Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1319

y² + xy + y = x³ − 170671598130x + 24898868382347720

a-invariants: [1, 0, 1, -170671598130, 24898868382347720]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 21257773462978
discriminant (Δ): 50353023815799767963666602409522924
Faltings height: 5.3978
naive height: 89.2026
primes of bad reduction: 2, 13, 19, 31, 83, 103, 397, 409
regulator: 3914.2779940292363748020915176307803194473405753398
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:31:27 UTC
last updated: 2026-09-24 17:31:27 UTC

Witness: 6 independent points log in to add more points →

(3453323, 6371491759)
(154027, 47515269)
(682760, 475733695)
(86495120/289, 122329965160/4913)
(1158136177/1024, 37033554373881/32768)
(38812605, 241768558195)

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 17:31:27 UTC · history

Log in to edit commentary.