Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1355

y² + xy + y = x³ − 854599144949838x + 9615970693708676495156

a-invariants: [1, 0, 1, -854599144949838, 9615970693708676495156]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 1281515541410622296170
discriminant (Δ): -246459034649676806065785083883173389562500
Faltings height: 7.1603
naive height: 114.7586
primes of bad reduction: 2, 5, 7, 19, 181, 313, 461, 487, 2861, 26479
regulator: 728607.023599016748482277175831665371133730533595763576
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:37:39 UTC
last updated: 2026-09-24 17:37:39 UTC

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

(9975245, 45642868187)
(-1895044, 105966357964)
(-21481450, 134403175912)
(16958875, 592770337)
(152194300/9, 7557693124/27)
(16745030, 952029937)
(152232835/9, 8232157019/27)
(69126075/4, 23034926171/8)

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 17:37:39 UTC · history

Log in to edit commentary.