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curve #4316

y² + xy = x³ − x² − 2392541286x + 267054697382768

a-invariants: [1, -1, 0, -2392541286, 267054697382768]
c-invariants: [114841981737, -230734741749793749]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 14240074980350502
discriminant (Δ): -29932816443462425984047504939116
Faltings height: 4.7207 ☆ record for ℤ/3ℤ torsion, rank ≥ 7
naive height: 79.9601 ☆ record for ℤ/3ℤ torsion, rank ≥ 7
primes of bad reduction: 2, 3, 73, 103, 151, 179, 523, 827
regulator: 46308.66264387900926986453242854385770711935338724826
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:11 UTC
last updated: 2026-10-17 09:50:11 UTC

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

(451303/4, 302424215/8)
(58864, -18200276)
(124807/4, 119281439/8)
(386147/4, 244332629/8)
(9968419/4, -31477265491/8)
(-1958, 16485268)
(9333283/4, 28498269725/8)

Commentary

Curve 3-7.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:50:11 UTC · history

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