curve #5740

y² + y = x³ + 55293555555810144

a-invariants: [0, 0, 1, 0, 55293555555810144]
c-invariants: [0, -47773632000219964632]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1320786987553495959933110666920909083
discriminant (Δ): -1320786987553495959933110666920909083
Faltings height: 5.6098
naive height: 90.6260
primes of bad reduction: 3, 223, 859109, 1154466611
regulator: 1739284378473.1743703606061408926855837318382241137317550534114
submitted by: jesper-petersen
submitted at: 2026-10-24 18:10:29 UTC
last updated: 2026-10-24 18:10:29 UTC

Witness: 12 independent points log in to add more points →

(-352548, 107122976)
(-46167/4, 1881140383/8)
(8316, 235147040)
(68508, 235828512)
(294273/4, 1887927589/8)
(364233/4, 1893966409/8)
(5835096, 14097186144)
(-44249871072/143641, 8788082077042208/54439939)
(-341478359/900, 700053278561/27000)
(1376272/9, 6551017669/27)
(8473084/225, 794000291552/3375)
(232906612/81, 3558583781767/729)

Commentary

Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic using parameters (u,v,w)=(7/6,-5/6,3/6) and specialization t=-11/336. The curve was selected by a three-stage Mestre–Nagao sieve over 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [12,12] for this model and its 3-isogenous partner.

last edited by jesper-petersen at 2026-10-24 18:10:29 UTC · history