curve #6435

y² + xy + y = x³ − 34806252650946064988570052985664x + 79037604039252461667758510732843216192208273486

a-invariants: [1, 0, 1, -34806252650946064988570052985664, 79037604039252461667758510732843216192208273486]
c-invariants: [1670700127245411119451362543311849, -68288489889914129386993544141293217967111763259893]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 374179550932488127122381505424798097010
discriminant (Δ): 3101455465548163978207648307800022510843399534515837083730233446854219001824390381640667200
Faltings height: 16.6803
naive height: 229.4957
primes of bad reduction: 2, 5, 7, 17, 29, 31, 41, 43, 61, 71, 109, 137, 173, 3234111343, 5482577311
regulator: 12669094259654.6488340157136681745291061008785762539265758425
submitted by: Maksym Voznyy
submitted at: 2026-11-03 04:27:19 UTC
last updated: 2026-11-03 04:27:19 UTC

Witness: 11 independent points log in to add more points →

(5126596264299196703552882/1494054409, 146474391504822700575443101737305086/57749685071077)
(195415012818733495085906/36711481, 46968678690082005995386572812165074/222434863379)
(86911168562110130152640131650929/25451635426561969, 3412940514011260869370350799944699087665917733/4060444143050101772487703)
(304595507542415941804062915689/88506531499681, -2972723305196454761285377131725207497122443/832650950483915414671)
(1635761923281474355778018/433514041, 340890604871717200630443794503064398/9026195847661)
(3179494544147180861876/790321, 45113989380790987607124142018513/702595369)
(191440768101641657812/56169, 249793309776168278458961674/13312053)
(18200773532215297391905/4626801, 544300151464806269217429067661917/9952248951)
(3227602887595252841/64, 5760544027255356564173990879/512)
(605401317837346639338532/175907169, 8351339201793767769279110483525591/2333056782447)
(382086369763131714523985729/13846934929, -7310315508440288428810165482125651135573/1629410373900217)

Commentary

Voznyy (2026), T = 2186/195 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645

last edited by Maksym Voznyy at 2026-11-03 04:27:20 UTC · history