curve #5328

y² = x³ + 9140862843x

a-invariants: [0, 0, 0, 9140862843, 0]
c-invariants: [-438761416464, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 297085772496135262752
discriminant (Δ): -48881165381889735319052377030848
Faltings height: 4.7700
naive height: 80.4217
primes of bad reduction: 2, 3, 7, 29, 109, 197, 233
regulator: 156737.1683995450342136315625902059925170241042899465
submitted by: The Wren
submitted at: 2026-10-21 13:14:09 UTC
last updated: 2026-10-21 13:14:09 UTC

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

(3052, 5284538)
(6757, 7878662)
(15957, 12244338)
(1792287, 2402859438)
(189196/9, 383216498/27)
(756784/9, 996873724/27)
(5155591/121, 28757886598/1331)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (2,20,22,23), 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 13:14:10 UTC · history