curve #5345

y² = x³ − 132097900x

a-invariants: [0, 0, 0, -132097900, 0]
c-invariants: [6340699200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1395988414752800
discriminant (Δ): 147525710410539119296000000
Faltings height: 3.7108
naive height: 67.7108
primes of bad reduction: 2, 5, 11, 29, 41, 101
regulator: 6652.9109736420795773172939918061661159807134436055
submitted by: The Wren
submitted at: 2026-10-21 14:46:03 UTC
last updated: 2026-10-21 14:46:03 UTC

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

(-9020, 676500)
(-5555, 749925)
(-4444, 706596)
(-1595, 454575)
(11716, 246036)
(-7975/4, 4043325/8)

Commentary

Rational 2-isogeny partner of curve #5344: https://elliptic-rank.icarm.cloud/curve/5344. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (6,10,20,29), 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 14:46:03 UTC · history