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curve #1685

y² + xy = x³ + x² − 94924250x + 963288615000

a-invariants: [1, 1, 0, -94924250, 963288615000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 4309549350 ☆ record for ℤ/4ℤ torsion, rank ≥ 5
discriminant (Δ): -346155653842848749275312500
Faltings height: 3.7782
naive height: 68.7105 ☆ record for ℤ/4ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 5, 29, 61, 109, 149
regulator: 344.956214439144990282542260566641956214566185253
submitted by: Michael Rubinstein
submitted at: 2026-09-25 04:48:37 UTC
last updated: 2026-09-25 04:48:37 UTC

Witness: 5 independent points log in to add more points →

(1850, 890150)
(429566, 281257988)
(-194494/49, 388369640/343)
(15625/169, 2146349600/2197)
(2095825/9, 3028441925/27)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 04:48:37 UTC · history

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