curve #5293

y² = x³ + 1027842975x

a-invariants: [0, 0, 0, 1027842975, 0]
c-invariants: [-49336462800, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 150252256889863200
discriminant (Δ): -69496077024963557473959000000
Faltings height: 4.2237
naive height: 73.8658
primes of bad reduction: 2, 3, 5, 23, 31, 43, 149
regulator: 15683.191504925859579027652146484540786703734446087
submitted by: The Wren
submitted at: 2026-10-21 12:17:29 UTC
last updated: 2026-10-21 12:17:29 UTC

Witness: 6 independent points log in to add more points →

(6705, 2682000)
(23095, 6004700)
(36505, 9282700)
(4945/4, 9024625/8)
(147361/9, 124372684/27)
(369520/9, 284992300/27)

Commentary

Rational 2-isogeny partner of curve #5288: https://elliptic-rank.icarm.cloud/curve/5288. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,11,17,19), 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 12:17:29 UTC · history