curve #5272

y² = x³ + 88032168x

a-invariants: [0, 0, 0, 88032168, 0]
c-invariants: [-4225544064, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 3444294490124544
discriminant (Δ): -43662054412241020559720448
Faltings height: 3.6093
naive height: 66.4932
primes of bad reduction: 2, 3, 7, 19, 29, 317
regulator: 6963.5217077078636442703882662254855369380350009688
submitted by: The Wren
submitted at: 2026-10-21 11:42:58 UTC
last updated: 2026-10-21 11:42:58 UTC

Witness: 6 independent points log in to add more points →

(609, 232029)
(928, 287216)
(2536, 489448)
(6657, 938637)
(9576, 1311912)
(38304, 7718256)

Commentary

Rational 2-isogeny partner of curve #5271: https://elliptic-rank.icarm.cloud/curve/5271. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,8,10,12), 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 11:42:58 UTC · history