Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4533

y² = x³ − x² − 681780495x + 6783916801632

a-invariants: [0, -1, 0, -681780495, 6783916801632]
c-invariants: [32725463776, -5861107763827424]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 622724943720
discriminant (Δ): 402168338455587393572955600
Faltings height: 3.9179
naive height: 72.6343
primes of bad reduction: 2, 3, 5, 11, 53, 89, 103, 971
regulator: 2468.91034289268540068620853370753489733706771854
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:18 UTC
last updated: 2026-10-17 10:34:18 UTC

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

(1203449/16, -1249264325/64)
(-8011, 3425125)
(16369, 97785)
(46327277/3481, 53318601391/205379)
(12724, 410850)

Commentary

BASE torsion/torsion_Z4.tsv.gz:2357 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:18 UTC · history

Log in to edit commentary.