curve #5786

y² + y = x³ + 14422381374283

a-invariants: [0, 0, 1, 0, 14422381374283]
c-invariants: [0, -12460937507380728]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 89858196506277679791362931603
discriminant (Δ): -89858196506277679791362931603
Faltings height: 4.2346
naive height: 74.1228
primes of bad reduction: 3, 317, 523, 6827, 50969
regulator: 41615892555174.85145421216440413324395849434959699215608230
submitted by: jesper-petersen
submitted at: 2026-10-25 08:37:19 UTC
last updated: 2026-10-25 08:37:19 UTC

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

(-1651, 3797088)
(-521741928965054686439039/26399974808284736400, 351200122800986896458504184553013791/135645461874685110054623112000)
(-83425337670509/4233714489, 716827536616222188703/275475100655763)
(161867331011/6235009, 87959667927432093/15568817473)
(2263891834289/1608010000, 244902692985139259337/64481201000000)
(5443359831319/111070521, 13455473055022612619/1170572220819)
(5866341936611/16589329, 14210909406535128226/67568337017)
(473319697834289/12973210000, 11727276095875627259337/1477648619000000)
(68778968661908423/87852367201, 18038067805349801525150575/26039353786009199)
(55773473549276376425057/13556191115072835856, 190007602158089302267067429080321487/49912178333182959734654418496)

Commentary

The rationally 3-isogenous partner of a specialization of a generic rank-four Burkhardt Mordell family. The underlying Burkhardt construction uses parameter triple (3,8,-6), with the sextic parameter specialized at t=-402/499.

last edited by jesper-petersen at 2026-10-25 08:37:19 UTC · history