Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1712

y² + xy = x³ + x² − 15875309375x + 847786354055625

a-invariants: [1, 1, 0, -15875309375, 847786354055625]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 74593639050
discriminant (Δ): -54438415484380881805657712812500
Faltings height: 4.8242
naive height: 82.2705
primes of bad reduction: 2, 3, 5, 7, 29, 41, 149, 401
regulator: 241.830714310966729635526902173219800741286576489
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:14:18 UTC
last updated: 2026-09-25 06:14:18 UTC

Witness: 5 independent points log in to add more points →

(-141700, 15950525)
(37696, -17423389)
(-104000, 37119075)
(157580, 47451485)
(3807521/25, 5528268316/125)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:14:18 UTC · history

Log in to edit commentary.