curve #1389

y² = x³ + x² − 3608975996914881702934954506710734505698825637260x + 2634661988487534421455537980870210739782157170272712211417642904894806224

a-invariants

[0, 1, 0, -3608975996914881702934954506710734505698825637260, 2634661988487534421455537980870210739782157170272712211417642904894806224]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

869493639020934570659290249779173738352593745265724582681944569627016656812704076398791694665931342420228609010298515208

discriminant (Δ)

9671169061356482847177163244963793350007233820686305649506691908016593616901437651048882773684722461852568936640042769068120664410653945624698112

Faltings height

26.7108

naive height

347.0361

primes of bad reduction

2, 3, 7, 11, 17, 19, 23, 29, 31, 37, 73, 211, 43727707, 11433516973691991097067, 247246872931454872073054325708225574439626719894485067604402689129292590839

regulator

69968165727236609753551524526135.56989149272581145600149940457293158686360673778848282678520062

submitted by

Ritik Jain

submitted at

2026-09-24 21:24:54 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:53:24 UTC

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

(1314617539626158304121814, -402723496627885440991782980719825518)
(-2187334225994066926921741, 252089257362551745600860090009957712)
(-628247659218758310706158454/289, 2235571229100940726838561350784512278534/4913)
(105847654899947842391218966277/20164, -32437190469662542317317077600866512952610545/2863288)
(3824349111937850725429046992120526/3320640625, 14611085114304751021062614782805234439023399676726/191351916015625)
(105774462728937077344167962, -1087681318716465402832458707175923698026)
(4530341121505818822462797/4, 27719306235746254558235867203649835/8)
(43301184762834361051534865/64, -362982486774894386116355375263730636391/512)
(6607786880589895089226190, -16349376390383917750255505925596001882)
(189419598966442316345908226/289, -3646205351571532556175385333657578586194/4913)
(-42841398318573414700854416/49, -776248717965417503906386257527459493228/343)
(1048570214266368334957106, 57442792309010209307061281115859554)
(-2262441435803961363738923635/1156, 58315729097923602348929877377536048235253/39304)
(-29906812967855614001806852903/30976, 12454755129475035314275050871936848892607331/5451776)
(2191505802817427321510066, -2291442775241579717906966059128220446)
(17695901314313763775125796646/15625, 1543903820646204564589854705520090636806/1953125)
(203791840666314290086261651149383512271683542571509586002776110241/101767064361113398779899629543839243420736, 60195449151495112139545874086116298938401567059844314147628498403571858751487526077420978360400239/32464660840024866070902262890003397628085298384789116577385984)
(1780997513168392337367426562636280715536/1452057709515625, 12775563663198878006173849288904863542764884481755575310284/55331929571588716796875)
(4629567053271988415766981359675708254055249/1843530292145422336, 7677788267355092807871123138268734678062249212981591672875759783/2503083960000993150858428416)
(-983036691915492141538442091312269522/746179809489, 1456010360996995429700855683766678893555107208906903498/644562804493359513)
(105932844355939719625440092956755278/92865858121, 1321429078132629528746133606761144048590931910006450/28299848737935419)
(16040820680539711983534525073385906906/16618349586721, 15213499710975327810673871052930526669834159596072833226/67745715809592946481)
(-15645770647010594558002367719/10000, 2109799205303862811190995025906118624615429/1000000)
(1938506613644145468868721894448789552582654550793054774/3787169145044937023211329586121, 7074792849924375227282751859822830412387549523985093762517594113530201883146603562/7370077478734905723334365701646549190955576581)
(-146665508711245622976618852231109470635093392909/90866233957107548020225, 56498959471034706209571507831629788791536981983836020834733866529820464/27390741733085738356467784159546625)
(16718105137825318162933341518/10609, 1013788546577300417353920546898365735640758/1092727)
(-59668471660066387701152033779064516139647772389549/147423302083741839086152225, 3592951086718582670941103273055095199576475353805500927623624772372891158976/1789984217937249813864919683146867304625)
(-47873689511380035128912353625936606719966970265303521758/22729244346575918656584789589441, 102345745770345713321417217719485569156074374974518773108552876642038998902649565714/108362120800296464858731259188313919349665062239)

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