curve #5791

y² + y = x³ + 239772429064

a-invariants: [0, 0, 1, 0, 239772429064]
c-invariants: [0, -207163378711512]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 8278677754469394930810441
discriminant (Δ): -24836033263408184792431323
Faltings height: 3.5517
naive height: 65.9291
primes of bad reduction: 3, 191, 5021412127
regulator: 12774979567631.376279124923852394267893814449656960685388
submitted by: jesper-petersen
submitted at: 2026-10-25 09:29:17 UTC
last updated: 2026-10-25 09:29:17 UTC

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

(-88253363294/78411025, 338976621989622896/694329626375)
(24474722803552/12275088849, 676859551386133409119/1359993918847257)
(9433910625706/949564225, 32324861451681162896/29260821593375)
(13593080269911284137/47389979185444, 50116303094051214827957007409/326234417531805542872)
(14848337738201899456/12566067868225, 57215907079515742510943388104/44545014173695414625)
(45461229434861401/4320328531600, 10643821214829375008040899/8979975666071864000)
(496560946907063872/52071853862889, 395338000578195446340889949/375754819438477643787)
(145509647656121079688/6981018752305081, 1778330070727996171030430872792/583281506472801509506771)
(1927644909054208070895001/163367371867296636900, 2864994989548366635930775178736733999/2088084087260221056053516847000)

Commentary

Specialization at t = 144/83 of a generic rank-four Mordell family constructed using the Burkhardt parametrization with parameters (7, -2, 10). The curve is its rationally 3-isogenous partner. The specialization was identified using an optimized Mestre–Nagao sieve evaluating 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].

last edited by jesper-petersen at 2026-10-25 09:29:17 UTC · history