Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1345

y² = x³ − x² − 218669600x + 794575772496

a-invariants: [0, -1, 0, -218669600, 794575772496]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 28330377346942896
discriminant (Δ): 396490027743027750450373632
Faltings height: 3.8057 ☆ record for ℤ/2ℤ torsion, rank ≥ 8
naive height: 69.2228 ☆ record for ℤ/2ℤ torsion, rank ≥ 8
primes of bad reduction: 2, 3, 17, 47, 53, 89, 101, 223, 409
regulator: 20695.3822687685902012221902204774081088598676857597227
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:35:57 UTC
last updated: 2026-09-24 17:35:57 UTC

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

(14558, 834462)
(1630, 665186)
(-5642, 1359662)
(165654, 67158738)
(80006, -22257774)
(3236, 347616)
(15509/4, -566307/8)
(-4244, 1283024)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:35:57 UTC · history

Log in to edit commentary.