curve #5796

y² = x³ − 954590169789700500

a-invariants: [0, 0, 0, 0, -954590169789700500]
c-invariants: [0, 824765906698301232000]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 16395531589168839108088089130800
discriminant (Δ): -393656713455943826985195020030508000000
Faltings height: 6.0846
naive height: 96.3233
primes of bad reduction: 2, 3, 5, 7, 1855374479669
regulator: 2917082875012906.86292839341424693289498808554144100975239287
submitted by: jesper-petersen
submitted at: 2026-10-25 10:34:28 UTC
last updated: 2026-10-25 10:34:28 UTC

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

(4870883812496254/4945324329, 10594444559852033824258/347770042788267)
(50262341043445045/5333234841, 11262019910431258125180325/389480807203389)
(51285532818274045/3693114441, -11612210228300910630537575/224434257694011)
(105441691723129405/64595780649, -30248994040749208296256825/16417469822407893)
(2133448862467024270/202940339121, 3114905450338471221241475050/91422390430280169)
(3053202918023470870/257727813561, 5333456899551488937007798250/130840421382699309)
(132992860718300657326/9329683129209, 1533454581380816694930333276574/28497078623061817677)
(195562948529824396945/62833460683536, 2691184581904208569589364954425/498065511473983089216)
(118730563553812945/108658573956, -21191907926870572279932775/35817560367412104)
(4334140451567966305/569560014864, -9013294189489102323988833775/429842386737741888)
(13086161867339580861814/11124926051805225, -962617435455372354688811387872762/1173398960956533932647125)

Commentary

The rationally 3-isogenous partner of the specialization t = 392/505 of the generic rank-four Burkhardt Mordell family with construction parameters (-9, 5, -5). PARI/GP 2.17.4 returned matching computational rank bounds [11,11].

last edited by jesper-petersen at 2026-10-25 10:34:29 UTC · history