curve #5749

y² = x³ + 1919519057859308

a-invariants: [0, 0, 0, 0, 1919519057859308]
c-invariants: [0, -1658464465990442112]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 33160980721365768720631700149776
discriminant (Δ): -1591727074625556898590321607189248
Faltings height: 5.0497
naive height: 83.9048
primes of bad reduction: 2, 3, 2256613, 212654879
regulator: 28211078726.0476593018847130635172015147451676085797783401936
submitted by: jesper-petersen
submitted at: 2026-10-24 18:42:36 UTC
last updated: 2026-10-24 18:42:36 UTC

Witness: 11 independent points log in to add more points →

(-80602, 37361390)
(-78914, 37790058)
(-8083, 43806289)
(35717, 44329261)
(592637, 458328119)
(18408598, 78982547550)
(-1961303/16, 563726229/64)
(-1959607/16, 580811845/64)
(223873/4, 366155073/8)
(459862/361, 300508839174/6859)
(5711849/4, 13655518069/8)

Commentary

Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-9/9,-12/9,-10/9) and specialization t=191/422. The curve was selected using a three-stage Mestre–Nagao sieve involving 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [11,11].

last edited by jesper-petersen at 2026-10-24 18:42:36 UTC · history