Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1351

y² = x³ + x² − 1913423065x + 32212145083239

a-invariants: [0, 1, 0, -1913423065, 32212145083239]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 6682940617328192 ☆ record for ℤ/2ℤ torsion, rank ≥ 8
discriminant (Δ): 75098172885467432959741952
Faltings height: 4.0010
naive height: 75.7301
primes of bad reduction: 2, 7, 31, 113, 193, 233, 281, 337
regulator: 16962.8641654017777536635610558167193774031442324139612
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:58 UTC
last updated: 2026-09-24 17:36:58 UTC

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

(-7583, 6803356)
(8930, 3979633)
(34879, 2811928)
(20725, 1207808)
(26815, -430808)
(224269/9, 2057048/27)
(26311, 288176)
(171701, 69033776)

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 17:36:58 UTC · history

Log in to edit commentary.