Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1577

y² + xy = x³ − 8474716297178877x + 301161814193541330007281

a-invariants: [1, 0, 0, -8474716297178877, 301161814193541330007281]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 64631018298
discriminant (Δ): -227418820069170773128669674352578474118539296256
Faltings height: 7.9512
naive height: 121.6470
primes of bad reduction: 2, 3, 7, 11, 19, 31, 109, 2179
regulator: 254.45559246791896913039497830139621089221012
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:21:19 UTC
last updated: 2026-09-25 01:21:19 UTC

Witness: 3 independent points log in to add more points →

(-4802152008/361, 4400197847688795/6859)
(6234364986, 492196479706815)
(353824722096/2809, 165250864406606043/148877)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:21:19 UTC · history

Log in to edit commentary.