curve #5284

y² = x³ + 387903x

a-invariants: [0, 0, 0, 387903, 0]
c-invariants: [-18619344, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4814999597088
discriminant (Δ): -3735505577418452928
Faltings height: 2.2532
naive height: 50.2191
primes of bad reduction: 2, 3, 31, 43, 97
regulator: 1077.62417267559002768601971126811684715959605326
submitted by: The Wren
submitted at: 2026-10-21 12:08:43 UTC
last updated: 2026-10-21 12:08:43 UTC

Witness: 5 independent points log in to add more points →

(31, 3472)
(97, 6208)
(129, 7224)
(1161, 44892)
(6321/16, 938217/64)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (3,5,11,19), 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 12:08:43 UTC · history