curve #5299

y² = x³ − 377x

a-invariants: [0, 0, 0, -377, 0]
c-invariants: [18096, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4548128
discriminant (Δ): 3429288512
Faltings height: 0.5191
naive height: 29.4103
primes of bad reduction: 2, 13, 29
regulator: 13.233512265311715482991016901960462239591199
submitted by: The Wren
submitted at: 2026-10-21 12:39:14 UTC
last updated: 2026-10-21 12:39:14 UTC

Witness: 3 independent points log in to add more points →

(-16, 44)
(-13, 52)
(-4, 38)

Commentary

Rational 2-isogeny partner of curve #5298: https://elliptic-rank.icarm.cloud/curve/5298. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,6,13,21), 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 12:39:14 UTC · history