curve #5307

y² = x³ − 12103099500492x

a-invariants: [0, 0, 0, -12103099500492, 0]
c-invariants: [580948776023616, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 32552226115291044424053792
discriminant (Δ): 113467055511133923083126332354062278111232
Faltings height: 6.5672
naive height: 101.9871
primes of bad reduction: 2, 3, 7, 11, 13, 19, 31, 43, 89, 149
regulator: 1072049.49983461761813084381343260322442462281433470833
submitted by: The Wren
submitted at: 2026-10-21 12:52:24 UTC
last updated: 2026-10-21 12:52:24 UTC

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

(-2457308, 3860430868)
(-573872, 2599353224)
(-560538, 2570627268)
(-483626, 2395883204)
(-58652, 842418676)
(7547446, 18400673348)
(-5528943/4, 30027689433/8)
(72785713/16, 400103064361/64)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (12,16,18,19), 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 12:52:24 UTC · history