curve #3763

y² = x³ + x² − 85395115418238222971927858500344931034775881x + 298145599443516098017951187934604973737606892220785229660003963675

a-invariants

[0, 1, 0, -85395115418238222971927858500344931034775881, 298145599443516098017951187934604973737606892220785229660003963675]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

330692557742877416613409885913347871617125497071636950426700483817553625152751722571151874458791482057141513960

discriminant (Δ)

1453830934257808753240806338790652665285109591553102014091401581375487162751551940677743126380248582155441337141150630867095281644800

Faltings height

24.1491

naive height

315.0812

primes of bad reduction

2, 3, 5, 7, 11, 13, 19, 61, 97, 139, 607, 163673618908529, 1212069226558893106217052354256348500254756640797553908710540792281682033911551

regulator

3458319027623557332920871290579.158499438798294112218980990270718784688020950136968343468349979

submitted by

Ritik Jain

submitted at

2026-10-01 19:42:04 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-01 20:02:07 UTC

Witness: 28 independent points log in to add more points →

(1483074047036185425547846/25, 1785367788228557411993770499246333931/125)
(-10274757703482486052634, 301408215815367671183280169052991)
(-263457198356682244572194/49, 266097058560086393671890078453732213/343)
(-10453126679675791276961, -220455899244947187224493089033034)
(7573785474087955672909, -292968448569654649239083533448166)
(1456990799283435052816819/225, 436164885693313701804994995065960522/3375)
(18338338781840330043667, -2213419666111276115041109178659370)
(115057723268348173655581/25, 6390351147465506527945205424098346/125)
(2548813679468441183394901/625, 2079838576735514151134268499432041726/15625)
(-10641346395245772535883, -43094391780733083246086556109470)
(2778161107600693740994219/625, -1248751672569808643530011015022762422/15625)
(910195960516288325036917, 868320506154304972916059454905172130)
(85201800057114222360139, -24729167736454663239390525802002534)
(-5006629069584867005258, 774718934206717612663057830145095)
(3080107425346178867173/4, -3860326601250588840608927734234905/8)
(5890893115107419721825953756543103433/305275256848384, 12885281376726538614552354855205132552269282072964866555/5333808362887841841152)
(301446053096388166571949607/44521, 1636673032673535432312938405303879039730/9393931)
(-223651111417079347834909073730918320738477208802830077/31835612805352755330547738651489, 133377360998053937418522481923399430744963011106488097603071046328709965395556010/179626257318247399057966755016863066480394449263)
(511987871605602224846492635726966530489911550496487764009690125411296198860716300545298456674755617579079703998/113032410691972525122011479283060037033644828838029747722347448826064960688248511165539289, 2484903108497962273305772676032132546811931767976921360808216142797282864382559894919216980156133595041646576345535634095939794164651530278347092319780454420854602465/38001827752293558330512303914241427368396208174213150779459980902906574866822304845716853400375951328831438554286998564672038561375587)
(734941471489928043988317405263025191920975/395519999663910652129, 3004383171569130274875352967817944927753344871762317364401081290/7865977015404921044391815512367)
(-2116164935080157826154747790849/2934063889, 95272970849347832859539156577174705124536032358/158929438675463)
(293936483995463787331740201822925946772278178549179947/74194961068332583771070395174441, 94826292018166125719588333240840165209986950798754781536363795824907121749691470/639089403777464579653942100633476400122559915989)
(338748194130020348516798710323225861783717734113444852591/74275652434348645908294562151879401, 1205562191545749982732584255675721393583008259700070146175247214086560468894794916866/20242759388074045179501321070936984176667613366547851)
(-298489789194046482895654946838187371731483090946959462681/311626304526502693419225196194791281, 107104164104396719360353081342450789221840420618828778995771154786239190603917158731786/173960707121214485979535471230827983988894039294241929)
(-2419853019206649226345362209139854938076938891162707928689512358142601/250538769118407983254183283887393670361036749401, 59074155802696127835780631789099055171733638356818599286154906656712198465246709704524865251468371024766/125404294464796486800308113748227961240592620287155006772479936618740899)
(35014873678079471772285051157120540223598818076611318738921252383/8027484434071871330934454118577210288773449, 2115527103748701216380898355678139076531259067095350699552703949864002377452789496215282610999810/22744123671009378041705376110055131790845003720202639296967973957)
(15510913911199813925595949509/3751969, 912638729303066808187144441323868228075218/7267563953)
(12573594645952733603050407258139397399099793723481381/2946768324014708637928747404241, 541466858871518340842134461725286654375597484673482729743951743369065113898674/5058467792965659426054354186863308631909812711)

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