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curve #2923

y² + y = x³ + 327425365005582080

a-invariants: [0, 0, 1, 0, 327425365005582080]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 35361939420602864667
discriminant (Δ): -46313583688384698669118088595804334107
Faltings height: 5.9063
naive height: 94.1832
primes of bad reduction: 3, 13, 19, 41, 139, 271
regulator: 225635.2346235257470791601227121801251417123674234633
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:32 UTC
last updated: 2026-09-26 20:28:32 UTC

Witness: 7 independent points log in to add more points →

(267748, 588744383)
(1235988, 1488490048)
(-333330, 538877944)
(-648774, 233133847)
(-422760, 501863680)
(5104008, 11545190143)
(-688974, 19483912)

Commentary

Elkies–Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank, §5, k=1144421889, rank ≥ 7; https://arxiv.org/abs/math/0403116

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:32 UTC · history

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