Torsion group Z/9Z, rank = 4

Fisher (2009)

y2 + xy = x3 - 210121912561076041141788727170x + 37072777483029442821111037453964917510678212

	Torsion points:

O, [277805513426364, -373688671662118340682], [264708943136484, -1413461833874258322], 
[497030711756964, 7444592848125263795118], [277805513426364, 373688393856604914318], 
[497030711756964, -7444593345155975552082], [264708943136484, 1413197124931121838], 
[265488709619364, 23578368188322342318], [265488709619364, -23578633677031961682]

	Independent points of infinite order:

P1 = [264624185910084, 161163173132978478] 
P2 = [278107166057028, 382329690016779874446] 
P3 = [256715819708964, 222495334012116159918] 
P4 = [165670235424549856/729, 20245451211609092105369194/19683] 

van Beek (2015)

y2 + xy = x3 + 2721419042645095050024690463410x + 70269004493489754502184256716133269311066066692

	Torsion points:

O, [19471437840246444, -2739634905721415222436942], [-3315317249972676, 157502052841253182426338], 
[-3315317249972676, -157502049525935932453662], [19471437840246444, 2739634886249977382190498], 
[4354838741124924, 405842589804263655207138], [4354838741124924, -405842594159102396332062], 
[8781565515324, 265128088832506426330338], [8781565515324, -265128088841287991845662]

	Independent points of infinite order:

P1 = [-1755829888879476, -245107199875348858468062]
P2 = [-2099693655522576, -235155076594372628504562]
P3 = [3412344195582694979150364/648669961, 7925940328633136022396959079148665642/16520975236709]
P4 = [6137687416909118095005788/4437291769, 81849725536339042483475587066252405370/295581316608397]

van Beek (2015)

y2 + xy = x3 - 178713244550246332063776938470605x + 28147864949458728271564240536379650884906835995025

	Torsion points:

O, [133912708523091330, -49047127766138759038618305], [-27152868437091390, 3602946370788681562165695], 
[-27152868437091390, -3602946343635813125074305], [133912708523091330, 49047127632226050515526975], 
[30955139510942010, -7230326827650168773227305], [30955139510942010, 7230326796695029262285295], 
[94583894516610, 5303862969614130650917695], [94583894516610, -5303862969708714545434305]

	Independent points of infinite order:

P1 = [101629293809588610, 32552494216369407363685695]
P2 = [-15202948761734070, -5229816529060178755649625]
P3 = [17334183174096114397199346/271227961, 74445992775872903454362900009494808403/4466853289709]
P4 = [862411646113780429977408418/151606660689, 308518103427511192437597862833954996411673/59030630652493863]

Dujella - Petricevic (2021)

y2 + xy = x3 - 8445699463299696674029285543155x + 9446705591085118541016112920676157302177853025

	Torsion points:

O, [6107748684767310, -430940347787010897522855], [1691846029928670, 725331036696178429545], 
[1691846029928670, -725332728542208358215], [6107748684767310, 430940341679262212755545], 
[2196311730564210, 38624509858323123981645], [2196311730564210, -38624512054634854545855], 
[1755963286477710, -5542293328217833386855], [1755963286477710, 5542291572254546909145]

	Independent points of infinite order:

P1 = [10126558784331150, 981005096699832933514905]
P2 = [440967195740498845510/194481, 3791112809372033023823906318545/85766121]
P3 = [11854019208662697790/8649, 16984323564080166071246200765/804357]
P4 = [328539759252576683735/206116, 548759545844829191241645301655/93576664]

Dujella - Petricevic (2021)

y2 + xy + y = x3 - x2 - 3957522204786046962200201992567404677x 
             + 3029988614585142118644653464298252623281447852094930301

	Torsion points:

O, [4521004755994053801, -8805964815708357348687805676], 
[1161690400268777391, 17401637462276995801474864], 
[1161690400268777391, -17401638623967396070252256], 
[4521004755994053801, 8805964811187352592693751874], 
[1565623400571099651, -819523482530368721814008576], 
[1565623400571099651, 819523480964745321242908924], 
[1216006149728586151, 125260735518914592603090424], 
[1216006149728586151, -125260736734920742331676576]

	Independent points of infinite order:

P1 = [278740355978639028799/324, 2985375750394264421113834704143/5832]
P2 = [93410653214501033409/64, 308488186632088692174687589523/512]
P3 = [19029226654785323829049791/16982641, 3423877156972834911022891319624984864/69985463561]
P4 = [3580024436460833576652855286390352541290023247188591771/9288521204880385620235290175140894121, 
     35379277977384751025092882844234659759886850651086816874574493227432324517604950656/28308696043763824276611476156575255353520928521305341419]

Dujella - Petricevic - Rathbun (2022)

y2 + xy = x3 - 23403453875708065582617252610904740290x 
             + 56740472134219104191564989530383862470828076555856412100

	Torsion points:

O, [-4218137338591198680, -8967021572535154083641586390], 
[11229784459520973780, 34786362994304982176007290910], 
[3565067747610092430, -4314689303713677524672841840], 
[3565067747610092430, 4314689300148609777062749410], 
[11229784459520973780, -34786363005534766635528264690], 
[-4218137338591198680, 8967021576753291422232785070], 
[1010362585608255180, -5841738524551665332313303090], 
[1010362585608255180, 5841738523541302746705047910]

	Independent points of infinite order:

P1 = [1183994360874580962, 5539917734246665612825389372]
P2 = [-2124831061815491209344/625, -153897336826049953226494844248254/15625]
P3 = [-25383574246817605139361514218789870/11541875487800641, 
      -12248431721078582644888104112139415756148879568434740/1239979705847820288430561]
P4 = [11039168903707688516615907465345318179937903715079971086630/254035585383892857719517730338266639041, 
      1153050961572815973856652265360603781222807961488616072729885712260634333824958537635010/4048944608766863824144593988025419443424110442121986160161]