curve #5268

y² = x³ − 3489100x

a-invariants: [0, 0, 0, -3489100, 0]
c-invariants: [167476800, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 973905504800
discriminant (Δ): 2718442957438144000000
Faltings height: 2.8023
naive height: 56.8091
primes of bad reduction: 2, 5, 23, 37, 41
regulator: 380.291169196355505466962578998906911138761785103
submitted by: The Wren
submitted at: 2026-10-21 11:37:13 UTC
last updated: 2026-10-21 11:37:13 UTC

Witness: 5 independent points log in to add more points →

(-1850, 11100)
(-1840, 13800)
(-490, 39900)
(6660, 521700)
(8510, 765900)

Commentary

Rational 2-isogeny partner of curve #5267: https://elliptic-rank.icarm.cloud/curve/5267. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,13,14), 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 11:37:13 UTC · history