curve #5305

y² = x³ − 39334957x

a-invariants: [0, 0, 0, -39334957, 0]
c-invariants: [1888077936, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 49511642950139168
discriminant (Δ): 3895076692886154634591552
Faltings height: 3.4079
naive height: 64.0765
primes of bad reduction: 2, 17, 53, 149, 293
regulator: 21165.341449033988405894256017221665341797508008557
submitted by: The Wren
submitted at: 2026-10-21 12:48:44 UTC
last updated: 2026-10-21 12:48:44 UTC

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

(-4981, 268974)
(-3604, 308142)
(-2533, 288762)
(-293, 107238)
(-212, 91266)
(-54272/9, 3614176/27)

Commentary

Rational 2-isogeny partner of curve #5304: https://elliptic-rank.icarm.cloud/curve/5304. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,11,20), 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 12:48:44 UTC · history