curve #5724

y² + y = x³ − 38202519071716

a-invariants: [0, 0, 1, 0, -38202519071716]
c-invariants: [0, 33006976477962408]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 864848867214699620202458547
discriminant (Δ): -630474824199516023127592280763
Faltings height: 4.3969
naive height: 76.0710
primes of bad reduction: 3, 5659632455069
regulator: 23676604646.44744079883208866094719591025392485856822155969
submitted by: jesper-petersen
submitted at: 2026-10-24 16:55:47 UTC
last updated: 2026-10-24 16:55:47 UTC

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

(36996, 3526195)
(66012, 15793996)
(583158588, 14082508226227)
(1121514/25, 902063588/125)
(3449818/9, 6405409961/27)
(9598956/121, 28579175204/1331)
(193682409/3844, 2257359405377/238328)
(255128361/4096, 3739140212395/262144)
(1755284248/7569, 73426869139924/658503)
(6965423718/182329, 326166541560364/77854483)

Commentary

Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-18/3,6/3,-8/3) and specialization t=7/179. The specialization was identified using a three-stage Mestre–Nagao sieve involving 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 16:55:47 UTC · history