curve #5752

y² + y = x³ + 1135749032909975

a-invariants: [0, 0, 1, 0, 1135749032909975]
c-invariants: [0, -981287164434218616]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1507693319606626100946419409
discriminant (Δ): -557247974006567826788099452824627
Faltings height: 4.9623
naive height: 82.8553
primes of bad reduction: 3, 13, 17, 58565651231
regulator: 98604969324305.21231744274241676780901491536714737670274490
submitted by: jesper-petersen
submitted at: 2026-10-24 18:45:05 UTC
last updated: 2026-10-24 18:45:05 UTC

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

(-455263773455/11999296, 1366699888839534025/41565561344)
(-356161424655/13424896, 1644022692120447031/49188818944)
(155947198897825/2633947684, 4954458313309015939827/135179463038248)
(4943938750377/59320804, 18918959483858179639/456888832408)
(30032310372145/178596496, 183186476922971102775/2386763572544)
(31647638348017/184742464, 197125763674631074249/2511019570688)
(78097297906088185/1623927143556, 73076674758706279230856271/2069425572556291704)
(3653942866914129/324341640100, 6229001580518115619816883/184715807453351000)
(198261326264256889/1616864833600, 112222350261473984641988787/2055940647812416000)
(22496188033587984770549193/1187006078878107521476, 1382350578083878890703249467461602945489/40895866514649299320500357431224)

Commentary

The rationally 3-isogenous partner of the Burkhardt-quartic Mordell specialization with parameters (u,v,w)=(6/8,7/8,-5/8) and specialization t=-641/625. PARI/GP 2.17.4 returned matching computational rank bounds [10,10,].

last edited by jesper-petersen at 2026-10-24 18:45:05 UTC · history