curve #1891

y² + xy = x³ − 35618757744448151892829943455794377276479950x + 81829052393335053959042598367869773898197695883213311167458409732

a-invariants: [1, 0, 0, -35618757744448151892829943455794377276479950, 81829052393335053959042598367869773898197695883213311167458409732]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 2315990875306640160302621235408001944719435973568438475351565678612772446627831493271926399765230
discriminant (Δ): -549518446790529249937851196364659055704597464880628151704403636419346740157138811608264193711322943664960634126750449436160000000
Faltings height: 23.7322
naive height: 312.4581
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 47, 53, 277, 2861, 17077, 183971, 29440224574349818293873490232762890482267577322176992842085523240585907
regulator: 124170836153017348698935339.4123161913428353995416372680636701053148705246238768614447329
submitted by: Ritik Jain
submitted at: 2026-09-25 17:36:54 UTC
last updated: 2026-09-25 17:36:54 UTC

Witness: 25 independent points log in to add more points →

(16534299813092612472922896/7225, 68113195356261373336471326125034558426/614125)
(6799890012434090828642060048911996885546626726021530364/1891160810584020047154912407484481, -1283177825162098679388484907655670315499625191202884982595088354724521056497005022/82241815618602294878728787115194408356282545601121)
(17929954288966535893252476/5329, 3374499484212069834040229169897558546/389017)
(35728955356184386056586/9, -1476878640937191803897417701933504/27)
(10003171389793873251912, -852338097643214630424435069443742)
(-667320054055650139497216/121, 442493371112544840218134731121024038/1331)
(3971172581626931652327336/1369, 2735037293195241821584860157446393114/50653)
(2262132150665860004995316/289, -2611777659577083325612008860650286366/4913)
(3426429176860366990404, -3407145837175464851651272675902)
(30667084992883842672526/9, 129052650270221156765667078464116/27)
(3422686387425905641932, -3638732274541349412572001437550)
(61142560757095420956444, 15049256952886493821117533204219138)
(66134816325928264471666704/10201, 361933316810697893549317351615911841398/1030301)
(-811462329985645092996696/361, -2661221473331519384138307054568418478/6859)
(651540355288769385248796/169, -93479685440112706094679564274870134/2197)
(102660591793294952220384/25, -8668185369504175652481894850969158/125)
(-1399521960131637262929372/361, 2757704073198237769369896416640039894/6859)
(708379065898945554176617308292062380036139/229069303400289211876, 122766005450613221777683782428658553873590744093484321980708483/3466972067786380160446722294376)
(-6253963524603347746381745508/3024121, 2013875732169851872695443663285894675462982/5258946419)
(2104528369511798942927067071405864473236/554513456391499609, 14965804410666549592902842885253698558637360975463404507846/412922106754282736913768227)
(-1130263562443193774947943986646400036/353457333812521, 2683114352346554829052424560428442403780532441373199178/6645160819506282372181)
(3096776332342221812246023767653223657526524/876435268524501612481, 243251490542011622796876716483199538179440279070916954860881058/25946558882396571556739235273121)
(27274932650658163581585613124364440682031613256/7792726440664131845915089, 134902977443116343169985583531669010833127614685955037589562709870226/21753750654413201017672699962502278937)
(64874296690807627252928283341106/17769689809, 50325430407278783608356081222324524410534419576/2368752960609127)
(12064377860449461448049822782696811368467/3605567149250942404, 71632179586033028439650467632905831366435561752876035944253/6846370254481463941410657208)

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