curve #5790

y² + y = x³ + 68672142559

a-invariants: [0, 0, 1, 0, 68672142559]
c-invariants: [0, -59332731171192]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 679084295569625540125521
discriminant (Δ): -2037252886708876620376563
Faltings height: 3.3434
naive height: 63.4284
primes of bad reduction: 3, 439, 1979, 316177
regulator: 769229157596.62409386731956462994870718473929615753066712
submitted by: jesper-petersen
submitted at: 2026-10-25 09:10:40 UTC
last updated: 2026-10-25 09:10:40 UTC

Witness: 9 independent points log in to add more points →

(-4303348056431/1117564900, 4019760690418659253/37360194607000)
(-65756952503/18164644, 11280701661646631/77417712728)
(-55476681047/22714756, 25181144399825537/108258527096)
(-2693409058943/1794200164, 19418969108834481469/75998730546712)
(99860685697/69089344, 153762482530131521/574270627328)
(895493761921/206209600, 1149023369916489281/2961169856000)
(2321964887833/374267716, 4014860161992287927/7240583233736)
(11147453712793/1043677636, 38253291621243342647/33717049708616)
(37950594055993/2352832036, 235696137315957094487/114126470738216)

Commentary

Specialization at t = -789/521 of a generic rank-four Mordell family obtained from the Burkhardt parametrization with construction parameters (-6,-1,-9). The specialization was identified by an optimized Mestre–Nagao sieve using 328 primes and examined using PARI/GP 2.17.4. PARI/GP returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 09:10:40 UTC · history