curve #5584

y² = x³ − 1192406728744872

a-invariants: [0, 0, 0, 0, -1192406728744872]
c-invariants: [0, 1030239413635569408]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 52660511361335064931572825792
discriminant (Δ): -614232204518612197361865440037888
Faltings height: 4.9704
naive height: 82.9526
primes of bad reduction: 2, 3, 406661, 13574947
regulator: 4683830870.066243569481301607602230135433453674307420075446
submitted by: The Wren
submitted at: 2026-10-23 20:09:19 UTC
last updated: 2026-10-23 20:09:19 UTC

Witness: 10 independent points log in to add more points →

(106122, 1651176)
(169482, 60628536)
(209838, 89706060)
(430113, 279959445)
(436782, 286594164)
(1397838, 1652305860)
(2004762, 2838324816)
(1943134/9, 2543140196/27)
(2038233/4, 2896775523/8)
(5760104673/54289, 17930131695243/12649337)

Commentary

Rational 3-isogeny partner of curve #5583. PARI/GP gives exact rank 10. Source curve from Jesper Petersen’s Burkhardt quartic specialization at t = 59/19 with affine quadruple (a,b,c,d) = (-11/2,12,6,3/2).

last edited by The Wren at 2026-10-23 20:09:20 UTC · history