curve #2010

y² = x³ + x² − 1622134663627906102989517251313911928437023485151082089360x − 17091609332392603228385382011443182443804623893742574971751280937165834047099354557100

a-invariants: [0, 1, 0, -1622134663627906102989517251313911928437023485151082089360, -17091609332392603228385382011443182443804623893742574971751280937165834047099354557100]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 349432175747971837118686050547170875372336606890306428283195130479920
discriminant (Δ): 146977651186617827750964062103175315315956928193198317183532106922511539184346823030945570289594549994475160342989130743757937229491233117662033047365618169336589670976000000
Faltings height: 31.9321
naive height: 406.8069
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 101, 131, 139, 149, 157, 179, 653, 829, 953, 1307, 4019, 7207, 29287, 44249, 121178117, 3622521358583
regulator: 282053570522126801497.1407025689485482358346803606640801211888713
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:59:09 UTC
last updated: 2026-09-26 04:59:09 UTC

Witness: 13 independent points log in to add more points →

(2413249810330928217169914837130/49, -1626166932858381823212569673930128284983036480/343)
(112600230993336504330212730520272505/524176, -37080855251013002986128217203759689487610952107691925/379503424)
(-27738050370011743489780420070, -2561562667440171398997022074594914519985600)
(-5321902179145672068805254751295/256, 11326163400530039116885869373121687791491882975/4096)
(-5081898014348225671363639736413655/389376, 331042003266177968378235372960628321946322911073365/242970624)
(-252145160456821536902805791554750534310/17803298041, -4142840545850507380074602580953855383861036819733909607360/2375476254312589)
(-1538505162226368562025905044119637163286/57264011401, 36505107081546022257556769414436408515053849453558859959680/13703220664247899)
(-660105310437683654568309729532604525/25836889, -363835150234895432231621395063950075938303224070879460/131328906787)
(-312072643093973591560706853293770499343981/13593519189721, 142188761329202257460454577757141065722884876923643848180428660/50118476047830754019)
(-538197842588243132031898469794433102836214/29725776058225, -408167809934095511359452137342996723473740814542577862827161984/162068944049210560375)
(-61091560928102200562313552085435523974734950/2479036034026561, -347309984167633787250023409273644807513710586111097508375065813120/123431003332263716038559)
(4575854620232110176834233042692096666849105/53017970446336, 8508805660152826158814478856630944040951837178343254542178052775/386042081001605955584)
(-1453721088837017689148971266312255121753758287/50155503405611536, 26522676885665180640860595653330586913977091846052295300592606287249/11232537847643156902558784)

Commentary

2-isogenous partner of curve#325 (Jack Cheng).

last edited by Steps Unbounded at 2026-09-26 21:38:45 UTC · history