Torsion group Z/2Z × Z/4Z, rank = 9

Dujella - Peral (2012)

y2 = x3 + x2 - 6141005737705911671519806644217969840x 
    + 5857433177348803158586285785929631477808095171159063188

	Torsion points:

O, [-2861469472720778854, 0], 
[1431017969855150171, 0], 
[1430451502865628682, 0], 
[1381707195787460036, -100990010591667129753450630], 
[1381707195787460036, 100990010591667129753450630], 
[1480328743922840306, -103337259355706972940063720], 
[1480328743922840306, 103337259355706972940063720]

	Independent points of infinite order:

P1 = [-612695149795875652, 3064309824349077381027308358] 
P2 = [-431590874944672564, 2903005768083873104158859430]
P3 = [187501554154394546, 2170847073897415394832351000]
P4 = [-1383500708967173302, 3421314943163833774567917408]
P5 = [1428519047239049546, 4551549120021779137548000]
P6 = [1430248713837731282, 818226000869154831593640]
P7 = [1429305792931194266, 2901212522992755483557760]
P8 = [103900694057898826, 2284841365124562079087206240]
P9 = [1429854291102331316, 1726936504767203175719910]

Dujella - Peral (2019)

y2 + xy = x3 - 1443705842368492991301675445569878391286260x 
    + 518524534126954116322153225511662398609137586525877978241619600

	Torsion points:

O, [405266783558457366120, -202633391779228683060], 
[946507577804847126120, -473253788902423563060], 
[-5407097445453217968961/4, 5407097445453217968961/8], 
[-168805805131761958680, -27521269452973351848551320510260], 
[-168805805131761958680, 27521269453142157653683082468940], 
[2061820960741456210920, -79415869652391657291324304635060], 
[2061820960741456210920, 79415869650329836330582848424140]

	Independent points of infinite order:

P1 = [128223174003353679720, 18317099368470117761199421172940]
P2 = [956390935331148119400, 3545768914293555321550146272460]
P3 = [1016377111024059996120, 10055611157530821697614783806940]
P4 = [1697827353996567683370, 54420111049349435946331048024440]
P5 = [56495946288484604961066, 13425433378463019292263609689408862]
P6 = [289704950331957158160, 11162008755000776928955192667940]
P7 = [103668184309638014012632296/625, 1055496671159222837902206275138714086956/15625]
P8 = [-11988121387712302153670/9, -238796691154542884537206928300120/27]
P9 = [-26537457561058268238635520/29929, -171844066225434189468646360371177721020/5177717]

Klagsbrun (2020)

y2 + xy = x3 - 160457317436491036800639760108090x 
    - 369449120458315595021673906507946532059648303900

	Torsion points:

O, [13690954102488980, -6845477051244490], 
[-2387265609517420, 1193632804758710], 
[-45214753971886241/4, 45214753971886241/8], 
[33737633510133740, -5711236043556808578342850], 
[33737633510133740, 5711236009819175068209110], 
[-6355725305155780, 627401339555848563015470], 
[-6355725305155780, -627401333200123257859690]

	Independent points of infinite order:

P1 = [-8450528037687760, -618898774000695657281350]
P2 = [-3593381099714128, -400918994155866467092678]
P3 = [-4813673043029260, -539814935920921995999850]
P4 = [-2652827186707420, -193770902631239314259290]
P5 = [-4626517877424970, -523335883699781103941590]
P6 = [59983109876191780, 14346548683378268587551910]
P7 = [-3961188083242030, -451660763783710695990940]
P8 = [16909838270812052, 1323815396421135305641526]
P9 = [24747665523582329837/16, 123108140081725236259934729483/64]
Some curves with torsion group Z/2Z × Z/4Z and rank = 6, 7 or 8
High rank curves with prescribed torsion Andrej Dujella home page