curve #5411

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y² + y = x³ − 9010558538560405866191094587247330877

a-invariants: [0, 0, 1, 0, -9010558538560405866191094587247330877]
c-invariants: [0, 7785122577316190668389105723381693877512]
rank (lower bound): ≥ 15
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 906640482317727900023195951228507775255643978301336452058030912615361
discriminant (Δ): -35074151356387897657017054927461708917819127808460908674494010774584575034323
Faltings height: 13.3665
naive height: 183.7061
primes of bad reduction: 3, 7, 19, 4729, 9829, 122693, 913527311, 14485206383
regulator: 433124771859935157037621378402.29196380270681543175162128828830957333
submitted by: Maksym Voznyy
submitted at: 2026-10-21 21:54:54 UTC
last updated: 2026-10-21 21:54:54 UTC

Witness: 15 independent points log in to add more points →

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(27255433316862994277389746512426209/148175777073112236100, -4499656093080632128704157935514116930263620597543427/1803706291773886645314359891000)
(3850583419088698373598091628407713/401413210507307988544, -237717821211690271365459698070406461153669555037169/8042433740022136812386109372928)
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(364254554488991114623297326909212356521/20968960323647508640000, -6951963544965867462191190506914423673358614951936344451819/3036444495846273292972290112000000)
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(84331727486562467402151494967339622803986369960353432408767762919479225631912518100462377031405897639257842412838921/14199713502090365626053669213895659008806461346271271845342681169274836788474788169977899473648450510400, 757598516527010831278683878608013460513356700485374876287211783830441833297799318955579943164504633130395969077314782185859197185504099142625471898534550921186797054079114469/53508080653123162489402764160964909522068334287969303720482537831041535711178027321129900962156925765632837587020326213579166104579513411407537907407808000)

Commentary

Reynya - Voznyy (2026), 3-isogenous to curve#5410

last edited by Maksym Voznyy at 2026-10-21 21:54:54 UTC · history