curve #1886

y² + xy + y = x³ − x² − 42296411935455995407763552717518009798422x + 3359890549538851657210171385096973534407856485882053923235365

a-invariants: [1, -1, 1, -42296411935455995407763552717518009798422, 3359890549538851657210171385096973534407856485882053923235365]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 2374829144944182718518490622415817981020347817798361891926024970755386858650001847515826286224721982
discriminant (Δ): -34056130449690478434181344536572000322323090220752739991075862717142106586420062228922828676518204007898493415874067693568
Faltings height: 22.1760
naive height: 292.2572
primes of bad reduction: 2, 7, 13, 19, 23, 29, 67, 71, 79, 1951, 6983, 201104594684144310899453166947924420211313814676994879385703504710195295484015663
regulator: 1127352209865563860447990228.566677502934347969762173081593342374214119737012583024743243
submitted by: Ritik Jain
submitted at: 2026-09-25 17:34:09 UTC
last updated: 2026-09-25 17:34:09 UTC

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

(12665016028517169872587/4, -1422373358135490433434802046773803/8)
(127491160929893548103, 199280513790520473268929247387)
(110447715084228895189455910518557454408140911771657/39290391805780041764359766689, 1157717782344296235710583476023906971537824905805176931952125518111452184549/7788064496629548001895793251811569707871887)
(31206988972690546184023819/15625, 173442519882870878557587372974683021247/1953125)
(42073744611359163636289/25, -8568501043159896139042616414515297/125)
(6975545977410991736673, -582345362622595473919426105488933)
(5914221444799544909125/49, 39300247722788044621213679404645/343)
(2761141352697088523625, 144697074644676447476630867293515)
(40050664719940393545609/289, 1964322730405151656509043120389211/4913)
(2673843271341240482123/4, 132370712896472994316763027028061/8)
(831110967879429230953, 23287185116236898759330059923787)
(-33345993929870160349, 2175598122404459511721544097011)
(6081184631162492020899/49, -51070213482463357376152004153227/343)
(415920403562019227908317, 268234901521240708211396202099977427)
(274093565573950118641, 3515483035704054348708216492091)
(-368341100919005257775/9, -60508888043163417872616638912695/27)
(1197945612130879791685227352825265/1351157486449, -40434215624262789440429829779039341170348813958285/1570576004145912457)
(257237700496997865110832353060078332683009/2455602140876270786521, 34129600749619523772694294085864984643755392523318283541805825/121684988391820784528236756606819)
(388389985279116604184466104663073404243697/3368849101883251427401, 24694896568455754950768930309561413028003539552587756432574135/195534023856147135150559839230149)
(9224436031155369474316422707011544825445841/111391078138175900869561, 24241255549491654719294600312964281813802812552002634492495839839/37177108692801737342700386636395309)
(-10609155983682639720802352224925783/78248230714809, 1778505517028452049879764487335193149260974453946529/692168434001749596627)
(236261026324736920226449/2025, 10494880052282296540584821525365703/91125)
(1314841085724245852958393315056768784900224564341/12135852919939216844473709329, 296299282551073783379569241547109370256360041705386176182593140321360405/1336920111782376683177648322578196857022983)
(18427201457164363234687777556829209264113295632915/195481558334841564616204718569, 39647871341880528282548666270943746707235658369385785728014459506825822315/86428840899905273545652821848713207349524747)
(-561118538270397782066393971697282100681704319740158461/5113109150174220972234319296809929, 944959685176062101576802483776866193487360933742526458337013894918544888200897489/365618022727435277470598892960532606316491940681467)

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