curve #6202

y² + xy + y = x³ − x² − 1560347053533709280852324905405163926152x + 23784990904828225913443129620814450920033639460526400228555

a-invariants

[1, -1, 1, -1560347053533709280852324905405163926152, 23784990904828225913443129620814450920033639460526400228555]

c-invariants

[74896658569618045480911595459447868455281, -20550232141771587188877829028820404390244962314327294389422985]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

62734529601340411829446284667729624113176033010518204048124701316812675720781265704143381712754

discriminant (Δ)

-1260721033275330938364122563134895915174573566420711865387316606583083225221517795810957865404918276801514053403312128

Faltings height

21.3389

naive height

282.3560

primes of bad reduction

2, 7, 11, 17, 19, 23, 43, 59, 97, 191, 17029967, 169459799472610815349777, 21276290061430098308890766658588204743752021759211

regulator

498298540154690897611811417.104399863879313602624078244266918577457450896810174835500686558

submitted by

Andrii Prokhorenkov

submitted at

2026-10-30 16:38:55 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-30 16:44:25 UTC

Witness: 26 independent points log in to add more points →

(-16223908647914711654715/361, -384282499554974309670781866720285/6859)
(-2017048219391998191119/121, -282860008703760974349542661246849/1331)
(-29424976061919191411, -210288282211470014044128604455)
(1099216243134289411081874366619158876358398659973594457216707386503955720444571832040512378663385687265091935401576629521968434872496099497121791481156747431276549/57368233698531500205897663739775216196352214403056471465300917418208499659909550413424994889885405861385618823867513828228428802278691625721369, 417262906395265823924682095647173350505379086042977308158137522323119267966095035621190218387463693406423064186411341144488819451975326959066344164749695771592906083326254149827107829995920076575869726209912302764678411884708561402648786934389/13740648118495923266957630217509824330725564174028818772742822682989944644795407111037852433465062749660173585699293329736577181478695862727472394847626048817098953378507644133017035332682831415031911465966795145597)
(11725095777042297965, -84271664645844948943070195975)
(1347260509565823118555933/27889, 1151647335712588936254584968597425375/4657463)
(139373307374442453389, -1585442979561931840540599649895)
(14246086072123436237, 66688900431290175100914656857)
(142735911471355359320009/6400, 4540628316170122701904825135304563/512000)
(19075462087260722605, 31011293101491800442483121945)
(21794957375515518887, -11416552657681738112342976295)
(22698766656178755373, 7887569220366000756099195417)
(22874618241758954033, -7858093264492563915092694991)
(23134452694578112461, -8297108782967737055313346983)
(24198840148219492141, 14030406663921738819611910681)
(2772450036948340528927/121, -10497927710969171345934580612195/1331)
(28809602620423767205/9, -3704318949652900878333992568845/27)
(305931637412656920973, 5308468908496813705037999385817)
(354277021643325878290095/961, 209706181663190690667574256970963449/29791)
(40290688645374629133, 162243655140098662975832322009)
(498642954066420996063/4, 10632888497122185008528615589091/8)
(61345001691379846669537/2304, 3693192851368606460814224031459703/110592)
(6956739805505076230413, -580231970546046776434800221251623)
(753526299868336126320963313/32993536, -1486214093396105319456434460632446442319/189514870784)
(8626854326026125357, 104719326000813965933650539545)
(89388326175845397197, -773657091958541540731558912423)

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