curve #5281

y² = x³ − 157485012321x

a-invariants: [0, 0, 0, -157485012321, 0]
c-invariants: [7559280591408, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 793648931383856697825312
discriminant (Δ): 249975623475070311275035268451338304
Faltings height: 5.4817
naive height: 88.9614
primes of bad reduction: 2, 3, 7, 13, 19, 43, 47, 83, 181
regulator: 1009740.59597191756267215143388706875330027807571326127
submitted by: The Wren
submitted at: 2026-10-21 12:01:12 UTC
last updated: 2026-10-21 12:01:12 UTC

Witness: 8 independent points log in to add more points →

(-290225, 145809040)
(-183911, 150807020)
(-30212, 68777618)
(518833, 240738512)
(553527, 287096004)
(670972, 443177006)
(1497561, 1767121980)
(2168439, 3139232460)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (3,6,9,17), 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 12:01:12 UTC · history