curve #4319

y² + xy = x³ + 836738300005291x + 411182108062709882259960

a-invariants: [1, 0, 0, 836738300005291, 411182108062709882259960]
c-invariants: [-40163438400253967, -355261341305936180672224489]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 975919424884519423407
discriminant (Δ): -73076046493421968572293293979344183203490123933503 ☆ record for ℤ/4ℤ torsion, rank ≥ 8
Faltings height: 8.2470 ☆ record for ℤ/4ℤ torsion, rank ≥ 8
naive height: 122.2698 ☆ record for ℤ/4ℤ torsion, rank ≥ 8
primes of bad reduction: 3, 11, 19, 31, 37, 73, 79, 127, 397, 733, 6367
regulator: 494976.202804998748747868148756259627374256316115655449
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:21 UTC
last updated: 2026-10-17 09:50:21 UTC

(12747577, -651097753277)
(459152577, -9879218339925)
(16934105512/49, -2222329858425524/343)
(480681024877/1681, 337855627491279983/68921)
(79326565, -988339350065)
(-66867173, 237212736700)
(3970342843/484, 6889122144113629/10648)
(188832536365/841, -84202931177354965/24389)

Curve 4-8.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 09:50:21 UTC · history