Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1358

y² + xy + y = x³ − x² − 5558495007053072x + 159508713196864012946419

a-invariants: [1, -1, 1, -5558495007053072, 159508713196864012946419]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 37226617173787496987970
discriminant (Δ): -23499793517379701583457790539842512215872000
Faltings height: 7.6019
naive height: 120.3759
primes of bad reduction: 2, 3, 5, 59, 67, 71, 373, 34501, 4241521
regulator: 581264.036320399424807669146757633525481820717736946229
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:10 UTC
last updated: 2026-09-24 17:38:10 UTC

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

(45859753, 32317867613)
(77879053, 446017422353)
(43440517, 4503911321)
(-4199139887/49, 27674128258223/343)
(79614205643/1849, 33296250761017/79507)
(148953457, 1623625530761)
(7629327517/81, 500576144351849/729)
(-60721033, 522663269911)

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 17:38:10 UTC · history

Log in to edit commentary.