curve #5753

y² = x³ + 14425386253757

a-invariants: [0, 0, 0, 0, 14425386253757]
c-invariants: [0, -12463533723246048]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 7491303668522930932678141764
discriminant (Δ): -89895644022275171192137701168
Faltings height: 4.2346
naive height: 74.1232
primes of bad reduction: 2, 3, 14425386253757
regulator: 21657595606270.54297326627687842581738767892177918067436276
submitted by: jesper-petersen
submitted at: 2026-10-24 18:45:54 UTC
last updated: 2026-10-24 18:45:54 UTC

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

(-292111227069689/12000107025, 46739425575082892066/1314551724053625)
(-14290272667673/603635761, 15957028666896056190/14830727012009)
(-272192957799023/13585301136, 4000298837208469374905/1583448359207616)
(-268763745671273/13848817761, 4347510040674510670070/1629742722932241)
(-3024995974607/192709924, 8692381473606686025/2675199164968)
(-94754857315439/25109571600, 15083851043754493408441/3978862715736000)
(4230128632831/568584025, 52223698035825292854/13557886076125)
(2832421185900727/123679525761, 223639218553848401329370/43495739299154241)
(125447945159203/3367132729, 1588989928694162376240/195384610865683)
(494536424988528361/5211860702500, 350698114143017389222038891/11898417390772375000)

Commentary

The rationally 3-isogenous partner of a Mordell specialization obtained from the Burkhardt quartic using the Bruin–Nasserden parameters (u,v,w)=(12/9,12/9,-11/9) and specialization t=947/181. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 18:45:55 UTC · history