Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #3466

y² + xy + y = x³ − 629556267118220x + 6080889056715818968350

a-invariants: [1, 0, 1, -629556267118220, 6080889056715818968350]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 312377498811002040962
discriminant (Δ): -4938502925948331729469816725702381516352996
Faltings height: 7.1963
naive height: 113.8420
primes of bad reduction: 2, 7, 13, 19, 31, 313, 463, 733, 1217, 22541
regulator: 3229434.76035366261947520684410682522598894193237771006
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:42:47 UTC
last updated: 2026-09-27 05:42:47 UTC

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

(15777394, -8699147137)
(84767984601/5329, -3724621783454311/389017)
(56639083801/3249, 3719913537840941/185193)
(-28331349545/2601, 14315952628729519/132651)
(918616711612/66049, -66457799650161743/16974593)
(-272072007/64, -47701226345369/512)
(6427765137/169, -423534182399067/2197)
(26257190279/25, -4253596162807577/125)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:42:47 UTC · history

Log in to edit commentary.