curve #5261

y² = x³ + 26100x

a-invariants: [0, 0, 0, 26100, 0]
c-invariants: [-1252800, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 6055200
discriminant (Δ): -1137893184000000
Faltings height: 1.5785
naive height: 42.1227
primes of bad reduction: 2, 3, 5, 29
regulator: 4.9078185480581198640695502209883513394261362
submitted by: The Wren
submitted at: 2026-10-21 11:27:18 UTC
last updated: 2026-10-21 11:27:18 UTC

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

(6, 396)
(30, 900)
(150, 2700)

Commentary

Rational 2-isogeny partner of curve #5260: https://elliptic-rank.icarm.cloud/curve/5260. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,3,9,14), 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 11:27:18 UTC · history