Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1645

y² = x³ − 6189969171x + 187021334913554

a-invariants: [0, 0, 0, -6189969171, 187021334913554]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 213471260496
discriminant (Δ): 69024141746336714063452065792
Faltings height: 4.4087
naive height: 79.2522
primes of bad reduction: 2, 3, 13, 23, 53, 139, 673
regulator: 706.834095426842623128642489800391977427585663815
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:19:19 UTC
last updated: 2026-09-25 02:19:19 UTC

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

(-70690, 16472612)
(8545, 11608272)
(124466, 36671258)
(11006401/225, 3817048976/3375)
(3561241, 6718880808)

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 02:19:19 UTC · history

Log in to edit commentary.