curve #3435

y² + y = x³ + x² − 9687757x + 12256549127

a-invariants: [0, 1, 1, -9687757, 12256549127]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 514514775019 ☆ record for ℤ/3ℤ torsion, rank ≥ 6
discriminant (Δ): -6740351853541051667131 ☆ record for ℤ/3ℤ torsion, rank ≥ 6
Faltings height: 2.9404 ☆ record for ℤ/3ℤ torsion, rank ≥ 6
naive height: 59.9823 ☆ record for ℤ/3ℤ torsion, rank ≥ 6
primes of bad reduction: 7, 19, 73, 83, 197, 463
regulator: 2554.4798349702663692162764566607795087561113397506
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:33:06 UTC
last updated: 2026-09-27 05:33:06 UTC

(2207, 40379)
(-1279, 150188)
(181337/64, 44523517/512)
(-23297/9, 3817945/27)
(-13747/4, 564007/8)
(-925, 142923)

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:33:06 UTC · history