curve #5332

y² = x³ − 3984479037x

a-invariants: [0, 0, 0, -3984479037, 0]
c-invariants: [191254993776, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 56448260253484257312
discriminant (Δ): 4048504373792309930445203433792
Faltings height: 4.5625
naive height: 77.9306
primes of bad reduction: 2, 3, 7, 11, 19, 23, 59, 223
regulator: 1542095.772995567599239786680588595186744462816762023
submitted by: The Wren
submitted at: 2026-10-21 13:30:07 UTC
last updated: 2026-10-21 13:30:07 UTC

Witness: 7 independent points log in to add more points →

(-22077, 8786646)
(-9812, 6176654)
(-6608, 5103028)
(-413, 1282778)
(124609, 37925614)
(-3457278272007/54804409, 225455428213522794/405717039827)
(9117801/25, 27116340174/125)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (1,8,23,25), 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 13:30:07 UTC · history