curve #5276

y² = x³ − 15380890602x

a-invariants: [0, 0, 0, -15380890602, 0]
c-invariants: [738282748896, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 15140594925484283033856
discriminant (Δ): 232875834198070099214143798221312
Faltings height: 4.9001
naive height: 81.9828
primes of bad reduction: 2, 3, 7, 11, 19, 23, 29, 37, 71
regulator: 93152.51643845675278625594380655289828714283742483164
submitted by: The Wren
submitted at: 2026-10-21 11:49:38 UTC
last updated: 2026-10-21 11:49:38 UTC

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

(-88550, 25838890)
(-29526, 20697726)
(-9798, 12237702)
(-3542, 7377986)
(143704, 27519316)
(-15922247/144, 32274394669/1728)
(533577/4, 143532213/8)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (3,4,6,10), 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 11:49:38 UTC · history