Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1357

y² + xy = x³ − 618120167801113x + 5915031717724666018617

a-invariants: [1, 0, 0, -618120167801113, 5915031717724666018617]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 325040992823102890550
discriminant (Δ): 28036239626257863184554820025491681280000
Faltings height: 7.0494
naive height: 113.7867
primes of bad reduction: 2, 5, 73, 127, 137, 1423, 1451, 1459, 1699
regulator: 477233.701896947959897615295202402904427977392292230497
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:00 UTC
last updated: 2026-09-24 17:38:00 UTC

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

(14330982, -139478721)
(14370986, -89673741)
(14430992, -506815451)
(9330482, 30978632779)
(14395098, 251607507)
(776420282/49, 3411284199861/343)
(14342372, -27927741)
(12430792, -12341998851)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:38:00 UTC · history

Log in to edit commentary.