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curve #4314

y² = x³ − x² − 2541594319889x − 158840777255686671

a-invariants: [0, -1, 0, -2541594319889, -158840777255686671]
c-invariants: [121996527354688, 137239163528077411840]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 16123341663260539584
discriminant (Δ): 1039848585560932572112814629035323572224
Faltings height: 6.1764
naive height: 97.3050 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 8
primes of bad reduction: 2, 3, 31, 47, 59, 97, 131, 193, 379, 1051
regulator: 213012.717321805152279611834950697361240593483331040837
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:49:59 UTC
last updated: 2026-10-17 09:49:59 UTC

Witness: 8 independent points log in to add more points →

(36965605, 224538992672)
(-642944, 1099765145)
(2146485, -2067697008)
(8500431, -24340395720)
(2776015, 3765413512)
(-79654883/81, 859336807760/729)
(-826061, -1173450316)
(-345251, 823100096)

Commentary

Curve 2x2-8.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 09:49:59 UTC · history

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