Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1653

y² + xy + y = x³ + x² − 4161127688x + 103298028771656

a-invariants: [1, 1, 1, -4161127688, 103298028771656]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 84289510725
discriminant (Δ): 1387611282752763473214140625
Faltings height: 4.2137
naive height: 78.0608
primes of bad reduction: 3, 5, 7, 31, 41, 59, 2141
regulator: 291.949263499520059760810575449623252151716349184
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:28:26 UTC
last updated: 2026-09-25 02:28:26 UTC

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

(42420, -1787048)
(-32005, -14256098)
(17328045/16, 71971656403/64)
(36840, 31567)
(36096, -378377)

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 02:28:26 UTC · history

Log in to edit commentary.