curve #5725

y² + y = x³ + 1414908113767

a-invariants: [0, 0, 1, 0, 1414908113767]
c-invariants: [0, -1222480610294904]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 864848867214699620202458547
discriminant (Δ): -864848867214699620202458547
Faltings height: 3.8476
naive height: 69.4793
primes of bad reduction: 3, 5659632455069
regulator: 1398079827768074.931730236003340270971304584008973594914878
submitted by: jesper-petersen
submitted at: 2026-10-24 16:56:45 UTC
last updated: 2026-10-24 16:56:45 UTC

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

(-1261401265567/152078224, 1723223843216959665/1875428658368)
(1664725533665/484176016, 12853426277407898127/10653809056064)
(2448358493106797540267489/37785993195350416, 3831003179997454577273804735824092337/7345075479326052253257536)
(-12062027801645551/3493871256100, 7654480824423149183497043/6530709213189559000)
(40945728032214248305/964000782883044, 264414819851032042083137122043/29930645275236153773928)
(7576975490273921033/1238770523453584, 55898812703502405014516048517/43599980412002376480448)
(-17457583043100656691223/16022165959714485796, 76251283640607938835928415463957449/64133041809822836930754959656)
(75375298102795238720873/29623400942499303424, 192898961908552980951778310283472075/161232420900388320559078572032)
(5341808320401211263456616225/209882353564575442257984, 406828547624570875639182048926515526009137/96153232366862206321402018400804352)
(-7262820993021011436559158175/982897705882594870643044, 980022284031695640473681463453006631745293/974456556659290321299886550546203928)

Commentary

The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve constructed from parameters (u,v,w)=(-18/3,6/3,-8/3) and specialization t=7/179. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 16:56:45 UTC · history