curve #3790

y² + xy = x³ − 66365915812210669946047223779623640972858804310x + 6622594767133479076646240715321142830655970753202648569566666889314596

a-invariants

[1, 0, 0, -66365915812210669946047223779623640972858804310, 6622594767133479076646240715321142830655970753202648569566666889314596]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

16771852010074538848591246789315396601859667580344218962817504421845301474357895126513536139770008351062674112223334602

discriminant (Δ)

-239506679656185571057194959016570754332749058415600657260285904023401842248169387311619904773488266887119204563883101005141628503109288214528

Faltings height

25.7674

naive height

335.0609

primes of bad reduction

2, 3, 19, 31, 43, 59, 67, 197, 709, 205289185165085733824003, 20442079886401506454204265437, 47633839956341517338707657822759815223370600932673719

regulator

90204734233850400499013234322261.88185971682118371458405740065927788485997905919669292760181887

submitted by

Ritik Jain

submitted at

2026-10-02 03:57:51 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-02 04:07:14 UTC

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

(103344332156560468579530889/1600, -3266803530862204122311014397944278204167/64000)
(2234477470057847061494365/16, -565334087384587085640093710768714759/64)
(128668714935680828635468, -14614046550985626814097665003666982)
(11197142254920191646005068/81, -6916336262691414254949639267447254774/729)
(-252804324012525250088948096/1849, 9114073622374237548672748523413446613582/79507)
(490243120301580033856816204/4489, 7827384914106182663705997026110211291518/300763)
(137007427736954820820648, 10086754113902841134384388420740698)
(6002334930852354371835280/49, 6241352474281158250270857219738021622/343)
(33250489108865792794259950/289, -110946802127089846570618408231219237132/4913)
(5392574394901218719915734/81, -36445334628091215609226876401884487700/729)
(231124944139087290326300620/2809, -6172627372259337002277392741641773287758/148877)
(15562577738130256128664204, 61385128821554558802816571767866378266)
(61104902978369948399773500/841, -1139826018664816342760163300952893835854/24389)
(203329009158592076340556, -39174561088093080534801600038071334)
(54584105154884435450353636/25, 400585349973669656587808835186767191826/125)
(4428006076884216915173866/25, 2575089778846677061781386501663698824/125)
(23471967883409220748312510553899642105130103930/160665991463056209279241, 432435489994570583012581665412370208266681854535849023482965884609494/64400010412899063291555637009874789)
(-77036933296621525027081673166615122/304948032841, 14354586609006935939243184696870232402029286073561174/168398707643489861)
(1271984602620461724962814084971867300349907754663777218748281/6318748023228961113981613004891074624, 598606649779182568672545643875656446403889624114435621105456970849053192941387332353381305/15883512736352497388362532874447420666790852163248045568)
(343961730844243056704814808001168210179414092071329720492421452/1686457259283226130576883531750410445361, 2745049453878126031736769753233565068347258275353882190901871042538252799190719561364114809174/69256893692117338853742814375434924593987087248854917154391)
(288041117033315840967236629746048904451190029617484502263948548/1786170431797850190843348540310873640041, 805934549153283558547512647095831819764389530014336279623046246940866228522849973221980632766/75489116696646612368774661945251086280356249868662025483339)
(15678721814404992178807871977136458760431700743004140/269410567093713712556789183881, 7604660439698958578456625612811664151073960089574697961088678785791624411489986/139836948757616119799009927943390158556989221)
(61108067985810106278815143282060685334084963647436947932849766026974160475553262933969049867931419813596279/407080584996924306126446791058557537360865653899001129447617498191587679976580223716, 1700010370695138010464307050813621305828051043349147121666996830397056486507847605063524140520078917221141270031860183585106112967984995740665317131168851613969/259729084628758334394264869804274829236127251970345913211771624603868108130124803455706747708307366063489170688930187529852264)
(-1073695047269133835194499265802/3613801, 73174031191116771683216426165575125495243948/6869835701)
(184866478614215571074792676919231279931543605284559649554982112851538300040/1820905402651308308074160787874643595939194415631801, 2371197110568905023800769555324496556014856974355568656738309474809774981583139869258270877827264713348288841094/77701799488978473512445665918630738146101710802858791664670706714679510662701)
(-22019719201076994888137958187140584706931489270819916093063144404535308831063007249190646444657730946336195977/137449698386700778240324387888674890523891430719462964059124367365341585145563225284836, 184740948468938429348296102478810158278967880446298727874690853262590941661919108862981962328766397507500776677175600386951199932323537563578879416745641145960413351/1611445740312866678040917469006043671335242294343001287810013460826759973552165917668299293196096331505901801289072601254153746584)
(-445231460085572623487204487342694102404354334629688819188894913352/1598471544582057664986289396990286053477441, 119535368713694019766578431825956940972137725800820583887491683030473035873373413350027024357335334/2020958354955413799363178491293792384050295582974235585714628511)
(-40072377661180987065478669734863690357926179899893089938576/170473567032101124196876846547776321, 6763730791224828530994120705683523071202490528404862743519420595485048970911293731573190/70385884546635562856956180007045332955613965969145119)

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