Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4068

y² + xy + y = x³ + x² − 1879195x + 978782432

a-invariants: [1, 1, 1, -1879195, 978782432]
c-invariants: [90201361, -846344531609]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 132957915
discriminant (Δ): 10188056578763300625
Faltings height: 2.4528 ☆ record for ℤ/4ℤ torsion, rank ≥ 4
naive height: 54.9527
primes of bad reduction: 3, 5, 19, 31, 101, 149
regulator: 36.96558338912886323614321168406648349085770738
submitted by: NDElkies
submitted at: 2026-10-09 03:05:44 UTC
last updated: 2026-10-09 03:05:44 UTC

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

(-1495, 21951)
(12052, 1308916)
(-658, 44271)
(-583, 43611)

Commentary

smallest Faltings height of a curve of naïve height at most 2^90 with this MW group

last edited by NDElkies at 2026-10-09 03:05:45 UTC · history

Log in to edit commentary.