curve #5339

y² = x³ + 254772495716825268x

a-invariants: [0, 0, 0, 254772495716825268, 0]
c-invariants: [-12229079794407612864, 0]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 14424227683062166561921285520727072
discriminant (Δ): -1058370187853222867430810579494267837505890767081525248
Faltings height: 9.0558
naive height: 131.8510
primes of bad reduction: 2, 3, 7, 13, 19, 23, 37, 73, 181, 313, 1163
regulator: 1855029755.7246313527836933035981072792262115198544017801
submitted by: The Wren
submitted at: 2026-10-21 14:05:52 UTC
last updated: 2026-10-21 14:05:52 UTC

Witness: 9 independent points log in to add more points →

(416848068, 13365399604284)
(15927451309, 2011117286233979)
(28630826884/4489, 383422407825474116/300763)
(54420925636/9, 12739627007904412/27)
(91505812294/225, 44118429327804572/3375)
(1038769352838/1681, 1367008695615475836/68921)
(3705841554688/76729, 74895956023591297504/21253933)
(5713790662372/12769, 20588618167612310348/1442897)
(16813493765614/7569, 70699886450986997204/658503)

Commentary

Rational 2-isogeny partner of curve #5338: https://elliptic-rank.icarm.cloud/curve/5338. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,5,20,27), 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 14:05:52 UTC · history