curve #1394

y² + xy + y = x³ − x² − 607862489002627389252372837419668437151468213951205x + 5726938297541853888303658086321807887103455945830691930818433755512840743197

a-invariants

[1, -1, 1, -607862489002627389252372837419668437151468213951205, 5726938297541853888303658086321807887103455945830691930818433755512840743197]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

8349736622217588344038662049010919030904299964554447700437147692670784369207409910254075684498614121565587520749619045424253590650

discriminant (Δ)

205948647098867563452017496969825038845345440944334499169121973780906183370876592262518028081685607729795803766562506955245030080897688886142443284480000

Faltings height

28.0523

naive height

362.4157

primes of bad reduction

2, 3, 5, 7, 11, 17, 31, 37, 107, 223, 16993, 2753599, 215993630267662851994879, 51245632899422112790440321101071509934299830053937250608421345840429495003657952423

regulator

1577462605257055622565023620537050.429036607255151720253246266937447173870044288058781897382359

submitted by

Ritik Jain

submitted at

2026-09-24 21:25:50 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:46:10 UTC

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

(4155122913712732684063821691/169, 165055964246192461256968397006503798748300/2197)
(-210331441853139588219457115081/7396, -2377771609392138405955993037583641982258575/636056)
(-12920072252749507063551745, 106882366666896424899704974817054522656)
(19319163567339374857128319, 34554832194813686482784544899920412960)
(2513747165470303418385140959/121, -60482784887382644140207065499435082958920/1331)
(-9044883069670730454229931, -102396398205375173173293071678035972780)
(13011656665765972000070447479/841, 123836521475685786284318445896194709451040/24389)
(-4951368086069358563409101, 92818647150910154398182389842795485920)
(7679478653082561418615051351/1369, -2529415008999073957001334638299654252052560/50653)
(194234604272056204594839877511/12769, -670495893583256463538243925451150933233960/1442897)
(1116849262828978754054833519, 37315295871424668894362483263976665613360)
(17325030024868012588502719, 19897880895987748972431378938567641760)
(126782747572504298736538840351/12769, -37357895947702755351138097525113069113911520/1442897)
(18490644103165258788491239, 28446318565083780866437414429308887000)
(1802800509766243289043792439/361, 363971464432243052733732142796149446848480/6859)
(342199196359966950162780462199399/54243225, 18494996596581525083732729594851716046927202190688/399501352125)
(6852301590286237440234314944270219197384435621051915552481039/598647444650217122283606878995122961, 7594430283802777430887536984772094786266479486305466367111221299265969526766164241514489920/463187360231920903408104210624041520715108466279234041)
(56918469478847727456957868235374135016221650904895317/6827118380614685077163086864, 19852883111034569127469758685854461931585286334838887233856648927670706374254377/564100065587546650203546069163116409522112)
(917170886311472122909220691184814487483109/135455652793344016, 2185338708961370992804593933797828936396343081878644752612948305/49853505362843322854064064)
(-547573054324659115044466297091864531/19824358401, 106057478168670755651075433558048061151059518867780940/2791249838502399)
(3028930167612105323495867480590441/356454400, 230712995807929797672195906014715475553564067876821/6729859072000)
(27468795831003855146540349391/113569, 2858933529025905027720133912622362290230327600/38272753)
(75430894285982565339821585391039061396931714523715/4924900234231598958519361, 34150368747492502571668143232409529816233345244866612402362422007342139168/10929395849215964129517858859300076641)
(-465239003908089067780327467678274820171262779020442369/170136368502676326600912572689, 6024084080613844845289701793907203243121721139036652865226549275879648980652777760/70177151807877916757409482167365169259418887)
(-298981555321151362163361107525387826163943/40495101425198809, 807219694917601299212559846014454036939137672804573963045546108/8148989093958081594769123)
(2998799137070492239390154386127432418298201824311/260455589244482393678569, 2120595270206131180631708813615543061069117979808739194726820194079810080/132923118724172283354451753769755253)
(-18040402929290380934151850266936041/786858601, 1925696300860607070751952573317640621601077047522400/22072170616651)
(854946574433892671905839557597959265/18227970121, 697798155398635939439761937288313759851499302852720188/2460976474006331)

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