Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4069

y² + xy + y = x³ + x² − 12704813x + 17424482906

a-invariants: [1, 1, 1, -12704813, 17424482906]
c-invariants: [609831025, -15059326963625]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 224902425
discriminant (Δ): 5264384537045390625
Faltings height: 2.7049
naive height: 60.6861
primes of bad reduction: 3, 5, 11, 41, 61, 109
regulator: 101.3233565306469461907577158749380813303591173
submitted by: NDElkies
submitted at: 2026-10-09 03:08:23 UTC
last updated: 2026-10-09 03:08:23 UTC

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

(-1656, 185017)
(-4035, 56917)
(3041, 81683)
(1776, 20710)

Commentary

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

last edited by NDElkies at 2026-10-09 03:08:23 UTC · history

Log in to edit commentary.