curve #5306

y² = x³ − 8816378537x

a-invariants: [0, 0, 0, -8816378537, 0]
c-invariants: [423186169776, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 2487312976245576331808
discriminant (Δ): 43858185477146180025894483209792
Faltings height: 4.7610
naive height: 80.3132
primes of bad reduction: 2, 19, 29, 37, 43, 89, 113
regulator: 243444.9407041256083788805319466785500944981967373493
submitted by: The Wren
submitted at: 2026-10-21 12:50:16 UTC
last updated: 2026-10-21 12:50:16 UTC

Witness: 7 independent points log in to add more points →

(-81700, 13227230)
(-43731, 17375784)
(-3268, 5364422)
(101232, 12038172)
(105203, 15389696)
(-2677309/121, 18066481132/1331)
(2303731/9, 3252868172/27)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (4,7,10,20), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.

last edited by The Wren at 2026-10-21 12:50:16 UTC · history