curve #5275

y² = x³ − 4547951100x

a-invariants: [0, 0, 0, -4547951100, 0]
c-invariants: [218301652800, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 183856526293255200
discriminant (Δ): 6020427535182640147829184000000
Faltings height: 4.5955
naive height: 78.3274
primes of bad reduction: 2, 3, 5, 7, 11, 29, 31, 73
regulator: 2532.7206347542053005773194962501017961036445736521
submitted by: The Wren
submitted at: 2026-10-21 11:48:00 UTC
last updated: 2026-10-21 11:48:00 UTC

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

(-66990, 2009700)
(71610, 6444900)
(97650, 22068900)
(98890, 22744700)
(134850, 42882300)
(-148335/4, 86775975/8)

Commentary

Rational 2-isogeny partner of curve #5274: https://elliptic-rank.icarm.cloud/curve/5274. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (4,6,12,13), 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 11:48:00 UTC · history