Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1800

y² + xy = x³ − 25805970x + 49666385412

a-invariants: [1, 0, 0, -25805970, 49666385412]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 41061390
discriminant (Δ): 34139715963820890624000
Faltings height: 3.1193
naive height: 62.8120
primes of bad reduction: 2, 3, 5, 29, 109, 433
regulator: 14.175487141619028975537086694659023643906818
submitted by: hdeping
submitted at: 2026-09-25 15:04:26 UTC
last updated: 2026-09-25 15:04:26 UTC

Witness: 3 independent points log in to add more points →

(2484, 28638)
(10404, 947358)
(3492, 44478)

Commentary

Specialization t=-4/1 of Eroshkin's exact rank-3 family with torsion Z/6Z (Dujella-Peral-Tadic, sec 5).

last edited by hdeping at 2026-09-27 08:32:05 UTC · history

Log in to edit commentary.