curve #5297

y² = x³ + 5328710675343x

a-invariants: [0, 0, 0, 5328710675343, 0]
c-invariants: [-255778112416464, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 100960559863162492971262752
discriminant (Δ): -9683813036365919776595610538225573030848
Faltings height: 6.3621
naive height: 99.5260
primes of bad reduction: 2, 3, 11, 19, 23, 31, 71, 107, 523
regulator: 93353143.8036141768350134145970603110357452701662717898
submitted by: The Wren
submitted at: 2026-10-21 12:31:06 UTC
last updated: 2026-10-21 12:31:06 UTC

Witness: 8 independent points log in to add more points →

(1449529, 3281733656)
(4101889, 9532790036)
(23554300, 114863216930)
(4807/289, 46253646208/4913)
(185342832/121, 4563650216628/1331)
(500367175/289, 18653917023280/4913)
(1303352127/529, 64479353674428/12167)
(488971626649/268324, 551820951571186891/138991832)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (3,9,17,18), 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 12:31:06 UTC · history