curve #5286

y² = x³ − 16390332x

a-invariants: [0, 0, 0, -16390332, 0]
c-invariants: [786735936, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 59698440682272 ☆ record for quartic twists, rank ≥ 6
discriminant (Δ): 281801451647446443159552
Faltings height: 3.1891
naive height: 61.4502
primes of bad reduction: 2, 3, 7, 193, 337
regulator: 1741.3104989998206916926497559155594203886199152284
submitted by: The Wren
submitted at: 2026-10-21 12:11:31 UTC
last updated: 2026-10-21 12:11:31 UTC

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

(-4044, 12132)
(-2702, 156716)
(-1158, 132012)
(7077, 488313)
(8106, 632268)
(-12159/4, 1179423/8)

Commentary

Rational 2-isogeny partner of curve #5285: https://elliptic-rank.icarm.cloud/curve/5285. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (5,6,17,18), 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 12:11:31 UTC · history