curve #6214

y² + y = x³ − 1864515923706717

a-invariants: [0, 0, 1, 0, -1864515923706717]
c-invariants: [0, 1610941758082603272]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1501813280054553636823661835963603
discriminant (Δ): -1501813280054553636823661835963603
Faltings height: 5.0449
naive height: 83.8467
primes of bad reduction: 3, 2027, 596069, 6172709
regulator: 256851610349.286783858920371669859901975962333545055064354205
submitted by: jesper-petersen
submitted at: 2026-10-30 19:33:12 UTC
last updated: 2026-10-30 19:33:12 UTC

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

(138243, 27883034)
(154599, 42784713)
(189747, 70477802)
(303447, 161483462)
(7143657/4, 19090170207/8)
(1982577/16, 394566633/64)
(2724393/16, 3547428875/64)
(27756013/81, 142801429375/729)
(66277381/225, 519517147904/3375)
(673149799/1521, 17276112191242/59319)
(937917967/7569, 4071142690802/658503)

Commentary

Generic-rank-4 Burkhardt fibration from quartic coordinates (-4, -5, 9, -12, -3), specialized at t=-844/331. PARI/GP 2.17.4 returned rank bounds [11,11].

last edited by jesper-petersen at 2026-10-30 19:33:13 UTC · history