curve #5283

y² = x³ − 8701x

a-invariants: [0, 0, 0, -8701, 0]
c-invariants: [417648, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 2422636832
discriminant (Δ): 42158726150464
Faltings height: 1.3038
naive height: 38.8272
primes of bad reduction: 2, 7, 11, 113
regulator: 86.10228215296920830306955004254528781215555484
submitted by: The Wren
submitted at: 2026-10-21 12:07:22 UTC
last updated: 2026-10-21 12:07:22 UTC

Witness: 4 independent points log in to add more points →

(-77, 462)
(-63, 546)
(99, 330)
(275, 4290)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (2,4,16,17), 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 12:07:22 UTC · history