curve #5295

y² = x³ + 93833252100x

a-invariants: [0, 0, 0, 93833252100, 0]
c-invariants: [-4503996100800, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 78263815108108039200
discriminant (Δ): -52874987712097610853290032704000000
Faltings height: 5.3522
naive height: 87.4080
primes of bad reduction: 2, 3, 5, 7, 31, 67, 71, 101
regulator: 77562.07791624930923657795050239162182382076088198468
submitted by: The Wren
submitted at: 2026-10-21 12:23:13 UTC
last updated: 2026-10-21 12:23:13 UTC

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

(9514, 29892988)
(37989, 60161913)
(43834, 64786652)
(223650, 179367300)
(501970, 416635100)
(4804570/49, 34544858300/343)
(5161345/4, 12051740575/8)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (2,6,16,17), 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 12:23:13 UTC · history