curve #6535

y² + xy + y = x³ − 10405486760504388834242599816160393x + 407468397307778948729488277555802904227815902413008

a-invariants: [1, 0, 1, -10405486760504388834242599816160393, 407468397307778948729488277555802904227815902413008]
c-invariants: [499463364504210664043644791175698841, -352052695273921012451472918564529705318300126448387389]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 1551271264741194849797376066540286441120214504315167468600933796181258751893805107510
discriminant (Δ): 380124386845886230191786600100271535243276193660238312698070802950022846320085975096639062869702687500
Faltings height: 18.3599
naive height: 246.5965
primes of bad reduction: 2, 3, 5, 11, 23, 41, 1051, 7577, 44383, 337111730466899711, 188175659272694814913217, 222335159547961391940662587
regulator: 1577715867007363023649707.8977548188773514295904931883047439530648816343736994629396135
submitted by: apkorte
submitted at: 2026-11-04 09:30:23 UTC
last updated: 2026-11-04 09:30:23 UTC

(-96480897632335461, 22656136693766914435957300)
(2562894477807594, 19514534759724227408348590)
(55565787511505994, -917525429570737157743385)
(-44802991440063156, -27995212542357154939107185)
(-36925545715224807, -27227721942993293560171772)
(14129432652733509, 16225461006187791445954480)
(1032773839124165277/16, -139506041592465845173837127/64)
(67827334412368869, 3706052695723863573482890)
(73293554425059339, 6208239580802038106108200)
(2768692849743024951/4, 4559493689048070486879656345/8)
(108222965267664354, 23428313669682167647807495)
(19388781683090619, -14594773428555971469096860)
(209010829753123494, -85810006586186998387906985)
(95921989337750091/4, -104836627758113886968321365/8)
(249254301862381707429/961, -3667693076667900453763434692240/29791)
(62008611159227514, -816046925677852787007650)
(437826742214779419, 282452941112817990313581040)
(2130692963343208602, 3106649054742402053543139262)
(34557210791992644, 9442036167662469125243215)
(-22397660963411286, 25085674378577769313811950)
(-100162361220220731, 21090940561334858182081840)
(61485656574936149, 354786599446357710177120)
(35032783298688744, 9269888116423489892851240)
(-19524027883924678269/169, -18078191088508356065394288740/2197)

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