Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #3800

y² + xy = x³ − 5298697071017420x + 148382367241514690201775

a-invariants: [1, 0, 0, -5298697071017420, 148382367241514690201775]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 22256740418115
discriminant (Δ): 9617385588037687162541537576472823716969140625
Faltings height: 7.7684
naive height: 120.2323
primes of bad reduction: 3, 5, 7, 17, 23, 53, 89, 281, 409
regulator: 1082.81322041822863965516287146756121440790425210
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:31:41 UTC
last updated: 2026-10-02 05:31:41 UTC

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

(-21852785/4, 3367319944565/8)
(139640335/4, 616940711165/8)
(47085151, 57254155927)
(59270275, 206226435670)
(298765615, 5023136335255)

Commentary

(u,v) = (22525,2484) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-02 05:31:42 UTC · history

Log in to edit commentary.