Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #3591

y² = x³ − x² − 55432612640x + 5019429042432000

a-invariants: [0, -1, 0, -55432612640, 5019429042432000]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 3415094160
discriminant (Δ): 17226541308161684144876945817600
Faltings height: 4.9173
naive height: 85.8289
primes of bad reduction: 2, 3, 5, 79, 281, 641
regulator: 1506.602476006220968652739918688435003612409282
submitted by: Daniel Błażewicz
submitted at: 2026-09-29 05:52:08 UTC
last updated: 2026-09-29 05:52:08 UTC

Witness: 4 independent points log in to add more points →

(100805, 21351330)
(2421296/25, 2955837456/125)
(6862384/49, 594933200/343)
(462461616/1225, 8346531448464/42875)

Commentary

(u,v) = (641,79) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.

last edited by Daniel Błażewicz at 2026-10-01 07:55:46 UTC · history

Log in to edit commentary.