Torsion group Z/7Z, rank = 6

Klagsbrun (2020)

y2 + xy = x3 - 326034514850898538462143577535732108974101688866x 
	   + 126139807177463916084745782524191445068029238338478785879968870214064452

	Torsion points: 

O, [1051169831707617676888332, 972070312188486608578007494208516526], 
[261128989506241684485156, -242505048365488244642094664608377394], 
[-459534130824818233238556, 422993178343374888295956229647650574], 
[-459534130824818233238556, -422993178342915354165131411414412018], 
[1051169831707617676888332, -972070312189537778409715111885404858], 
[261128989506241684485156, 242505048365227115652588422923892238]

	Independent points of infinite order: 

P1 = [349621108430722643628612, 234280103165415296096052964651107726]
P2 = [408970490120129839927524, 247395296205394205764203536688391182]
P3 = [-394276731764242099773348, -439767756206926097966811118650051474]
P4 = [15487208600555969620583619/4, 60348540330823105469521400748864009759/8]
P5 = [488457152640052085194896, 288837495697090305635327960027037486]
P6 = [6109083865034034966377150522923236/6323271361, 424558236702135759868877367327409557236105861623602/502820215355359]

Park (2026)

y2 + xy = x3 - 43128485719048848336369206448280318892347450080x 
	   + 3447421838942387338178506897552142828531443641216593953476007557350400

	Torsion points: 

O, [119898414743603536633560, -1361909634029984176145062004280], 
[103593551329626583695360, -9555933695823167239831519979885280], 
[120094230241774124698560, -116141564796404303407977660269280], 
[119898414743603536633560, 1361909514131569432541525370720], 
[103593551329626583695360, 9555933695719573688501893396189920], 
[120094230241774124698560, 116141564676310073166203535570720]

	Independent points of infinite order: 

P1 = [50798922139514599258560, 37250898222335131335742765268370720]
P2 = [119999412193898113546560, 59251534775685673426877063010720]
P3 = [7628522959761523258560, 55846746838515789423651556724370720]
P4 = [201698493548336332227303360/1681, 3579009567529347903127103527951449120/68921]
P5 = [231553407938098170224960, 76655519059820459068632001220652320]
P6 = [32529425855908735368240449330161050/22084040449, 5811571220685218557713606468665058529890464193853110/3281842999004543]
Some curves with torsion group Z/7Z and rank = 5
High rank curves with prescribed torsion Andrej Dujella home page