - 55954234334768328$	$9$	[3,3]	$-\,2^{9}\cdot 3^{13}\cdot 13^{6}\cdot 463^{7}$	$4$	$6398.28679074$	$13526.121045889007$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 311766]$	$2$	$5$	$1296407.1079993355$
9.3.281...000.1	$x^{9} - 7833 x^{7} - 154049 x^{6} + 20679120 x^{5} + 817921860 x^{4} - 10296478500 x^{3} - 1098270413100 x^{2} - 21904052373000 x - 146020198499000$	$9$	[3,3]	$-\,2^{9}\cdot 3^{12}\cdot 5^{3}\cdot 7^{7}\cdot 373^{7}$	$5$	$6725.09038985$	$19254.432748637053$	?	$S_3\times C_3$ (as 9T4)	$[3, 3, 21, 267414]$	$2$	$5$	$1578972.4007431671$
9.3.298...992.1	$x^{9} - 1284 x^{6} - 686976 x^{3} - 78402752$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 31^{6}\cdot 277^{6}$	$4$	$6768.674367421575$	$7194.6613653247505$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 342, 2394]$	$2$	$5$	$591066.281449638$
9.3.439...203.1	$x^{9} - 4900 x^{7} - 3 x^{6} - 630 x^{5} + 9800 x^{4} - 24 x^{3} + 630 x^{2} - 4900 x - 1$	$9$	[3,3]	$-\,3^{3}\cdot 37^{6}\cdot 73^{6}\cdot 127^{6}$	$4$	$7067.393753816128$	$8487.494335737842$	?	$S_3\times C_3$ (as 9T4)	$[6, 6, 18, 18, 2232]$	$2$	$5$	$1675675.4950873558$
9.3.517...728.1	$x^{9} + 129 x^{7} - 1055 x^{6} + 5547 x^{5} - 7845686 x^{4} - 7503644408 x^{3} + 7512601669 x^{2} + 124405243 x - 2977187665$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 23^{6}\cdot 79^{6}\cdot 97^{6}$	$5$	$7196.889860506576$	$8643.010995813815$	?	$S_3\times C_3$ (as 9T4)	$[3, 18, 1183014]$	$2$	$5$	$1865847.9892370193$
9.3.567...768.1	$x^{9} - 5041 x^{7} - 3 x^{6} - 639 x^{5} + 10082 x^{4} - 24 x^{3} + 639 x^{2} - 5041 x - 1$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 37^{6}\cdot 691^{6}$	$5$	$7270.745720058749$	$8731.707226906306$	?	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 38052]$	$2$	$5$	$4845966.580675788$
9.3.137...000.1	$x^{9} - 24000 x^{6} - 1601610000 x^{3} - 512000000000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 73^{6}$	$6$	$8018.3433183492325$	$8522.978319669548$		$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 63, 63, 252]$	$2$	$5$	$199532361.75235197$
9.3.504...827.1	$x^{9} - 20910 x^{6} - 6658886859 x^{3} - 338608873000$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}\cdot 37^{6}$	$5$	$9268.229580837024$	$9851.526262092819$		$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 63, 8190]$	$2$	$5$	$708050372.2496096$
9.3.439...875.1	$x^{9} - 960 x^{6} - 23568225 x^{3} - 32768000$	$9$	[3,3]	$-\,3^{15}\cdot 5^{6}\cdot 7^{6}\cdot 31^{6}\cdot 163^{6}$	$5$	$19661.36442381817$	$20898.753778208567$		$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 6, 6, 18, 18, 126]$	$2$	$5$	$3312716174.869721$
9.1.965...784.1	$x^{9} - 3 x^{8} + 4 x^{7} + 38111 x^{6} - 8080190 x^{5} - 360114827 x^{4} + 5331730773 x^{3} + 503351244410 x^{2} + 9153587484812 x + 54306800283630$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 37^{7}\cdot 73^{7}\cdot 127^{7}$	$5$	$46236.23159873343$	$112725.16476206973$	?	$S_3^2$ (as 9T8)	$[3, 9, 9, 9, 9, 1080]$	$2$	$4$	$83562901750.60939$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.