Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1592

y² + xy = x³ − x² − 29301x + 1919681

a-invariants: [1, -1, 0, -29301, 1919681]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 16064082
discriminant (Δ): 30167092997604
Faltings height: 1.4017 ☆ record for ℤ/3ℤ torsion, rank ≥ 4
naive height: 42.4698
primes of bad reduction: 2, 3, 17, 19, 307
regulator: 11.25338819855786612111536980430416869313230933
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:23:50 UTC
last updated: 2026-09-25 01:23:50 UTC

Witness: 4 independent points log in to add more points →

(-196, 421)
(1096, 35305)
(-26, 1645)
(32, 991)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 01:23:50 UTC · history

Log in to edit commentary.