Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #3777

y² + xy = x³ − 6145633054189x + 5390564941733100104

a-invariants: [1, 0, 0, -6145633054189, 5390564941733100104]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 9144620727627
discriminant (Δ): 2302105467479718040170725088829955917089
Faltings height: 6.2926
naive height: 99.9539
primes of bad reduction: 3, 7, 11, 17, 23, 61, 71, 97, 241
regulator: 6740.64460193911750505568559848700687213604373613
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:47:29 UTC
last updated: 2026-10-01 19:47:29 UTC

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

(13690559/4, 39544401301/8)
(30545804, 168265183694)
(8814994241/4489, 284172772093097/300763)
(17981429096/2209, 2308870344582376/103823)
(702314650241/215296, 447211900723596343/99897344)

Commentary

(u,v) = (4284,1633) 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 2026-10-01 19:47:30 UTC · history

Log in to edit commentary.