Torsion group Z/4Z, rank = 13

Elkies - Klagsbrun (2020)

y2 + xy +  y = x3 - x2 - 184499078723795351292402856849265045735050014057471578105x
         + 964453138489564009753345308467213074059220517883096279979317728176086605791569407897

	Torsion points: 

O, [7916233831700838401879851239, -3958116915850419200939925620], 
[6045085651919380689061398759, 264662683137960188526472910463163437889420], 
[6045085651919380689061398759, -264662683137966233612124829843852499288180]

	Independent points of infinite order: 

P1 = [7418352899754542002943351239, 63406316661285351331864627295671267054380]
P2 = [7286937435690559834493694759, 83380557155352348480312965602823251681420]
P3 = [8037226651605469079356275909, 27803852934375457248797010898116969096970]
P4 = [70594220244765751149904359, 975412180414299465471847572346217983163020]
P5 = [-15150446782016794020242767641, -531152603661737065821842721173593751691380]
P6 = [4580987484186293888529481959, 464111231280810991878992761972220074254220]
P7 = [7715831643760301910832693509, 15622959943417757044865134109639017460170]
P8 = [7297441578037124868028579209, 81792534573736410869729303627374153838320]
P9 = [647230548488490804676664166679/81, 14422769082216109590544410090151354658788780/729]
P10 = [4084165098248306300189178589, 528255588322186869887672878165776482675280]
P11 = [1381338270999194880352191971559, 1623413482664505888468114703672093496102363020]
P12 = [8594988189780810279566435559, 116749146919433564970236535528450528193420]
P13 = [3278964307389947632795365271473, 5937468430761268981169399541683914667468744080]

Elkies - Klagsbrun (2020)

y2 + xy +  y = x3 + x2 - 62567866563741209951076219033072398452307404054845393938x
         + 190491265471364425314030862500734330699185709037646180838115059299563818726701936031

	Torsion points: 

O, [4568293142682466316128016665, -2284146571341233158064008333], 
[4368192796111742726082171545, -23080756376712992459909568427810967122573], 
[4368192796111742726082171545, 23080756376708624267113456685084884951027]

	Independent points of infinite order: 

P1 = [4558605665741491355288960045, 947294848874354296877229543522035810527]
P2 = [-7287328329039647624534080735, -509361519482732606832330160150157801204333]
P3 = [-6114466113616553353118054555, -586907727393166774178165578041114100760173]
P4 = [4162938925878945304973163545, 46572971665370560190189017803900962061427]
P5 = [-1260145601589984620133324055, -517044309291902107607923017734664705044173]
P6 = [6758529895986107600322149395, 276294675885672711822625183672118744105477]
P7 = [4564572468874153614771800345, 201728715671393249465445874353976583027]
P8 = [35922258661656712682968304890319/11449, 193955272921595967329755824908328738720948950629/1225043]
P9 = [97077179220453965996266175774345/7921, 792737671912824357948666003119556337114605221963/704969]
P10 = [80455314704368947610726303492565/22201, 352290034777633737341720978678255330978132766583/3307949]
P11 = [4302626795197794458885287961, 30624885865611638490727536491801094928243]
P12 = [-4677633058276326924348103386335/841, -14763483773060365677969959804737674309074580737/24389]
P13 = [4341864183441428105718170495, 26114649109698076841404659050696758181177]

Elkies - Klagsbrun (2020)

y2 + xy +  y = x3 + x2 - 284223355086479201781741517789301698531784400402276823264x
         + 1795273070993309604429144564052942175172562915080364861669114008722745205559477017601

	Torsion points: 

O, [11002331345601296481036359445, -5501165672800648240518179723], 
[2118045779011076615536033813, -1096711811090241693370898590518827918257035], 
[2118045779011076615536033813, 1096711811090239575325119579442212382223221]

	Independent points of infinite order: 

P1 = [385496609315749408609376868693, 239123331882085908795731854660301679907025461]
P2 = [-18968535870874970339841890147, -601326226579389214419745559072337763363659]
P3 = [91451660676881912814205409045, 27214884987075469097642448040693294649594997]
P4 = [7275041860595260281583829845, 335524713528058123897295485527725479736437]
P5 = [-2419783919884453859414015555, -1571261748819393789303920738760860055108723]
P6 = [3910840647682747981579300629, 862285252052882206778025083899962904695925]
P7 = [7521014414523279304910639381, 288194809635800604448728101810817284232309]
P8 = [784318941707968502084419733, 1254126703561001175476611236447601779569781]
P9 = [-18928881084933733084227040123, -626926634791280467694160764880189144137355]
P10 = [-5536060941530726459594611723, -1788597733410534924868036128558681020732523]
P11 = [12631413381351557752142849813, 469579894789089375474615757410497400751221]
P12 = [-627958389623764394436901171, -1404815250281336994539578044768481042947915]
P13 = [12673722046261993285751494381, 478329851855161085196678850064794332758709]