curve #814

y² + xy = x³ − 494355259854509078136774704240186572076087706930x + 135024373357959839542688531300947153392196878202077028440027598741509252

a-invariants: [1, 0, 0, -494355259854509078136774704240186572076087706930, 135024373357959839542688531300947153392196878202077028440027598741509252]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 601241911086984133771692051973210071180003378727462396676347680429041091426440101586799323847490353845318647727198490
discriminant (Δ): -143943346292121883054687068917747642243324386664677515185510882933765555466101806219325369774062290338439475110908112534315769917608515584000000
Faltings height: 26.2856
naive height: 341.0908
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 29, 41, 43, 937, 265567, 121739607199655953, 2335180297877785921439, 119970124471922993794758803136135094834641323384757276670577
regulator: 71970295364898204883063208971265.019571602433524562247557384863403110665555967879699075803903
submitted by: 7fff-zip
submitted at: 2026-09-21 06:13:48 UTC
last updated: 2026-09-21 06:13:48 UTC

Witness: 27 independent points log in to add more points →

(-542487385674147505884545052/1369, -26256444757671882114412797218071684268346/50653)
(86583628013273049631229988/169, -279878439358994892951085667567389105194/2197)
(478553703970446813251964876/529, 7961171181304858216439724393256764412626/12167)
(3070349576222326817053599636/169, -170004790809208617632430937267939815302634/2197)
(442227809231516558844689316/1369, 4816161659438305552897831420732101215814/50653)
(-1050431248435718191978004156/1521, 22746477674868502037799190625354065356562/59319)
(715253855046818739221057796/2209, -9796333411142836786891767181567429935006/103823)
(7279730619419170403467985364/11881, 322860216080567812827169750125616290741462/1295029)
(1608158733943666739465247/4, -283745247531874226390780129164556247/8)
(344665139069254377643252036/1089, -3641191210264862417691301610758371376834/35937)
(1127525158387784335600177827/1156, 29952506015188588751149024030102358458635/39304)
(-563488343914319705859996, -484426960937453465440541439650151042)
(-19993027045792211205511224/25, 17187401260685880654923600394964342086/125)
(385595864215111005423144, 41653702404891053943022125556605978)
(2258122844480693556442344, 3245480869355305403068126898052390078)
(340908509842575408302694, -78194451525435069700583148997494072)
(19983602845472297187159241981082616/56200762489, 863511959584401703676351334624375808704078311450814/13323346160979763)
(985467557916112455118131589348/6095961, -3666132036105144382719250180572871883098453946/15050927709)
(952629327048390224701295107498959052356/63104959362769, 29371281419302130660877592440232964630783242423134857072946/501297151798404236647)
(141726710041350010413429454187616/274465489, 600472796964000954900860522373615356911407496914/4547069756263)
(815145517751424394380060649711043844/2112048917521, 127225963760014892658620380196666443482525351797098062/3069417459295176569)
(65257276017815594933082698672561222697138/179448499896731641, -4394002208752625731050262446224058701019578183644895101132644/76016828824272616509282061)
(31430860617627318967374600116093364/25677178081, 4805404944104697872341050637717849351286834579764638/4114536692877521)
(75630153804610342584175868661924571476/33203605734049, 629540706581826972425464165547620399633472767326056247774/191327709566263988593)
(-7851360942725227667863456134/12769, -655722296866583981228072822705854421884494/1442897)
(13639808304618807336482868, -50309061453697936073896969750451178354)
(44047284670716538816797841716845244/88580640625, 2906795503143629680692471103331892864641287275208278/26363813166015625)

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